Michael Flacandji

Nina Krey

Remembering shopping experiences: The Shopping Experience Memory Scale

Keywords: Shopping experience, Memory of shopping experience, Shopping Experience Memory Scale (SEMS), Customer experience, Scale development

Companies strive to enhance customer experiences and to foster positive consumer behaviors.

While there is extensive literature on how to create enjoyable and conducive customer experiences, limited research focuses on memories associated with shopping experiences.

However, the decision to repeat an experience is based more on the memory of that experience than on the actual experience itself. The current research draws on a series of qualitative and quantitative studies to develop and to validate the four-dimensional Shopping Experience Memory Scale (SEMS). Findings suggest that the scale's four dimensionsattraction, structure, affect, and socialare reliable and consistent across different consumption environments (in-store, mall, and online) and across different time intervals. SEMS reflects nuances of memory and of experience constructs forming the basis of theoretical and practical contributions in the ability to assess the progression of memory associated with shopping experiences over time.

Introduction

Since [START_REF] Holbrook | The experiential aspects of consumption: Consumer fantasies, feelings, and fun[END_REF] seminal paper, the notion of creating consumption experiences continues to gain relevance among scientific and professional communities. Retailers often enhance customer experiences to differentiate themselves from competitors and to achieve a competitive advantage [START_REF] Pine | The experience economy: Work is theatre and every business a stage[END_REF][START_REF] Schmitt | Experiential Marketing[END_REF].

To achieve this experience-based differentiation, retailers provide their customers with events that are pleasant, meaningful, and memorable [START_REF] Kwortnik | The role of positive emotions in experiential decisions[END_REF]. In turn, these customer-optimized interactional experiences foster customer loyalty and attachment to the retailer [START_REF] Brakus | Brand experience: What is it? How is it measured? Does it affect loyalty?[END_REF]). [START_REF] Kahneman | Thinking Fast and Slow[END_REF] research highlights the importance of differentiating and studying the memory of an experience rather than the actual experience, since a customer decides to repeat a past experience solely on the basis of the associated memory. Nevertheless, the memory connected with an experience is not commonly incorporated in marketing research studies even though the underlying construct or premise is often included in the conceptualization of such studies [START_REF] Antéblian | Consumption experience in retail environments: A literature review[END_REF][START_REF] Kranzbühler | The multilevel nature of customer experience research: An integrative review and research agenda[END_REF][START_REF] Puccinelli | Customer experience management in retailing: Understanding the buying process[END_REF]. This lack of empirical investigation of consumer memory is attributed to methodological and measurement challenges related to assessing an experience over time. According to the memory literature, the memory of an experience and the actual experience cannot be assessed with the same measurement toolswhich is a current practice in marketing research studies. Instead, memory has several additional properties that need to be taken into consideration by scales in the marketing literature to accurately capture the intended element of the consumer experience, i.e. memory vs. actual experience. Given the identified lack of a suitable measurement tool, it is necessary to develop a scale of the memory of an experience that merges key concepts from both marketing and psychology literature. Therefore, the current research proposes to approach consumer experience from the perspective of its memory and introduces a measurement tool that is an improvement over existing scales. Specifically, it develops a theory-and data-driven scale to capture consumers' memories linked to consumption experiences in retail contexts.

Another focus is the examination of how memory of a shopping experience evolves over time and how it influences the customer-retailer relationship. Qualitative interviews and quantitative surveys from both France and the U.S. across different retail settings (in-store, mall, and online) and different points in time provide the data to conceptualize and develop the Shopping Experience Memory Scale (SEMS). In an omni-channel shopping environment, the key theoretical contribution of this research is the identification of the four dimensions (attraction, structure, affect, and social) of SEMS. Furthermore, the current research contributes to the body of knowledge about shopping experience by bridging the gap between the customer experience literature in marketing and the memory literature in psychology.

Managerial implications include a tool to assess how customers' memory progresses along one or more dimensions of SEMS, information which could ultimately be used to modify how customers form and retain memories.

Literature review

Customer experience in marketing

Numerous definitions of an experience prevail in the literature, which is fragmented across the discipline [START_REF] Homburg | Customer experience management: Toward implementing an evolving marketing concept[END_REF]. Researchers apply the construct either to a general context or investigate specific service, brand, retail, or product contexts.

Although there is no overall consensus, customer experience is often defined as a set of interactions between a customer and a product, a company, or part of an organization in a specific situation, which induces reactions [START_REF] Gentile | How to sustain the customer experience: An overview of experience components that co-create value with the customer[END_REF]. Considering that customers can express different types of reaction (e.g., affective and social) during experiences, researchers consider customer experience as a multidimensional construct [START_REF] Verhoef | Customer experience creation: Determinants, dynamics and management strategies[END_REF]. Several firm-controlled and macro factors (e.g., promotion, price, and location) in retail environments can shape these customer experiences and responses [START_REF] Grewal | Customer experience management in retailing: An organizing framework[END_REF]. Previous research has mainly involved exploratory attempts to conceptualize this holistic construct to better comprehend the various facets of an experience (Table 1).

[Please insert Table 1 about here]

As Table 1 indicates, conceptualizations and thus dimensions of what constitutes an experience vary across studies. This phenomenon can easily be explained: customers do not recognize or distinguish between different facets of the overall experience. [START_REF] Gentile | How to sustain the customer experience: An overview of experience components that co-create value with the customer[END_REF] confirm that consumers are aware of the entire experience yet fail to knowingly differentiate between its individual components. There are, therefore, various conceptualizations that attempt to capture the whole experienceoften with interrelated dimensions.

A thorough qualitative review and comparison of previous customer experience research focused on synergies across experience constructs and identifies seven dimensions of experience that are shared between these studies: 1) affective, 2) physical, 3) cognitive, 4) sensorial, 5) social, 6) symbolic, and 7) temporal (Table 1). These seven dimensions consistently emerge despite the different contexts of the various research studies. The first dimension, affective, appears in all conceptualizations and is also referred to as affect, feeling, emotional, hedonico-sensorial, or pleasure. This dimension includes affective consumer responses such as emotions and moods [START_REF] Gentile | How to sustain the customer experience: An overview of experience components that co-create value with the customer[END_REF] and relates to the pleasure or displeasure associated with an experience. The physical dimension (i.e. praxeological, behavioral) describes actions and activities taking place during a consumption experience (e.g. consumers walking around a store or sampling product offerings). Thinking and conscious mental processing reflect the cognitive dimension of an experience. Here, consumers may think of related and unrelated matters during a shopping experience, such as the store atmosphere or items to purchase. The sensorial dimension is aligned with the sensory stimulation or sensory cues contained within a customer experience, which can lead to pleasure or excitement. Social interactions during the experience are captured by the social dimension, also known as social-identity [START_REF] Schmitt | Experiential Marketing[END_REF], relational [START_REF] Gentile | How to sustain the customer experience: An overview of experience components that co-create value with the customer[END_REF][START_REF] Pentina | Exploring effects of online shopping experiences on browser satisfaction and e-tail performance[END_REF], or praxeological [START_REF] Roederer | A contribution to conceptualizing the consumption experience: Emergence of the dimensions of an experience through life narratives[END_REF]. The symbolic dimension (i.e. lifestyle, ideological, and rhetorical) relates to notions of value and belief.

Lastly, the temporal dimension only appears in two studies [START_REF] Michaud-Trevinal | Toward a conceptualization of the online shopping experience[END_REF][START_REF] Roederer | A contribution to conceptualizing the consumption experience: Emergence of the dimensions of an experience through life narratives[END_REF]. Here, time is not only the moment when the experience takes place, but also an inherent feature of the experience itself. [START_REF] Roederer | A contribution to conceptualizing the consumption experience: Emergence of the dimensions of an experience through life narratives[END_REF] considers time and duration as a space or a resource that must be managed.

As mentioned before, an experience is a P.O.S. interaction (Person x Object x Situation) [START_REF] Punj | An interaction framework of consumer decision making[END_REF], which is divided into four major stages [START_REF] Arnould | Consumers[END_REF]: 1) pre-consumption experience including planning and anticipation of the experience; 2) purchase experience including choice, payment, and exchange act; 3) core consumption experience including sensation, satiety, satisfaction/dissatisfaction, irritation/flow, and transformation; and 4) remembered consumption experience and nostalgia experience including consumption memories, stories, and re-living of the experience. While researchers have widely studied the first three stages of an experiencepre-consumption, purchase, and core consumption (i.e. before and during the experience)limited research focuses on the remembered or "post-experience" (i.e. consequences of the experience).

Memory

In cognitive psychology, memory is the process which encodes, stores, and retrieves information. The encoding process translates information from the outside world through the senses into usable information that is saved as memory. This storage allows maintaining of information over time, while retrieval enables recall of previously stored information. With regard to an experience, remembering involves an effort of reminiscence and reflexivity to recall and retrieve specific details of the encounter. When a customer remembers a particular shopping experience upon exiting a store, he or she uses long-term rather than short-term memory. Short-term memory involves recalling a limited number of readily available pieces of information that are accessible for a short period. However, this short-term memory does not correspond to the memory of a particular shopping experience assessed several minutes after exiting the store. Furthermore, it is important to distinguish between early and late longterm memory. Even though both are categorized as long-term memory, early long-term memory refers to memory recalled immediately after encoding (a few moments upon completion of the experience), while late long-term memory encompasses retrieval after a more substantial temporal delay (e.g. [START_REF] Talmi | Enhanced emotional memory: Cognitive and neural mechanisms[END_REF].

