Syntyche Gbèhounou
email: syntyche.gbehounou@univ-poitiers.fr

François Lecellier
email: francois.lecellier@univ-poitiers.fr

Christine Fernandez-Maloigne

Evaluation of local and global descriptors for emotional impact recognition

Keywords: images, local descriptors, subjective evaluations, emotions, classification

In order to model the concept of emotion and to extract the emotional impact from images, one may search suitable image processing features. However, in the literature, there is no consensus on the ones to consider since they are often linked to the application. Obviously, the perception of emotion is not only influenced by the content of the images, it is also modified by some personal experiences like cultural aspects and semantic associated to some colours or objects. In this paper, we choose low level features frequently used in CBIR especially those based on SIFT descriptors. To take into account the complex process of emotion perception, we also consider colour and texture features and one global scene descriptor: GIST. We supposed the chosen features could implicitly encode high-level information about emotions due to their accuracy in the different CBIR applications of the literature. We test our methodology on two databases: SENSE and IAPS.

Introduction

In past decades, many achievements have been made in computer vision in order to replicate the most amazing capabilities of the human brain, for example image classification according semantic content or people tracking in video surveillance. However, there are some aspects of our behaviour or perception which remain difficult to apprehend, for example emotion prediction from an image or a video. This has several application such as: film classification, road safety education, advertising or e-commerce, by selecting appropriate images depending on the situation.

In order to predict the emotional impact of an image or a video, one first need is to describe what an emotion is and how to categorize them. There are two emotion classifications used in the literature [1]:

1. Discrete approach: emotional process can be explained with a set of basic or fundamental emotions, innate and common to all human (sadness, anger, happiness, disgust, fear, . . . ). There is no consensus about the nature and the number of these fundamental emotions. This modeling is usually preferred in emotion extraction based on facial expressions. 2. Dimensional approach: on the opposite, the emotions are considered in this model as the result of fixed number of concepts such as pleasure, arousal or power, represented in a dimensional space. The choosen dimensions vary depending to the needs of the model. Russel's model is the most considered, Fig. 1, with the dimensions valence and arousal:

• The valence corresponds to the way a person feels when looking at a picture. This dimension varies from negative to positive and allows to distinguish between negative emotions and pleasant ones.

• The arousal represents the activation level of the human body.

The advantage of the dimensional approach is to define a large number of emotions whithout the limitation of a fixed number of concept as the discrete ones. In spite of this advantage, some emotions can be confused (such as fear and anger in the circumplex of Russel) or unrepresented (among others surprise in Russel's model).

In the literature, a lot of works are based on the discrete modeling of the emotions; for example those of Paleari and Huet [START_REF] Paleari | Toward emotion indexing of multimedia excerpts[END_REF], Kaya and Epps [START_REF] Kaya | Color-emotion associations: Past experience and personal preference[END_REF], Wei et al. [START_REF] Wei | Image Emotional Classification Based on Color Semantic Description[END_REF] or Ou et al. [START_REF] Ou | A study of colour emotion and colour preference. part i: Colour emotions for single colours[END_REF][START_REF] Ou | A study of colour emotion and colour preference. part ii: Colour emotions for two-colour combinations[END_REF][START_REF] Ou | A study of colour emotion and colour preference. part iii: Colour preference modeling[END_REF]. In this paper, our goal is to obtain a classification into three different classes "Unpleasant", "Neutral" and "Pleasant". To tackle this objective, we choose a dimensional approach, since in discrete one the number and nature of emotions remain uncertain. Moreover, there are concepts which cannot be assigned to a specific class (surprise for example can be pleasant or unpleasant). The extraction of emotional impact is an ambitious task since the emotions are not only content related (textures, colours, shapes, objects, . . . ), but also depend on cultural and personal experiences.