"Every act of remembering involves a reconstruction of information, and this process at times leads to inaccuracies" (Braun-Latour & Zaltman, 2006, p.59). Discrepancies can occur between actual and remembered encounters because memory processes rely on heuristics or 'shortcuts' [START_REF] Kahneman | Thinking Fast and Slow[END_REF][START_REF] Morewedge | The least likely of times: How remembering the past biases forecasts of the future[END_REF]. As a result, memory differs from the original experience [START_REF] Braun | Post-experience advertising effects on consumer memory[END_REF] with each memory being a dynamic, context-sensitive progression [START_REF] Edelman | Wider than the sky: The phenomenal gift of consciousness[END_REF][START_REF] Schacter | The seven sins of memory: How the mind forgets and remembers[END_REF] even if it is often accompanied by a belief that it is a truthful record of the experience [START_REF] Brewer | What is autobiographical memory?[END_REF]. [START_REF] Nenycz-Thiel | Investigating the accuracy of self-reports of brand usage behavior[END_REF] add that all these memory-creation processes are often associated with over-or under-estimations of responses. Moreover, memories evolve over time [START_REF] Averell | The form of the forgetting curve and the fate of memories[END_REF][START_REF] Bartlett | Remembering: A study in experimental and social psychology[END_REF][START_REF] Ebbinghaus | Memory: A contribution to experimental psychology[END_REF][START_REF] Schacter | The seven sins of memory: How the mind forgets and remembers[END_REF] and are subject to natural biases [START_REF] Bartlett | Remembering: A study in experimental and social psychology[END_REF] as well as to forgetfulness [START_REF] Ebbinghaus | Memory: A contribution to experimental psychology[END_REF]. In other words, memories associated with the same experience may not remain consistent at each recall.

Since consumers savor their memories of enjoyable and meaningful experiences [START_REF] Alba | Pleasure principles: A review of research on hedonic consumption[END_REF], it is essential to study the memory of a customer experience and not the actual experience. It is important to note that it is the memory of an experience that determines whether the consumer repeats, recommends, or talks positively about it [START_REF] Kahneman | Thinking Fast and Slow[END_REF][START_REF] Pedersen | The role of predicted on-line experienced and remembered satisfaction in current choice to use public transport services[END_REF][START_REF] Robinson | Recall of vegetable eating affects future predicted enjoyment and choice of vegetables[END_REF][START_REF] Wirtz | What to do on spring break? The role of predicted, on-line, and remembered experience in future choice[END_REF]. Furthermore, future intentions are based on memory of past experiences and only indirectly on actual experiences [START_REF] Stragà | Memory underpinnings of future intentions: Would you like to see the sequel?[END_REF]. In addition, when customers justify repeating an activity, the experience is often reconstructed as more positive [START_REF] Cowley | Looking back at an experience through rose-colored glasses[END_REF]. Thus, the memory reflects an altered image of the actual experience.

In the psychology literature, [START_REF] Sutin | Phenomenology of autobiographical memories: The memory experiences questionnaire[END_REF] identify ten dimensions of the memory of an experience: vividness, coherence, accessibility, time perspective, sensory details, visual perspective, emotional intensity, sharing, distancing, and valence. Similarities exist between these memory dimensions and the experience dimensions identified in marketing studies (affective, physical, cognitive, sensorial, social, symbolic, and temporal).

For example, valence, which "refers to the degree to which the experience described in the memory is perceived to be positive or negative" (Sutin & Robins, 2007, p. 394), is similar to affect, traditionally conceptualized in experience research in marketing. In contrast, memory also appears to differ from experience on a range of dimensions, such as recency or vividness [START_REF] Baumgartner | Autobiographical memories, affect, and consumer information processing[END_REF]. As a result, memory has unique properties that differ from experience.

One major challenge is measuring an experience and, more importantly, the memory of it. Since it is difficult to assess an experience while the consumer is going through it, it has to be assessed upon completion. One potential exception is the use of neuroscientific tools including eye tracking and electroencephalograms to capture customers' experiences more precisely an experience [START_REF] Plassmann | Consumer neuroscience: Applications, challenges, and possible solutions[END_REF]. While these inthe-moment measures of customer experience are very accurate and useful, they are also expensive and difficult to implement, making them sparsely utilized research tools.

Traditional, self-administered measurement scales are, therefore, more convenient and practical for academic and practitioner research. However, as mentioned above, these tools are administered after the completion of the experience and thus assess the memory rather than the actual customer experience itselfwhich can be quite different. As a result, any scale trying to capture a consumer experience is inherently memory-based and the memory associated with an experience collected by questionnaire is viewed as a "proxy" for the actual experience [START_REF] Kahneman | New challenges to the rationality assumption[END_REF]. Nevertheless, experience and memory are both distinct multidimensional constructs with several unique properties. Most importantly, memory evolves (e.g. Ebbighaus, 1885) and fades over time (e.g. Lau-Gesk & Mukherjee, 2017), which existing consumer experience scales in marketing do not account for. In addition, most research studies do not provide details about the timing or time progression associated with the experience (e.g. [START_REF] Brakus | Brand experience: What is it? How is it measured? Does it affect loyalty?[END_REF][START_REF] Roederer | A contribution to conceptualizing the consumption experience: Emergence of the dimensions of an experience through life narratives[END_REF], which are essential temporal components of memory given the proxy role of experience scales. As a result, a bias prevails related to the timing of an experience itself and its assessment, which is addressed by the new scale development below. [START_REF] Verhoef | Customer experience creation: Determinants, dynamics and management strategies[END_REF] invite researchers to develop a scale that measures the full complexity of customer experience. In addition, [START_REF] Antéblian | Consumption experience in retail environments: A literature review[END_REF] stress the importance of the memory of an experience and propose longitudinal research to assess the interaction between customer experience and retail environmentsphysical store vs. virtual store. The current research meets these requirements and follows commonly accepted, psychometric scale development and validation procedures [START_REF] Babin | Work and/or fun: Measuring hedonic and utilitarian shopping value[END_REF][START_REF] Churchill | A paradigm for developing better measures of marketing constructs[END_REF][START_REF] Gerbing | An updated paradigm for scale development incorporating unidimensionality and its assessment[END_REF][START_REF] Rauschnabel | Brand management in higher education: The University Brand Personality Scale[END_REF]. The first step involves defining the construct and the domain. The working definition of shopping experience memory involves information stored in memory after a shopping experience, consciously or subconsciously, that the customer can retrieve during a remembered experience with some degree of accuracy and certainty [START_REF] Flacandji | De l'expérience au souvenir de l'expérience : Etude des invariants et des décalages entre parcours de magasinage et souvenir immédiat[END_REF]. Therefore, the memory of an experience can be viewed as an "output" of the experience. Table 2 presents an overview of the complete scale development process used in the current research study.

Development of the Shopping Experience Memory Scale

[Please insert Table 2 about here] The process begins with a literature review of existing, related constructs and qualitative studies. Specifically, semi-structured interviews with French consumers produce the first item pool that is rated by experts for refinement (study 1). Studies 2 and 3 focus on item purification, using online and paper-pencil surveys. Both studies use consumer samples based on in-store, mall, and online experiences. Study 4 incorporates a new data set to validate the dimensionality of the scale and to assess nomological validity by examining the scale's influence on two outcome variables (satisfaction and brand attachment). The final step entails further scale validation and extension to a new cultural context by using a U.S. data set.

Study 1: Initial item generation

Study 1 utilizes literature reviews and semi-structured interviews to identify initial scale items. Existing scales provide a foundation for item generation after adapting them to a retail context [START_REF] Brakus | Brand experience: What is it? How is it measured? Does it affect loyalty?[END_REF][START_REF] Mehrabian | An approach to environmental psychology[END_REF][START_REF] Roederer | A contribution to conceptualizing the consumption experience: Emergence of the dimensions of an experience through life narratives[END_REF]. In addition to measurement tools used in marketing studies, common psychology scales offer further items. The three most widely used measures are the Memory Characteristics Questionnaire (MCQ, [START_REF] Johnson | Phenomenal characteristics of memories for perceived and imagined autobiographical events[END_REF], the Autobiographical Memories Questionnaire (AMQ; [START_REF] Rubin | Belief and recollection of autobiographical memories[END_REF], and the Memory Experiences Questionnaire (MEQ; [START_REF] Sutin | Phenomenology of autobiographical memories: The memory experiences questionnaire[END_REF].

Methodology

Upon reviewing existing scales, semi-structured interviews with French consumers provide additional insights into the operationalization of shopping experience memory and provide further sources for potential scale items. Interviews include questions about a consumer's recent shopping trip, specific stores visited during the trip, and overall perception of the experience [START_REF] Roederer | A contribution to conceptualizing the consumption experience: Emergence of the dimensions of an experience through life narratives[END_REF]. All interviews began with the following instructions: "Please take a few moments to remember your shopping experience, then, when you are ready, describe this experience, discuss everything you did, everything that came to mind during the shopping trip, including specific details…." Data were collected using a longitudinal approach on three different occasions: faceto-face immediately after the shopping experience in a store (t), by phone two weeks later (t+1), and by phone two months later (t+2) to capture the progression of memory. These three time periods were selected to ensure enough passing of time between t and t+1 as well as t+2 to identify a progression of memory based on tapping into early and late long-term memory.

In addition, the selection was influenced by the shopping habits of regular customers of the companies that were used for data collection. 1 To minimize pro-active interference resulting from new shopping experiences [START_REF] Underwood | Interference and forgetting[END_REF], two weeks and two months after the initial shopping experience were deemed appropriate time intervals. Respondents were recruited at the different stores for face-to-face interviews and gave consent to be contacted again via phone for two additional interviews. All participants completed the same interviews at the three time periods. The sample consists of 132 consumers (70.5% female; 32.6% between 35-44 years of age). Table 3 details the current and all additional samples from the different studies. In line with other qualitative research approaches, interviews were recorded and fully transcribed. Data analysis involved systematic analytical procedures common in qualitative research [START_REF] Spiggle | Analysis and interpretation of qualitative data in consumer research[END_REF].

[Please insert Table 3 about here]

Results

Even though respondents had the option to report positive and negative retail experiences, only positive experiences were reported. After carefully reviewing the interviews, communalities and patterns between questions as well as interviews were identified. This two-way coding approach allows for comparison and cross-referencing of common themes based on frequency of occurrence across interviews followed by sorting into theoretically-grounded themes: memory or experience dimensions. The findings of the content analysis include 11 themes associated with the memory of a shopping experience: 1) cognitive, 2) symbolic, 3) social, 4) physical, 5) affective, 6) sensorial, 7) temporal, 8) vividness, 9) coherence, 10) accessibility, and 11) distancing. As previously shown in Table 1, the first seven themes are consistent with the dimensions of an experience.

Vividness, coherence, accessibility, and distancing represent the specific features of the memory of an experience discussed in the psychology literature. These themes specifically focus on the structure of the memory more than on its content.

Overall results of the interviews and the literature review provide the first item pool.

For example, the response of one of the participants "I felt a bit uncomfortable when I entered this store that I did not know" translates to the scale item "During my shopping experience, I felt very comfortable." A panel of nine expert judges with marketing or psychology backgrounds evaluated the comprehensiveness and appropriateness of the first 76 items by ranking each item according to the shopping experience memory concept. Mean scores are a screening mechanism, allowing only highly ranked items to remain in the item pool. Consequently, the expert reviews eliminate 12 items and refine 4 items leading to a final pool of 64 items.

Study 2: Initial purification

The second study involves initial purification of scale items by identifying the potential factor structure of memory of a shopping experience using calibration procedures. A total of 989 French consumers (74.5% female; 43.0% between 18-24 years of age) took part in a survey enquiring about a recent shopping experience. Participants were recruited at a mall, a train station, and online via social media messages as well as emails. Online and paper-pencil surveys include questions assessing reasons for shopping, products purchased, memory of a shopping experience items, and demographic questions. Participants categorize their experience as either in-store (N=367), mall (N=420), or online (N=202) with time frames ranging from less than two days (N=226), less than one week (N=265), less than two weeks (N=195), less than one month (N=166) to less than two months (N=137). Respondents then indicate the name of the retailer and rate their memory of the experience using a 7-point Likert scale (1=strongly disagree, 7=strongly agree). Although instructions allowed respondents to report positive or negative experiences, participants provided only positive retail experiences.

Results

Principal component analysis (PCA) with Oblimin rotation enables an assessment of dimensionality and suggests items for elimination. Items with a factor loading below 0.50, high cross-loadings above 0.30, and low communalities below 0.50 are candidates for deletion [START_REF] Hair | Multivariate data analysis[END_REF]. The final factor structure contains four dimensions with eigenvalues greater than 1 and explaining 68.9% of the total variance. For the total sample, factor loadings exceed 0.70, which is above the established cutoff of 0.50.

Cronbach's alpha values for the four factors range between 0.74 and 0.87.

Scale inspection

In line with memory and experience scales, the four factors are named attraction, structure, affect, and social. The attraction dimension expresses the consumer's overall attraction to the retail environment and products he/she wants to try or purchase. The second factor, structure, contains items capturing the nature of the memory including vividness, accessibility, and coherence. The third factor reflects affect perceived during the memory of an experience, including valence of the memory and well-being. The last factor, social, is other-oriented and captures the development of a sense of belonging to a social group.

Replication of the four-factor structure across several sub-samples (in-store, mall, and online) leads to a similar solutions, therefore results are stable regardless of the type of experience.

However, the online sub-sample has one cross-loading (0.62 and 0.35) and the online plus instore sub-samples have a Cronbach's alpha value below 0.70 for one dimension.

Study 3: Final purification

The four-factor solution from study 2 is further refined in study 3. A second exploratory factor analysis (EFA) with a new sample (N=1,100) provides final purification of scale items. This step is necessary since results of the initial purification could be improved for the online sub-sample. The data collection and recruitment methods are consistent with study 2, except for adding an option of engaging in a shopping experience on the same day as survey completion. As in the previous study, respondents were asked to remember a recent retail experience in-store (N=433), mall (N=335), or online (N=332), followed by questions about their memory of that experience.

Results

PCA with Oblimin rotation reports no factor loading below 0.50, no high crossloadings above 0.30, and no low communalities below 0.50 [START_REF] Hair | Multivariate data analysis[END_REF]. The new factor structure includes four dimensions with eigenvalues greater than 1 and explains 76.8% of the total variance. Cronbach's alpha values for the four factors are above the 0.70 threshold ranging between 0.86 and 0.90 [START_REF] Nunnally | Psychometric theory[END_REF]. See Table 4 for EFA results.

[Please insert Table 4 about here]

Scale inspection

Final EFA results include 14 items spanning the four dimensions of SEMS. These dimensions are 1) attraction, 2) structure, 3) affect, and 4) social. To assess the robustness of the scale, the four-factor solution is replicated again across several sub-samples. Results confirm a stable dimensionality of the scale across types of experience (in-store, mall, online), timing (today, less than 2 days, less than 1 week, less than 2 weeks), gender (female, male), and occupation (students, workers).

Study 4: Validation

The purpose of study 4 is the validation of the underlying structure of memory of a shopping experience established in study 3 and the assessment of convergent as well as discriminant validity. Confirmatory factor analysis (CFA) with appropriate constraints applied to the items covariance matrix offers a tool for scale validation [START_REF] Rauschnabel | Brand management in higher education: The University Brand Personality Scale[END_REF]. Using Amos 21 and maximum likelihood estimation, the CFA uses a new sample of 655 French consumers (in-store: N=350; mall: N=227; online: N=188). The same online survey used for study 3 is administered. Furthermore, the study has a longitudinal focus by collecting data at three time points: t, t+1 (two weeks after the first questionnaire) and t+2 (two months after the first questionnaire). Respondents were contacted by e-mail to complete the online survey and consented at the end of the survey to be contacted twice again for research purposes. To ensure respondents answered surveys based on the same shopping experience at t+1 and t+2, the name of the retailer was used as an attention check. Again, participants reported only positive retail experiences.

Fit validity

CFA results in t give a χ 2 -value of 250.43 (df=71) that is significant at p < 0.001. The corresponding CFI of 0.97 (above 0.90), RMSEA of 0.06 (less than 0.08), and SRMR of 0.04 (less than 0.05) provide an acceptable fit validity to move forward. Fit indices for model t+1 and t+2 are also adequate. All fit measures are shown in Table 5.

[Please insert Table 5 about here]

Convergent and discriminant validity

Factor loadings, composite reliability (C.R.), and average variance extracted (AVE) assess convergent and discriminant validity. Factor loadings exceed the cutoff value of 0.50 for all items [START_REF] Hair | Multivariate data analysis[END_REF][START_REF] Fornell | Evaluating structural equation models with unobservable variables and measurement error[END_REF]; specifically, all items exceed 0.69 in t, t+1, and t+2. C.R. values range between 0.83 and 0.91 (t), between 0.90 and 0.92 (t+1), and between 0.88 and 0.93 (t+2), thus exceeding the 0.70 cutoff. In addition, AVE are above 0.50 for all models (t=0.63-0.77; t+1=0.71-0.80; t+2=0.71-0.82) [START_REF] Bagozzi | On the evaluation of structural equation models[END_REF]. These findings therefore further validate the four-dimensional SEMS.

Nomological validity

Nomological validity results if the relationship between SEMS dimensions and other key variables behaves as expected according to the academic literature. Previous research links customer experiences to satisfaction and brand attachment (e.g. [START_REF] Brakus | Brand experience: What is it? How is it measured? Does it affect loyalty?[END_REF][START_REF] Brun | Impact of customer experience on loyalty: A multichannel examination[END_REF][START_REF] Dolbec | The impact of a flagship vs. a brand store on brand attitude, brand attachment and brand equity[END_REF]) using a memory-based approach. Specifically, experience positively influences satisfaction and brand attachment. Therefore, the SEMS dimensions are expected to directly affect customer satisfaction and brand attachment. While satisfaction is adapted from [START_REF] Oliver | A cognitive model of the antecedents and consequences of satisfaction decisions[END_REF], brand attachment is measured using the parsimonious [START_REF] Park | Brand attachment and brand attitude strength: Conceptual and empirical differentiation of two critical brand equity drivers[END_REF] scale. Table 6 shows scale items, reliability assessments, and other details for these two outcome variables.

[Please insert Table 6 about here] Concerning nomological validity, the results reveal associations among the constructs.

Satisfaction and brand attachment correlate significantly with different dimensions of SEMS at different time intervals. At t, the affect dimension correlates with satisfaction (r=0.62; p < 0.05), while attraction (r=0.56; p < 0.05) and social (r=0.22; p < 0.05) dimensions correlate with brand attachment. Results are the same at t+1. At t+2, affect correlates with satisfaction (r=0.78; p < 0.05), while attraction (r=0.57; p < 0.05) and social (r=0.32; p < 0.05) correlate with brand attachment. More interestingly, structure does not significantly correlate with any construct at t and t+1, but significantly correlates with brand attachment at t+2 (r=-0.14; p < 0.05). Even though not all dimensions relate to both outcome variables, there is overall support for nomological validity.

Robustness tests

To further enhance scale generalizability, invariance was tested between different subsamples (survey administration techniques: online vs. paper-pencil; randomized order of scale constructs; gender and occupation). This test compares the goodness of fit criteria of a fully constrained model against the proposed baseline model [START_REF] Byrne | Testing for multigroup invariance using AMOS graphics: A road less traveled[END_REF]. The analyses reveal a non-significant chi-square difference test between the groups, thereby indicating equivalence of the measurement instrument across samples [START_REF] Hair | Multivariate data analysis[END_REF]. In sum, supplementary analyses support the robustness of the scale.

Post-hoc analysis of temporal effects

Repeated measures ANOVA and post-hoc tests using Bonferroni correction is performed to check the progression of memory of a shopping experience, satisfaction, and brand attachment over time. Construct means are computed without considering the weighting of the items. Table 7 summarizes the main results.