In the past decade, lots of papers have been devoted to the links between emotions and colours [START_REF] Wei | Image Emotional Classification Based on Color Semantic Description[END_REF][START_REF] Ou | A study of colour emotion and colour preference. part i: Colour emotions for single colours[END_REF][START_REF] Ou | A study of colour emotion and colour preference. part ii: Colour emotions for two-colour combinations[END_REF][START_REF] Ou | A study of colour emotion and colour preference. part iii: Colour preference modeling[END_REF][START_REF] Boyatziz | Children's emotional associations with colors[END_REF][START_REF] Lucassen | Adding texture to color: quantitative analysis of color emotions[END_REF][START_REF] Bradley | Emotion and motivation ii: Sex differences in picture processing[END_REF][START_REF] Beke | Color preference of aged observers compared to young observers[END_REF]. Several of them consider emotions associated with particular colours through culture, age, gender or social status influences. There is a consensus among the authors to conclude that a link exists between colours and particular emotions. As stated by Ou et al. [START_REF] Ou | A study of colour emotion and colour preference. part i: Colour emotions for single colours[END_REF], colours play an important role in decision-making, evoking different emotional feelings. The research on colour emotion or colour pair emotion is now a well-established area of research. Indeed, in a series of publications, Ou et al. [START_REF] Ou | A study of colour emotion and colour preference. part i: Colour emotions for single colours[END_REF][START_REF] Ou | A study of colour emotion and colour preference. part ii: Colour emotions for two-colour combinations[END_REF][START_REF] Ou | A study of colour emotion and colour preference. part iii: Colour preference modeling[END_REF] studied the relationship between emotions, preferences and colours and have established a model of emotions associated with colours from psychophysical experiments. Another part of the literature is dedicated to facial expression interpretation [START_REF] Paleari | Toward emotion indexing of multimedia excerpts[END_REF]. In this work, emotions are associated with facial features (such as eyebrows, lips). Since facial expressions are common among humans to express basic emotions (happy, fear, sadness, surprise, . . . ), it seems to be the easiest way to predict them. Nevertheless, in this case, the authors extract emotions carried by the images and not really those felt by someone looking at these pictures. More recently some authors looked at the emotion recognition as a Content Based Image Retrieval (CBIR) task [START_REF] Solli | Emotion related structures in large image databases[END_REF][START_REF] Machajdik | Affective image classification using features inspired by psychology and art theory[END_REF][START_REF] Yanulevskaya | Emotional valence categorization using holistic image features[END_REF]. Their underlying idea consists in considering the traditional image retrieval techniques to extract the emotional impact of images. To achieve this goal, the authors used a multistage method, at first by extracting traditional image features (colours, textures, shapes) and then combined those features into a classification system after a learning step. For example, Wang and Yu [START_REF] Wang | Image emotional semantic query based on color semantic description[END_REF] used the semantic description of colours to associate an emotional semantic to an image. Concerning textures, the orientation of the different lines contained in the images is sometimes considered. According to Liu et al. [1], oblique lines could be associated with dynamism and action; horizontal and vertical ones with calm and relaxation.

Our work is part of this last family of approaches. We evaluated some low level features well adapted for object recognition and image retrieval [START_REF] Abdel-Hakim | CSIFT: A SIFT Descriptor with color invariant characteristics[END_REF][START_REF] Jégou | Aggregating local descriptors into a compact image representation[END_REF][START_REF] Ke | PCA-SIFT: a more distinctive representation for local image descriptors[END_REF][START_REF] Lowe | Object recognition from local scale-invariant features[END_REF][START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF][START_REF] Nistér | Scalable recognition with a vocabulary tree[END_REF][START_REF] Van De Sande | Evaluating color descriptors for object and scene recognition[END_REF] and conducted our work on two databases:

• A set of natural images that was assessed during subjective evaluations:

Study of Emotion on Natural image databaSE (SENSE) [START_REF] Denis | Improvement of natural image search engines results by emotional filtering[END_REF];

• A database considered as a reference on psychological studies of emotions: International Affective Picture System (IAPS) [START_REF] Lang | International affective picture system (IAPS): Affective ratings of pictures and instruction manual[END_REF].

This paper is organized as follow. We describe the image databases in Section 2 and the features used for emotion recognition in Section 3. The classification process is explained in Section 4. In Section 5 we summarize our results. We conclude about our study and provide some perspectives in Section 6.