[Please insert Table 7 about here] Results indicate that respondents tend to evaluate their memory less positively over time. However, this progression is not consistent across all dimensions. The structure dimension of SEMS decreases more steeply than any other dimension. More specifically, it reduces from a mean of 5.41 (t; p < 0.001) to 4.2 (t+1; p < 0.001) to 3.6 (t+2; p < 0.001) across the different time intervals. This result upholds findings of the qualitative study and previous literature [START_REF] Averell | The form of the forgetting curve and the fate of memories[END_REF][START_REF] Bartlett | Remembering: A study in experimental and social psychology[END_REF][START_REF] Ebbinghaus | Memory: A contribution to experimental psychology[END_REF][START_REF] Schacter | The seven sins of memory: How the mind forgets and remembers[END_REF]. The slower progression of the affect, attraction, and social dimensions confirms that the more emotionally charged elements of an experience are more stable over time, even if two of them decrease significantly. Satisfaction also decreases over time. Indeed, details of a shopping experience become inaccessible over time, which encourages people to use semantic knowledge and inferences to retrieve memories of past emotional experiences (Robinson and Clore, 2000). Finally, brand attachment does not change over time, confirming its constancy [START_REF] Park | Brand attachment and brand attitude strength: Conceptual and empirical differentiation of two critical brand equity drivers[END_REF].

Study 5: Scale replication/extension in the U.S.

The final study aims to replicate and validate the four SEMS dimensions in a different cultural context. This step is important to enhance the generalizability and applicability of the scale. The questionnaire consists of the same questions as in the previous studies, including the SEMS items, satisfaction, and brand attachment. A professional translator was hired to translate and back-translate the original scale items, in addition to two independent translators with a marketing background. Furthermore, a marketing expert fluent in French and English assessed both sets of items prior to data collection for content validity. Appendix A includes these items.

The sample consists of American consumers recruited by a panel data company. In total, the number of usable, appropriately completed questionnaires is 338 (in-store=24.9%; mall=34.6%; online=40.5%). Respondents (male = 46.4%; female = 53.6%) ranged in age from 18 to 24 years (10.9%), 25 to 34 years (16.6%), 35 to 44 years (13.3%), 45 to 54 years (18.9%), 55 to 64 years (27.5%), to 65 and older (12.7%). In line with the previous studies, none of the participants discussed negative experiences.

Construct validity results

As in the previous analyses, the 14 SEMS items are subject to CFA. Fit for the measurement model is once again strong. The completely standardized loadings are presented in Table 5. The 2 is 118.86 (df=71). The CFI, TLI, and NFI are 0.98, 0.98, and 0.96, respectively. SEMS reflects good psychometric properties in the U.S., meeting construct validity, fit validity, and convergent validity concerns based on factor loading estimates exceeding 0.50, C.R. values between 0.83 and 0.89, and AVE values between 0.59 and 0.72 [START_REF] Hair | Multivariate data analysis[END_REF].

Nomological validity

Nomological validity is once again assessed with the two theoretically based outcome variables: satisfaction (=0.88) adapted from [START_REF] Oliver | A cognitive model of the antecedents and consequences of satisfaction decisions[END_REF] and brand attachment (=0.83) by [START_REF] Park | Brand attachment and brand attitude strength: Conceptual and empirical differentiation of two critical brand equity drivers[END_REF]. Additional scale assessment information is summarized in Table 6.

Results show that affect (r=0.73, p < 0.05) and structure (r=0.13, p < 0.05) correlate with satisfaction, while attraction correlates with brand attachment (r=0.74, p < 0.05). Findings support nomological validity, similarly to the previous results in study 4. However, no longitudinal comparison is possible in study 5 since data were only collected at time t. In addition, differences in SEMS dimension effects on outcome variables can be attributed to cultural differences since French and American consumers seem to express different relationships between the social dimension and brand attachment. Therefore, even if not all dimensions are related to both constructs included in the assessment, the overall pattern suggests nomological validity [START_REF] Rauschnabel | Brand management in higher education: The University Brand Personality Scale[END_REF].

General discussion and conclusion

Summary

Memorable experiences remain an essential tool for companies to attract and retain loyal customers. As previous research has shown, the memory associated with an experience differs from the actual experience on numerous facets such as vividness, coherence, and accessibility of the memory [START_REF] Kahneman | Thinking Fast and Slow[END_REF][START_REF] Sutin | Phenomenology of autobiographical memories: The memory experiences questionnaire[END_REF])these facets not only translate to the structure of memory, but also to the newly developed Shopping Experience Memory Scale (SEMS). These distinct factors are essential to consider beyond previous experience dimensions, because memory is the best predictor of future behavior [START_REF] Kahneman | Thinking Fast and Slow[END_REF][START_REF] Pedersen | The role of predicted on-line experienced and remembered satisfaction in current choice to use public transport services[END_REF][START_REF] Wirtz | What to do on spring break? The role of predicted, on-line, and remembered experience in future choice[END_REF]. Therefore, the current research takes an important first step in assessing retail experiences based on the consumer's memory by developing the four-dimensional SEMS including: 1) attraction, 2) structure, 3) affect, and 4) social.

Theoretical contributions

The major theoretical contribution of this research is introducing and validating a measurement theory related to the memory of a consumer shopping experience. The four dimensionsencompassing a total of 14 items that capture SEMSshow acceptable levels of internal consistency and discriminant validity. Overall, the new scale contributes to a better conceptualization of the customer shopping experience and thus advances theoretical contributions by 1) including nuances of both memory and experience to assess consumer responses, 2) integrating a comprehensive validation of the scale across multiple countries and shopping contexts, 3) considering temporal progression of memory in the development and validation of the scale, and 4) establishing relationships between the SEMS dimensions and two commonly applied outcome measures in experience researchsatisfaction and brand attachment.

As evident by the four dimensions and the corresponding individual items of SEMS, the new scale reflects nuances of the previously identified memory as well as experience dimensions. Specifically, the structure dimension relates to the vividness, coherence, and accessibility themes of memory while the attraction, affect, and social dimensions tap into the cognitive, symbolic, social, physical, affective, and sensorial themes of an experience. It is important to note that, by following commonly accepted, data-driven, psychometric scale development procedures [START_REF] Babin | Work and/or fun: Measuring hedonic and utilitarian shopping value[END_REF][START_REF] Churchill | A paradigm for developing better measures of marketing constructs[END_REF][START_REF] Gerbing | An updated paradigm for scale development incorporating unidimensionality and its assessment[END_REF][START_REF] Rauschnabel | Brand management in higher education: The University Brand Personality Scale[END_REF], findings produce a parsimonious measurement theory across two countries: France and the U.S. As a result, the new scale is bilingual in French and in English (see Appendix A), thus enhancing its applicability and generalizability to international and cross-cultural research. Another unique contribution of the scale is the inclusion of three distinct retail contexts: in-store, mall, and online. The fact that these different retail contexts were included during the scale development process will allow researchers to apply SEMS to these different contexts in future research studies since the scale has been validated across these settingsthe only proper way of ensuring methodological rigor without having to implement scale development procedures when adapting a scale [START_REF] Ortinau | Writing and publishing important scientific articles: A reviewer's perspective[END_REF]. Furthermore, a longitudinal assessment (study 4) confirms the stable factor structure and effects of the scale. When comparing effects immediately after the experience to effects two weeks and two months later, the four dimensions of SEMS remain consistent. This finding is especially important since memory is often assessed after some time has elapsed: thus the scale must be suitable for longitudinal researchwhich is the case with SEMS. Furthermore, while a successful experience is often equated with a memorable experience (e.g. [START_REF] Kwortnik | The role of positive emotions in experiential decisions[END_REF][START_REF] Pine | The experience economy: Work is theatre and every business a stage[END_REF], 'memorable' does not mean that the customer will remember the experience in every detail. As study 4 confirms, the structure dimension of the memory tends to diminish over time. Specifically, it becomes more challenging for the consumer to readily and accurately remember the experience. These findings are consistent with empirical studies in the memory literature reporting decreased memory capacity [START_REF] Averell | The form of the forgetting curve and the fate of memories[END_REF][START_REF] Bartlett | Remembering: A study in experimental and social psychology[END_REF][START_REF] Schacter | The seven sins of memory: How the mind forgets and remembers[END_REF].

Managerial contributions

The findings have significant managerial implications. According to [START_REF] Verhoef | Customer experience creation: Determinants, dynamics and management strategies[END_REF], retailers not only face controllable (e.g. atmosphere, service interface), but also uncontrollable (e.g. shopping purpose, influence of others) elements that contribute to a consumer's overall consumption experience. However, managers can facilitate the memory process to their advantage by tapping into one or multiple of the SEMS dimensions most relevant to the offered experience (i.e. product or service). These dimensions can be used to create or strengthen the competitive advantage associated with an experience. For example, according to the attraction dimension, retailers can encourage customers to try numerous products to increase product interactions and in turn positively influence customer's longterm memory storage of the entire experience. Furthermore, retailers need to make sure that customers feel comfortable by enhancing atmospheric cues (e.g., lighting, music) and social interactions if they want to reinforce the affect dimension. [START_REF] Lee | Consumers' desire to interact with a salesperson during eshopping: Development of a scale[END_REF] suggest that e-tailers should implement effective customerbased information and e-contact features to fulfil consumers' desire to interact with a salesperson. This finding confirms the importance of the social dimension of SEMS. The salesperson needs to answer customers' questions, but also needs to make them feel special and important. However, retailers should be careful. Discrepancies between the evoked and actual properties of in-store merchandise may lead to inferences of manipulative intent, which can lead to negative consequences in terms of trust and attitude towards the retailer [START_REF] Lunardo | When atmospherics lead to inferences of manipulative intent: Its effects on trust and attitude[END_REF].

Overall, Customer Experience Management (CEM) is often viewed as an important element in sustaining long-term customer loyalty [START_REF] Homburg | Customer experience management: Toward implementing an evolving marketing concept[END_REF]. Beyond CEM, we invite companies to rethink the experience from the perspective of its memory and to move towards what we call Customer Experience Memory Management (CEMM). Considering that an experience is transformed into a memory and that memory is more important than actual experience in future relationships with the customer [START_REF] Kahneman | Thinking Fast and Slow[END_REF][START_REF] Pedersen | The role of predicted on-line experienced and remembered satisfaction in current choice to use public transport services[END_REF][START_REF] Wirtz | What to do on spring break? The role of predicted, on-line, and remembered experience in future choice[END_REF], CEMM appears to be more relevant.

Finally, this research reminds practitioners and scholars why it is essential to integrate a temporal variable into their marketing studies. They must be aware that memory is evolving (e.g. [START_REF] Averell | The form of the forgetting curve and the fate of memories[END_REF][START_REF] Bartlett | Remembering: A study in experimental and social psychology[END_REF][START_REF] Ebbinghaus | Memory: A contribution to experimental psychology[END_REF] and that results of their studies will depend on the time of data collection.

Limitations and future research

As with any research, this study has its limitations. First, the empirical validation of the scale is limited to France and the U.S. Additional contexts and countries should be included in future research to further increase the generalizability of the scale. In addition, the temporal assessment of memory focuses on immediately after the experience, two weeks later, and two months after experience completion, which should be expanded in the future to estimate a point of diminishing returns associated with memory progression. Practitioners could determine when to selectively target consumers with promotions or reminders based on past shopping experiences once additional time lags have been established.

Even though participants had the option to report positive or negative retail experiences, only positive experiences were reported. Therefore, negative experiences should be investigated in the future as it remains unclear what memory customers retain after a retailer-attributed service failure and if that memory has a negative influence on the customer-retailer relationship. For example, [START_REF] Kalamasa | Reaching the boiling point: Consumers' negative affective reactions to firm-attributed service failures[END_REF] show that angry customers are less satisfied and give lower service evaluations. Does the memory of a bad shopping experience evolve in the same way as a positive experience? Moreover, the four-dimensional structure of SEMS reflects core facets of the literature on cognitive psychology and experience and its impact on two common outcome variables used in these two areas: satisfaction and brand attachment. However, a thorough assessment with additional constructs, such as brand loyalty, brand attitude, brand perceptions and repurchase intention, is necessary to enhance the applicability and robustness of the new measurement tool. As such, an additional avenue for future research is examining how the new scale relates to commonly tested attitudinal, behavioral, and cognitive constructs in related research streams.

Furthermore, the current study is unable to isolate the effect of a single touchpoint between the customer and the firm, yet customers interact with companies through several touchpoints in multiple channels and media [START_REF] Lemon | Understanding customer experience throughout the customer journey[END_REF]. Each customer experience informs subsequent experiences as it is encoded and stored in memory [START_REF] Puccinelli | Customer experience management in retailing: Understanding the buying process[END_REF]. It would be useful for retailers who offer products through multiple channels to know whether they should manage customer experiences in the same way for each channel.

Here, store formats could impact the linkage between stored memory and customer-retailer relationship. For example, the shopper satisfaction-loyalty link is different for supermarkets and hypermarkets (Kamran-Disfani, Mantrala, Izquierdo-Yusta, & Martinez-Ruiz, 2017).

Hence, future studies should investigate the customer's responses to a firm's offerings during the entire purchase journey by focusing on individual touchpoints.

According to the literature, it is the memory of an experience that influences customer's choice to repeat, to recommend, to engage in positive WOM, and other actions.

However, additional factors apart from memory might contribute to customer attitudes and behaviors. An experience that the customer does not remember may have a stronger influence than a clearly-remembered experience, depending on the type of emotion or cognitive appraisal it elicits.

In conclusion, the current research examines different conceptualizations and the role of memory in shopping experiences to develop a new psychometric measure. Findings support the four dimensions of the new scale across different shopping environments and across time. Researchers can thus use this measurement tool to investigate consumer experience, while managers can create memorable experiences by focusing on key dimensions relevant to their business.

Tables

Table 1

 1 Prior research conceptualizing experience.

	Authors	Context	Dimensions	Scale Item reduction based on:	Factor extraction and validation
					Experts Consumer	Consumer
						interviews	ratings
	Schmitt (1999)	Conceptual article	Sensory (sense), affective (feel),
			cognitive (think), physical (act),
			social-identity (relate)
	Gentile et al. (2007) Study on several	Sensorial, pragmatic, relational,	✓			✓	Study 1: N=2,368 consumers,
		widely-known brands	emotional, cognitive, lifestyle					(EFA), Italy
	Verhoef et al. (2009) Conceptual article	Cognitive, affective, emotional,
			social, physical
	Brakus et al. (2009) Empirical study on a	Sensations, feelings, cognitions,	✓	✓	✓	✓	Study 1: N=267 students
		variety of brands	behavioral					(EFA), U.S.
								Study 2: N=193 students (EFA/
								CFA), U.S.
								Study 3: N=150 consumers
								(EFA/CFA), U.S.
								Study 4: N=144 consumers
								(EFA), U.S.
	Pentina et al. (2011)	Online shopping experience	Sensorial, cognitive, emotional, pragmatic, relational
	Roederer (2012)	Qualitative study on a	Hedonico-sensorial,
		variety of consumption	praxeological, rhetorical,
		experiences	temporal
	Michaud-Trévinal &	Qualitative study on	Physical, ideological, pragmatic,
	Stenger (2014)	online shopping	social
		experience

Table 3

 3 Samples descriptive.

	Study 1	Study 2	Study 3	Study 4	Study 5
	(N=132)	(N=989)	(N=1,100)	(N=655)	(N=338)

Note: *All respondents were interviewed on exiting the store, as well as two weeks and two months later.

Table 4

 4 Exploratory factor analysis of final item purification in t (study 3).

	Item	Attraction Structure Social	Affect Communalities
	ATTRAC1	0.84	0.02	-0.03	0.03	0.77
	ATTRAC2	0.83	-0.00	-0.10	0.01	0.77
	ATTRAC3	0.77	0.01	-0.08	0.11	0.75
	ATTRAC4	0.95	-0.01	0.10	-0.06	0.78
	STRUC1	0.07	0.78	-0.02	0.02	0.65
	STRUC2	-0.05	0.89	0.05	0.00	0.75
	STRUC3	0.01	0.85	-0.06	-0.07	0.75
	STRUC4	-0.03	0.86	0.02	0.05	0.74
	AFFEC1	-0.05	-0.03	-0.88	-0.01	0.72
	AFFEC2	0.05	0.06	-0.89	-0.00	0.86
	AFFEC3	0.05	0.01	-0.88	0.02	0.83
	SOCIAL1	0.02	-0.01	-0.02	0.89	0.83
	SOCIAL2	0.10	-0.01	0.07	0.85	0.78
	SOCIAL3	-0.08	0.02	-0.05	0.88	0.75
	Eigenvalue	6.13	2.65	1.50	1.16	Total
	% of trace	39.6%	18.5% 10.7%	7.9%	76.8%
	Cronbach's alpha	0.90	0.87	0.86	0.87
	Method: Principal component analysis, Oblimin-rotation (δ=0).
	Loadings above 0.50 shown in bold.

Attrac: attraction; struc: structure; affec: affect.

Table 5

 5 Overview of confirmatory factor analysis results.

	Dataset	Study 4 -t	Study 4 -t+1	Study 4 -t+2	Study 5 -t
	Sample	655	655	655	338
	Country	France	France	France	U.S.
	Overall Model Fit
	² (p)	250.43	250.95	238.67	118.86
	²/71 df	3.53	3.53	3.36	1.71
	CFI	0.97	0.98	0.98	0.98
	TLI	0.96	0.97	0.97	0.98
	NFI	0.96	0.97	0.97	0.96
	RMSEA	0.06	0.06	0.06	0.05
	SRMR	0.04	0.04	0.04	0.04
	Factor 1: Attraction
	C.R.	0.90	0.92	0.93	0.85
	AVE	0.70	0.75	0.78	0.59
	ATTRAC1	0.83	0.89	0.89	0.66
	ATTRAC2	0.87	0.89	0.90	0.85
	ATTRAC3	0.85	0.83	0.88	0.79
	ATTRAC4	0.81	0.86	0.87	0.74
	Factor 2: Structure
	C.R.	0.87	0.91	0.91	0.89
	AVE	0.63	0.71	0.72	0.68
	STRUCT1	0.78	0.87	0.89	0.77
	STRUCT2	0.83	0.89	0.91	0.81
	STRUCT3	0.70	0.76	0.71	0.88
	STRUCT4	0.86	0.85	0.88	0.84
	Factor 3: Affect
	C.R.	0.91	0.92	0.93	0.89
	AVE	0.77	0.80	0.82	0.72
	AFFECT1	0.69	0.73	0.76	0.68
	AFFECT2	0.97	0.98	0.98	0.92
	AFFECT3	0.95	0.95	0.95	0.93
	Factor 4: Social
	C.R.	0.83	0.90	0.88	0.83
	AVE	0.63	0.74	0.71	0.63
	SOCIAL1	0.87	0.90	0.89	0.81
	SOCIAL2	0.79	0.88	0.85	0.77
	SOCIAL3	0.70	0.79	0.78	0.79

Notes: Attrac: attraction; struc: structure; affec: affect.

The companies involved in this research project were Nespresso, Desigual, Printemps, Ralph Lauren, Adidas Originals and Fnac.


Jérôme Darmont
email: jerome.darmont@univ-lyon2.fr

Emerson Olivier

A COMPLEX DATA WAREHOUSE FOR PERSONALIZED, ANTICIPATIVE MEDICINE

INTRODUCTION

With the growing use of new technologies, healthcare is nowadays undergoing significant changes. The development of electronic health records shall indeed help enforcing personalized, lifetime healthcare and pre-symptomatic treatment, as well as various analyses over a given population of patients. Such an information-based medicine has to exploit medical decision-support systems and requires the analysis of various, heterogeneous data, such as patient records, medical images, biological analysis results, etc. [START_REF] Saad | Information-based Medicine: A New Era in Patient Care[END_REF].