Image databases

In the domain of emotion extraction, the choice of the database is not trivial since there is no reference for all emotion studies and applications, some authors even built their own dataset without spreading it. We choose in this study to considered two databases: the first one is composed of low semantic images and the second of more semantic ones. In this paper, "low-semantic" means, that the images do not shock and do not force a strong emotional response. We think that even low semantic images, including abstract representation, may produce emotions according to the viewer sensitivity and the viewing time. We define this "low-semantic" criteria in response to some high semantic images on IAPS [START_REF] Lang | International affective picture system (IAPS): Affective ratings of pictures and instruction manual[END_REF], a reference in psychological studies on emotions. In this database, which will be described in subsection 2.1, there are images with blood, dirt, high semantic photomanipulations or naked people which might induce a bias in the assessment of the images. There is a risk of overreaction to neutral images viewed right after strong pleasant or unpleasant ones. Our aim in this paper is to evaluate the behaviour of our strategy developed for a low semantic database on a more semantic one.

The International Affective Picture System (IAPS)

This dataset is developed since the late 1980s at NIMH Center for Emotion and Attention (CSEA) at the University of Florida [START_REF] Lang | International affective picture system (IAPS): Affective ratings of pictures and instruction manual[END_REF], which is composed of photographs used in emotion research. It is considered as a reference in psychological studies and many papers present results on this base [1, [START_REF] Machajdik | Affective image classification using features inspired by psychology and art theory[END_REF][START_REF] Yanulevskaya | Emotional valence categorization using holistic image features[END_REF]. The images of IAPS are scored according to the affective ratings: pleasure, arousal and dominance. It corresponds to a dimensional representation of emotions. The affective norms for the pictures in the IAPS were obtained in 18 separate studies involving approximately 60 pictures for each session. Each of the 1182 images from their dataset was evaluated by about 100 participants. 1 The emotion of the images we have chosen is based of those defined in different papers [START_REF] Bradley | Brain potentials in perception: Picture complexity and emotional arousal[END_REF][START_REF] Bradley | A multi-process account of startle modulation during affective perception[END_REF][START_REF] Keil | Large-scale neural correlates of affective picture processing[END_REF] using three class classification: "Pleasant", "Neutral" and "Unpleasant".

SENSE

Study of Emotion on Natural image databaSE (SENSE) is the database used in [START_REF] Denis | Improvement of natural image search engines results by emotional filtering[END_REF][START_REF] Gbèhounou | Can salient interest regions resume emotional impact of an image?[END_REF]. It is a low semantic, natural and diversified database containing 350 images free to use for research and publication. It is composed of animals, food and drink, landscapes, historic and tourist monuments as shown on Fig. 2 with some examples. Some transformations were applied on some images of the database: geometric modifications and changes on colour balance, so some images are repeated twice or more. In this database, only 17 images (4.86%) contain human faces to ensure that the facial expression does not induce bias. It is composed of low semantic images since they minimize the potential interactions between emotions on following images during subjective evaluations. This aspect is important to ensure that the emotion indicated for an image is really related to its content and not to the emotional impact of the previous one. In fact, in case of strong emotions, one can imagine that the emotion felt for an image could modify the decision for the following image(s). This lowsemantic aspect also allow different applications, for example, an application of re ranking images according to their emotional impact or an application of cook recipe image retrieval that eventually contains low semantic images. The short viewing duration is another constraint in the evaluation to reduce the semantic interpretation. During the tests the observers assessed nature and power of emotional impact of the images. For the nature, the different choices are "Negative", "Neutral" or "Positive" and the power varies from "Low" to "High". These information where chosen as the easiest way to evaluate a "primary" emotion for low semantic images. Discrete modeling is not adapted in this case. In fact, as stated in introduction, in a discrete representation of emotions, emotional process is explained with a set of basic or fundamental emotions, innate and common to all human, often based on facial expressions. In this database, each image was assessed by an average of 104.81 observers and the emotion is given after an average observation time of 6.5 seconds.