In this context, we work with a physician on large amounts of data relating to high-level athletes. His aim is to make the analyzed subjects the managers of their own health capital, by issuing recommendations regarding, e.g., life style, nutrition, or physical activity. This is meant to support personalized, anticipative medicine. To achieve this goal, a decision-support system must allow transverse analyses of a given population and the storage of global medical data such as biometrical, biological, cardio-vascular, clinical, and psychological data.

Data warehousing technologies are now considered mature and can form the base of such a decision-support system. Though they primarily allow the analysis of numerical data, the concepts of data warehousing remain valid for what we term complex data. In this context, the warehouse measures, though not necessarily numerical, remain the indicators for analysis, and analysis is still performed following different perspectives represented by dimensions. Large data volumes and their dating are other arguments in favor of this approach. Data warehousing can also support various types of analysis, such as statistical reporting, on-line analysis (OLAP) and data mining.

In this paper, we present the design of the complex data warehouse relating to high-level athletes. It is original in two ways. First, it is aimed at storing complex medical data. Second, it is designed to allow innovative and quite different kinds of analyses to support:

1. personalized and anticipative medicine (in opposition to curative medicine) for wellidentified patients; 2. broad-band statistical studies over a given population of patients. Furthermore, the system includes data relating to several medical fields. It is also designed to be evolutionary to take into account future advances in medical research.

WAREHOUSE MODEL

Global Architecture

To make our solution evolutionary, we adopted a bus architecture [START_REF] Kimball | The Data Warehouse Toolkit[END_REF]. It is composed of a set of conformed dimensions and standardized definitions of facts. In this framework, the warehoused data related to medical field we need to take into account represent datamarts that are plugged into the data warehouse bus and receive the dimension and fact tables they need. The union of these datamarts may be viewed as the whole data warehouse.

Figure 1 represents the global architecture of our data warehouse. Straight squares symbolize fact tables, round squares symbolize dimensions, dotted lines embed the different datamarts, and the data warehouse bus is a rounded rectangle. It is constituted by dimensions that are common to several datamarts. The main dimensions that are common to all our datamarts are patient, data provider, time, and medical analysis (that regroups several kinds of analyses). Of course, some datamarts (such as the cardio-vascular datamart) do have specific dimensions that are not shared. Our data warehouse also includes a medical background datamart (not depicted), and more datamarts are currently being developed. Input biological data are the results of various biological examinations (biochemistry, protein checkup, hematology, immunology, toxicology…), which are themselves subdivided into actual analyses (e.g., an hematology examination consists in reticulocyte numbering and an hemogram). These data are available under the form of unnormalized spreadsheet files from different sources. They are thus heterogeneous and often refer to the same examination using different terms or abbreviations, use different units for the same numerical values, etc. This heterogeneity is dealt with during the ETL (Extract, Transform, Load) process.

Biometrical data are measured during medical examinations. They include weight, height, pulse rate, fat percentage, and blood pressure. Though their structure is simpler than that of the biological data, they require a fine granularity. For example, the weight of an athlete may be measured twice a day, before and after training. This has an impact on data warehouse More precisely, it helps defining the granularity of the time dimension hierarchy (see below).

Figure 2 represents the architecture of our biological and biometrical datamarts. The biological fact table stores an exam result under the form of a numerical value (e.g., a reticulocyte numbering). It is described by four dimensions: patient, time of the examination, data provider (typically the laboratory performing the analysis), and the analysis itself. The biometrical fact table stores numerical biometrical values (e.g., weight). It is described by the same dimensions than the biological datamart, the "analysis" actually representing a measurement. The patient, data provider, time, and medical examination dimensions are thus all shared, conformed dimensions. Attributes in dimension tables are not detailed due to confidentiality constraints.

Figure 2: Biological and biometrical datamarts' architecture Note that the medical analysis and time dimensions are further organized into hierarchies, to take into account the particularities identified into the source data. Here, biological and biometrical data are distinguished: the simple biometrical data are not normalized nor organized in a hierarchy, while the biological data are. Hence, the description of biometrical facts only appear in the medical analysis dimension table, while biological facts are further described by a hierarchy of biological examinations and categories.

Each datamart is thus modeled as a snowflake schema rather than as a simpler, classical star schema. Since the biological and biometrical fact tables share their dimensions, our overall data warehouse follows a constellation schema. In such an architecture, it is easy to add in new fact tables described by existing dimensions.

Finally, our data warehouse also includes metadata that help managing both the integration of source data into the warehouse (e.g., correspondence between different labels or numerical units, the French SLBC biomedical nomenclature, etc.) and their exploitation during analysis (e.g., the interval between which an examination result is considered normal).

Complex Datamart: the Cardio-Vascular Datamart Figure 3 represents the architecture our cardio-vascular datamart. Here, the complex nature of source data, which are constituted of raw measurements (e.g., ventricle size), multimedia documents (e.g., echocardiograms) and a conclusion by a physician, cannot be embedded in a single, standard fact table. Hence, we exploit a set of interrelated tables that together represent the facts. They are represented as dotted, straight squares. The report mainly contains the physician's conclusion. It is the central element in our "complex fact". It is linked to several numerical analysis results that help building the physician's conclusion. It is also related to multimedia documents such as medical images that also help devising the diagnosis. Note that this relationship, which is represented as a bold line, is a many-to-many relationship. Some documents may indeed be referred to by several reports, for instance to take into account a patient's evolution over time, through distinct series of echocardiograms. Each component of our "complex fact" may be individually linked to the dimensions. Cardio-vascular documents and results are indeed not descriptors of the would-be fact: report, they are part of a fuzzier fact that is composed of several entities.

Finally, note that cardio-vascular documents cannot currently be exploited by OLAP technologies. However, we need to store them and have them accessible for medico-legal reasons. Furthermore, extensions to the usual OLAP operators should make this exploitation possible in the near future [START_REF] Ben Messaoud | OpAC: A New OLAP Operator Based on a Data Mining Method[END_REF].

RELATED WORK

The first family of medical data warehouses we identify are repositories tailored for later data mining treatments. Since data mining techniques take "attribute-value" tables as input, some of these warehouses do not bear a multidimensional architecture [START_REF] Prather | Medical Data Mining: Knowledge Discovery in a Clinical Data Warehouse[END_REF][START_REF] Sun | RgS-Miner: A Biological Data Warehousing, Analyzing and Mining System for Identifying Transcriptional Regulatory Sites in Human Genome[END_REF], and might prove less evolutionary than the solution we selected. second family is constituted of biological data warehouses that focus on molecular biology and genetics [START_REF] Schönbach | Data Warehousing in Molecular Biology[END_REF][START_REF] Eriksson | dimensional data warehouse for biological data[END_REF][START_REF] Sun | RgS-Miner: A Biological Data Warehousing, Analyzing and Mining System for Identifying Transcriptional Regulatory Sites in Human Genome[END_REF], which bear interesting characteristics. For instance, some of them include metadata and ontologies from various public sources such as RefSeq or Medline [START_REF] Engström | A Data Warehouse Approach to Maintenance of Integrated Biological Data[END_REF][START_REF] Shah | Atlas -a data warehouse for integrative bioinformatics[END_REF]. The incremental maintenance and evolution of the warehouse is also addressed [START_REF] Engström | A Data Warehouse Approach to Maintenance of Integrated Biological Data[END_REF]. However, the particular focus of these approaches makes them inappropriate to our current needs, which are both different and much more diversified. The future developments of our data warehouse will probably exploit this existing work, though.

To sum up, the existing medical warehouse that is closest to our own is a cardiology data warehouse [START_REF] Tchounikine | Information Warehouse for Medical Research[END_REF][START_REF] Miquel | Software Components Integration in Medical Data Warehouses: a Proposal[END_REF]. Its aim is to ease medical data mining by integrating data and processes into a single warehouse. However, raw sensor data (e.g., electrocardiograms) are stored separately from multidimensional data (e.g., patient identity, therapeutic data), while we seek to integrate them all in our cardio-vascular datamart.

RESEARCH PERSPECTIVES

This work opens up two kinds of perspectives. The first one concerns the actual contents and significance of the data warehouse. It involves modeling and adding in new datamarts. The cardio-vascular and psychology datamarts are already implemented and more are currently being developed (such as the medical background datamart) or scheduled. This helps broadening the scopes of analyses. Other output than statistical reports are also envisaged. Since we adopted a dimensional modeling, OLAP navigation is also definitely possible, and "attributevalue" views could easily be extracted from the data warehouse to allow data mining explorations.

The second kind of perspectives is more technical and aim at improving our prototype. This includes automating and generalizing the ETL process on all the datamarts, which is currently an ongoing task. We also follow other leads to improve the user-friendliness of our interfaces and the security of the whole system, which is particularly primordial when dealing with medical, personal data.

Figure 1 :

 1 Figure 1: Data warehouse global architecture

Figure 3 :

 3 Figure 3: Cardio-vascular datamart's architecture

ACKNOWLEDGMENTS

The authors thank Dr Jean-Marcel Ferret, the promoter of the personalized and anticipative medicine project. This work has been co-funded by the Rhône-Alpes Region.


Marouane Hachicha

Hadj Mahboubi

Jérôme Darmont

Expressing OLAP operators with the TAX XML algebra

Keywords:

With the rise of XML as a standard for representing business data, XML data warehouses appear as suitable solutions for Web-based decision-support applications. In this context, it is necessary to allow OLAP analyses over XML data cubes (XOLAP). Thus, XQuery extensions are needed. To help define a formal framework and allow much-needed performance optimizations on analytical queries expressed in XQuery, having an algebra at one's disposal is desirable. However, XOLAP approaches and algebras from the literature still largely rely on the relational model and/or only feature a small number of OLAP operators. In opposition, we propose in this paper to express a broad set of OLAP operators with the TAX XML algebra.

INTRODUCTION

Data warehouses and OLAP (On-Line Analytical Processing) are nowadays technologically mature. However, their complexity makes them unattractive to many potential users, thus DSS (Decision Support System) vendors start developing simple, user-friendly Web-based interfaces. Furthermore, many decision-support applications (e.g., competitive monitoring) require data that are external to the institution exploiting them. In this context, the Web is a tremendous data source and a new trend toward on-line data warehousing is currently emerging, including approaches such as XML warehousing [START_REF] Boussaïd | X-Warehousing: An XML-Based Approach for Warehousing Complex Data[END_REF][START_REF] Pokorný | XML Data Warehouse: Modelling and Querying[END_REF][START_REF] Zhang | X-warehouse: building query pattern-driven data[END_REF].

The XML language is indeed becoming a standard for representing business data [START_REF] Beyer | Extending XQuery for Analytics[END_REF]. It is also particularly adapted for modeling complex data from heterogeneous sources, and particularly the Web. Data we term complex are not only numerical or symbolic, but may be represented in various formats (databases, texts, images, sounds, videos...); diversely structured (relational databases, XML documents...); originating from several different sources; described through several channels or points of view (a video and a text that describe the same meteorological phenomenon, data expressed in different scales or languages...); changing in terms of definition or value (temporal databases, periodical surveys...) [START_REF] Darmont | An Architecture Framework for Complex Data Warehouses[END_REF]. Such data are much easier to logically model and store with XML than with relational models.

Many studies aim at performing OLAP analyses over XML data (XOLAP [START_REF] Wang | OLAP for XML Data[END_REF]). A first family mainly rely on the power of relational implementations of OLAP [START_REF] Chantola | OLAP Query Processing for XML Data in RDBMS[END_REF][START_REF] Jensen | Specifying OLAP cubes on XML data[END_REF][START_REF] Niemi | Constructing an OLAP cube from distributed XML data[END_REF][START_REF] Pedersen | Integrating XML Data in the TARGIT OLAP System[END_REF]. However, in these approaches, no or very few XML-specific OLAP operators are defined. Most recent studies directly relate to XOLAP [START_REF] Park | XML-OLAP: A Multidimensional Analysis Framework for XML Warehouses[END_REF][START_REF] Wang | OLAP for XML Data[END_REF][START_REF] Wiwatwattana | X ∧ 3: A Cube Operator for XML OLAP[END_REF]. However, each approach focuses on defining one cube operator only. In this paper, we propose to express a broad set of OLAP operators with an existing XML algebra (namely, TAX [START_REF] Jagadish | TAX: A Tree Algebra for XML[END_REF]), so that OLAP analyses can be applied onto native-XML data. On the long run, we are actually aiming at three objectives: (1) contribute to define a formal framework that does not currently exist in the XOLAP context; (2) support the effort for extending the XQuery language to allow OLAP queries, especially with XML-specific operators; (3) allow query optimization for OLAP XQueries. Native-XML DBMSs (Database Management Systems), though in constant progress, are indeed limited in term of performance and would greatly benefit from automatic query optimization, especially for costly analytical queries.

In this paper, we particularly focus on the first objective, i.e., defining XOLAP models. Computational issues shall be addressed later, but they are out of the scope of this paper, which is organized as follows. First, we present the context of this work and our motivation (Section 2). Second, we present the data model supporting our proposal (Section 3). Then, we express OLAP operators in TAX and present three detailed examples of XOLAP operators (Section 4). Finally, we compare our approach to X ∧ 3's [START_REF] Wiwatwattana | X ∧ 3: A Cube Operator for XML OLAP[END_REF], which is in spirit the most closely related work to ours in the literature (Section 5). We conclude this paper and provide future research directions (Section 6).

CONTEXT AND MOTIVATION

Rather than designing an XOLAP algebra from scratch, we chose to express a selection of "basic" OLAP operators with an existing XML algebra. Many such algebras exist in the literature [START_REF] Fernández | An Algebra for XML Query[END_REF][START_REF] Frasincar | XAL: An Algebra For XML Query Optimization[END_REF][START_REF] Novak | An XML Algebra for XQuery[END_REF]. Among them, we selected TAX (Tree Algebra for XML [START_REF] Jagadish | TAX: A Tree Algebra for XML[END_REF]) for its richness. TAX indeed includes, under its logical and physical forms, more than twenty operators, which allows us many combinations for expressing XOLAP operators. Furthermore, TAX's expressivity is widely acknowledged. This algebra can be expressed with most XML query languages, and especially XQuery, which we particularly target because of its standard status. Finally, TAX and its derived algebra TLC [START_REF] Paparizos | Tree Logical Classes for Efficient Evaluation of XQuery[END_REF] provide a query optimization framework that we can exploit in the future, since performance is one of our main concerns when desining decision-support applications that are integrally based on XML and XQuery. Unfortunately, due the space constraints, we cannot present the TAX elements that are necessary to understand our XOLAP operators in this paper. The interested reader may refer to the original paper describing TAX [START_REF] Jagadish | TAX: A Tree Algebra for XML[END_REF] for full specifications.

In order to propose a broad range of XOLAP operators, we selected the most common OLAP operators to express them in TAX. When some of them had conflicting definitions, we selected the one that had the broadest acceptation. Before presenting them, we define in Section 3 the data model they are based on, which incorporates multidimensional concepts within the TAX data model. The OLAP operators we selected to express in TAX are structural operators: rotate, switch, push and pull (Section 4.1); set operators: slice and dice (Section 4.2); and granularity-related operators: cube, roll-up and drill-down (Section 4.3). To express these operators, we adapted their formal definition in the classical OLAP context to the XML context by using the possibilities offered by TAX. Each XOLAP operator is actually represented as a combination of TAX operators. In this process, we took care of conserving the formal definitions and properties of OLAP operators, and used the TAX operators exactly as specified by TAX authors.

We define each XOLAP operator formally and, for one of each type (namely, the rotate structural operator, the slice set operator, and the roll-up granularity-related operator), illustrate how it operates on the three levels of the data model: XOLAP cube (conceptual), XOLAP TAX tree (logical) and XML multidimensional document (physical). These multiple representations are aimed at empirically checking whether a given operator proceeds as expected. In Section 4, we use the TAX notations introduced in [START_REF] Jagadish | TAX: A Tree Algebra for XML[END_REF].

DATA MODEL

A fact modeled in XML (or XML fact) is, classically, composed of dimension and measure elements. We term a set of XML facts an XML multidimensional document. Since TAX trees can model any XML document, XML multidimensional documents can be represented in TAX, in what we call multidimensional TAX trees, or XOLAP TAX trees. XOLAP TAX trees are thus a subset of TAX trees. An XO-LAP TAX tree embeds a collection of fact elements, each described by dimension members and measure values. For instance, Figure 1 features an XOLAP TAX tree that contains sale XML facts described by three dimensions: city where the sale took place, sold product, and sale year. Selling amount is the measure. Although logically modeled in XML, such facts are still conceptually multidimensional. Thus, we can represent an XML fact by a cube cell. We name such a cube an XOLAP cube, and its cells XOLAP cells. In classical OLAP, the concept of order of dimensions is very important. The switch operator's purpose is indeed to manipulate it. Dimensional order is easy to achieve in XML documents and tree representations. In our data model, we thus define a dimension reading direction for XOLAP TAX trees and XML facts: from left to right (in breadth first) and from top to bottom (in depth first), respectively. In addition, in both cases, fact measures must always be placed last in a subtree, with respect to these reading orders (e.g., amount in Figures 1 and2). This ordering has a very important role in the definition of some XOLAP operators, such as pull and push (Section 4.1).

Finally, our data model takes dimension hierarchies into account, to allow snowflake and constellation-like schemas. Each dimension's hierarchy is represented in a separate TAX tree. An example of such metadata TAX tree is provided in Figure 3. It refines the sample XOLAP TAX tree from Figure 1's geographical dimension by specifying that cities belong to departments (which are characterized in France by a department number). Note that, though the XOLAP TAX tree from Figure 1 represents only the finest granularity level (city), each city name is a reference to the geographical hierarchy TAX tree. We denote the set constituted of all dimension hierarchy trees H.

Rotate

Rotate permutes the dimensions of a cube and simulates its rotation around one of its axes, so as to present different faces of the cube. In other words, rotating helps select cube faces rather than measures. In an XOLAP TAX tree, we must exchange the positions of rotated dimensions for every subtree. Hence, the rotate operator may be expressed in TAX by a selection. Formally, its expression is: Rotate(C) = σP,SL(C), where the rotated dimension is specified in pattern tree P and dimension members and fact measures are specified in selection list SL.

Let us now take the example of rotating the XOLAP cube from Figure 2(a) around the product dimension. Figure 4 represents the rotated XOLAP cube (upper left), XOLAP TAX tree (bottom) and XML multidimensional document (upper right). In the selection, dimension order in the input pattern tree indicates the order of the edges in the output tree. Selection list SL must contain the sale node to retain all its children in output.

Switch

Switch exchanges the positions of two or several members of a given dimension. Like a rotation, this operation is mainly characterized by a visual effect and preserves measure values when changing the corresponding facts' positions. In an XOLAP TAX tree, we must reorder all subtrees. Hence, the switch operator may simply be expressed in TAX by using the reordering operator: Switch(C) = ̺P,o,RL(C), where order TVF o and reorder list RL specify the new subtree order.

Push

Push associates the members of a dimension to measures of the cube, i.e., it transforms these members into cell contents. In TAX, push restructures the witness tree. For example, to transform the city dimension into a measure, we associate the corresponding edge to the measure. Hence, the edge expressing this measure becomes composed of two subedges: city and amount. The push operator may thus be expressed in TAX with the copy-and-paste operator: P ush(C) = κP,CL,US(C), where copy list CL and update specification U S specify how a dimension element is copied into the target fact element.

Pull

Although pull is defined as push's reciprocal operator (transforming a measure into a dimension), it would be a mistake to express it in TAX push's reverse way. Moreover, in an XOLAP TAX tree, a measure is always represented by the last edge of the fact subtree (from left to right). Then, the pull operator just needs to move the measure before other dimensions. In TAX, this may be achieved with the projection operator, the new position being given by projection list P L and pattern tree P : P ull(C) = πP,P L(C ).

Set operators

Slice

A data cube may be seen as a set of slices arranged horizontally or vertically. The slice operator dissociates one or several of such slices with respect to one or several attributes from a given dimension. In TAX, we need to select the trees corresponding to these slices. As rotate, the slice operator may be expressed in TAX by the selection operator, but it is also combined to product to attach fact subtrees output by selection under the same root. Moreover, in the rotate operator, the selection operator's pattern tree P indicates dimension order in the output, whereas in the slice operator, it determines the slicing dimension values. Formally, the expression of the slice operator is: Slice(C) = ×(σP,SL(C)).

As an example, let us extract, from an initial XOLAP tree, the subtrees corresponding to slices of the corresponding XOLAP cube. Figure 5 shows how the XOLAP cube from Figure 2(a) is sliced on the Keyboard instance of the product dimension. It represents the sliced XOLAP cube (upper left), XOLAP TAX tree (bottom) and XML multidimensional document (upper right). Selection pattern tree P determines the slicing dimension member value (Keyboard, here). Selection list SL must contain the sale node to retain all its children in output. Finally, the resulting sale subtrees must be attached under a common root (sales) with the product operator.

Dice

The dice operator extracts a subcube from a data cube with respect to predicates defined on its dimensions. In other words, dicing extracts measures from a cube for a given number of members, which must be identical in all dimensions. In TAX, we may express the dice operator by selecting the corresponding subtrees from the XOLAP TAX tree with a simple pattern tree P and attaching them to the same root with a product: Dice(C) = ×(σP,SL(C)). Note that this is again different from the slice operator, in which P specifies the slicing member element(s).

Granularity-related operators

Roll-up

Roll-up represents a given data cube at a higher (more general) level of granularity, with respect to a dimension hierarchy (e.g., moving from the city granularity to the department granularity along the geographical dimension from Figure 3). During this transition, measures must be aggregated with respect to a grouping operation. In a TAX OLAP tree, this translates as replacing all subtrees with the subtrees resulting from the roll-up operation. The roll-up operator may be expressed in TAX by a combination of the selection, grouping, join, aggregation, node deletion and node insertion operators. Formally, its expression is: Roll up(C, H) = ιP ι ,IS (δP δ ,DS (AP A ,g,U S (1P 1,SL1 (γP γ ,g,o(σPσ ,SLσ (C)), H)))), where P1 specifies the rolled-up dimension and the selected granularity level, and H ∈ H this dimension's hierarchy.

Its execution is illustrated by the following example: perform a roll-up on the department dimension (department number 69, here) of the XOLAP TAX tree from Figure 1. Thus, grouping occurs on (product, year ). We use the sum aggregation function on amount. Figure 6 represents the rolled-up XOLAP cube (upper left), XOLAP TAX tree (bottom) and XML multidimensional document (upper right). The corresponding sequence of TAX operator combination is detailed thereafter.

(1) Selection: We must first separate subtrees from the input to prepare them for the next step. (2) Grouping: Then, we group the different subtrees by product and year. Grouping is achieved with respect to all possible combinations of modalities in both dimensions. (3) Join: For each tree resulting from grouping, we join subtrees corresponding to the rolled-up dimension (i.e., city, here) and to the corresponding dimension hierachical tree H (to retrieve department 69, here). (4) Aggregation: Now, for each tree resulting from the previous step, we aggregate all measures (i.e., amount here) in one node by using the specified aggregation function (sum, here). ( 5) Tree updates: Finally, we must prune from the output tree the measures at the previous granularity level, which are retained (node deletion) and add a new node describing the resulting granularity level (department in our case) with node insertion.

Drill-down

Drill-down is roll-up's reciprocal operator. It helps refine a cube dimension at a lower aggregation level, e.g., moving from the department granularity to the city granularity along the geographical dimension from Figure 3. First, the drilled-down dimension must be selected, then it must be joined to its hierarchy specification H ∈ H and the finestgranularity cube C0 (to retrieve non-aggregate measure values). Then, we must use the projection operator to mask the remaining coarser level member. Finally, measures must be reaggregated to the correct hierarchy level and all subtrees are attached to a single root (product). Formally, the drilldown operator is expressed as follows: Drill down(C, H) = ×(AP A ,g,U S (πP π ,P L(1P1,SL1 (σP σ ,SLσ (C), H, C0)))).

Cube

Cube is an aggregation operator that generalizes grouping, roll-up and join on a data cube to produce a more general (aggregate) cube. In TAX, we first must complete a roll-up for each cube dimension (Section 4.3.1). Then, resulting subtrees must be grouped with respect to every possible combination of dimensions. Finally, these subtrees are joined into one tree, with all measures being aggregated. The grouping, join and aggregation TAX operatiors are combined as follows: Cube(C) = AP A ,ag,U S (1P 1,SL1 (AP A ,ag,U S (γP γ ,g,o(Roll up(C, H))))).

COMPARISON TO X ∧ 3

Let us eventually discuss the differences between X ∧ 3 [START_REF] Wiwatwattana | X ∧ 3: A Cube Operator for XML OLAP[END_REF] and our own XOLAP approach, which have been developed in parallel without knowledge of the other effort. First, we use TAX to support our proposal by expressing each XO-LAP operator with one TAX operator or more. On the other hand, Wiwatwattana et al. exploit the principle of TAX's grouping operator, but X ∧ 3 stands as is and is not based on TAX operators. Thus, it addresses the issues of summarizability and heterogeneity in XML tree structures in an ad-hoc fashion, while our approach is more general.

Another difference between X ∧ 3 and our approach lies at data model level. While we exploit TAX's pattern and witness trees, Wiwatwattana et al. have based X ∧ 3 on relaxed tree patterns, which were initially introduced for approximate XML query matching [START_REF] Amer-Yahia | Tree Pattern Relaxation[END_REF]. Hence, X ∧ 3 outputs a lattice whose nodes represent a cuboid, while our result trees are simpler. We indeed do not explicitely take the specificities of the XML model into account and rather trust TAX to do so instead.

Finally, to take on an algorithmic metaphor, X ∧ 3's authors have adopted a depth-first approach by fully developping one operator only (which is of little use alone), while we have adopted a breadth-first approach by proposing a wider range of operators (which only apply onto quite "regular" XML data without ragged hierarchies nor missing values, though). Both approaches should aim at completion, in breadth and depth, respectively, to achieve a full XOLAP environment. We actually think they are quite complementary and should be combined, since our XOLAP approach provides modeling/logical functionalities, while X ∧ 3 bestows computational support on native XML data.

CONCLUSION AND PERSPECTIVES

In this paper, we have completed a first step toward an XOLAP framework, by initiating a previously inexistant formal background (Section 1, objective 1). To achieve this goal, we have demonstrated how the TAX XML algebra could support OLAP operators, by expressing in TAX the main usual OLAP operators (cube, rotate, switch, roll-up, drill-down, slice, dice, pull and push). By doing so, we significantly expanded the number of available XOLAP operators, since up to now, related papers only proposed at most three operators each (always including the cube operator).

The perspectives opened by this work are numerous. The main issue we are currently working on is to adapt the classical OLAP operators we expressed in TAX to actual specificities of XML. More precisely, we are addressing the four following issues, essentially when performing roll-up and drilldown operations: (1) ragged hierarchies [START_REF] Beyer | Extending XQuery for Analytics[END_REF] in dimensions, i.e., multivalued and multi-granularity dimension members;

(2) facts that are defined at heterogeneous levels of granularity (e.g., sales might be detailed at the city level in some countries, while only available at the region level in others);

(3) missing (unavailable) dimension information in facts; (4) facts with changing dimensional order (e.g., time and location in one fact, location and time in the next). Our final objective here is to support the XQuery extension effort for decision-support applications (Section 1, objective 2).

Though a non-trivial task that we have postponed for now, we also plan complexity analyses to provide a sounder comparison between the XOLAP operators from the literature and our own proposal. Furthermore, to allow experimentally validating our set of XOLAP operators, we have also started implementing it into a software prototype that helps generate the corresponding XQuery code. This simple Web-based querying interface is currently coupled to the TIMBER XML-native DBMS, but it is actually independent and could operate onto any other DBMS supporting XQuery. Our prototype currently features the rotate, slice and roll-up operators.

This software plaform shall also allow us to initiate a cycle of experimental cost evaluations and optimizations for each XOLAP operator, to find the most efficient expression of each XOLAP operator in TAX (there are, of course, often several solutions for expressing a given XOLAP operator in TAX). In our first experiments, the efficiency of XQuery indeed proved limited when processing complex analytical queries. Hence, we also plan on the long run to exploit our OLAP TAX expression as a basis for automatically optimizing XOLAP queries expressed with XQuery (Section 1, objective 3).

Figure 1 :

 1 Figure 1: Sample TAX data tree

  Figure 2(a) shows an example of XOLAP cube. The (physical) XML document corresponding to one of its XOLAP cells is also presented in Figure 2(b).

Figure 2 :

 2 Figure 2: Sample XOLAP cube and XML fact

Figure 3 :

 3 Figure 3: Sample hierarchical dimension specification

Figure 4 :Figure 5 :

 45 Figure 4: Rotate result example

ACKNOWLEDGMENTS

The authors would like to thank Dr. Alfredo Cuzzocrea for his thoughtful comments on this paper.