Images features

As stated is the introduction, many works find a link between colours or textures and emotions, we choose to extract those information using local features (interest point descriptors) and global ones (textures, colours). Since SIFT and other local descriptors are well adapted for CBIR, we will sum-marize some important information about them and their colour extensions. Then, we present global descriptors considered in this work.

Features based on local information

In order to extract local features, one will always need a two step algorithm:

1. Find a set of interest points; 2. Compute the descriptor associated to each point.

In this work, to detect the interest points, we choose Harris-Laplace [START_REF] Mikolajczyk | Indexing based on scale invariant interest points[END_REF] which has shown good performance for category recognition according to Zhang et al. [START_REF] Zhang | Local features and kernels for classification of texture and object categories: A comprehensive study[END_REF]. As far as descriptors are concerned, we opt for those evaluated by van de Sande et al [START_REF] Van De Sande | Evaluating color descriptors for object and scene recognition[END_REF]:

• SIFT and some colours extensions (CSIFT and OpponentSIFT),

• Colour Moments,

• Colour Moment Invariants.

Those choices were lead by the efficiency of SIFT and its extensions, in the domain of image retrieval. SIFT, introduced by Lowe [START_REF] Lowe | Object recognition from local scale-invariant features[END_REF][START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF] was originally computed on greyscale images so, for this descriptor we converted the images to greyscale with the formula of NTSC standard (Equation ( 3)). The original version, proposed by Lowe, is invariant to translation, image scaling, rotation, change in illumination and affine or 3D projection. We also compute two colour extensions of SIFT. The first one, OpponentSIFT, was proposed by van de Sande et al. [START_REF] Van De Sande | Evaluating color descriptors for object and scene recognition[END_REF]. They describe all the channels in the opponent colour space using SIFT descriptors as shown in equation (1):

  0 1 0 2 0 3   =    R-G √ 2 R+G-2B √ 6 R+G+B √ 3    . (1)
The information in the O 3 channel is equal to the intensity information, while the two others describe the colour information in the image. We consider also a second colour extension of the greyscale SIFT: C-SIFT. This descriptor was firstly suggested by Abdel-Hakim and Farag [START_REF] Abdel-Hakim | CSIFT: A SIFT Descriptor with color invariant characteristics[END_REF] using the colour invariants developed by Geusebroek et al. [START_REF] Geusebroek | Color invariance[END_REF]. This approach builds the SIFT descriptors in a colour invariant space. Its performance was proved in the evaluations made by van de Sande et al. [START_REF] Van De Sande | Evaluating color descriptors for object and scene recognition[END_REF] on PASCAL VOC 2007 [START_REF] Everingham | The PASCAL Visual Object Classes Challenge[END_REF].

Besides SIFT descriptors (and extensions), we also tested colour moments and colour moment invariants in order to deal with fully colour descriptors. Colour moments are measures used to differentiate images based on their colour features. Once calculated, these moments provide a measurement for colour similarity between images. For a colour image corresponding to a function I with RGB triplets, for image position (x, y), the generalized colour moments are defined by the equation ( 2):

M abc pq = Ω x p y q [I R (x, y)] a [I G (x, y)] b [I B (x, y)] c dxdy, (2)
where Ω is a region around the local feature. M abc pq is known as generalized colour moment of order p+q and degree a+b+c. Only generalized colour moments up to the first order and the second degree are considered to avoid numeric instability, thus the resulting invariants are functions of the generalized colour moments M abc 00 , M abc 10 and M abc 01 :

with (a, b, c) ∈   
(1, 0, 0) , (0, 1, 0) , (0, 0, 1) (2, 0, 0) , (0, 2, 0) , (0, 0, 2) (1, 1, 0) , (1, 0, 1) , (0, 1, 1)

   .
Those moments are only invariant to light intensity shift [START_REF] Van De Sande | Evaluating color descriptors for object and scene recognition[END_REF]. In order to add some colour invariants, there is also an invariant version of colours moments: colour moment invariants proposed by Mindru et al. [START_REF] Mindru | Moment invariants for recognition under changing viewpoint and illumination[END_REF]. The authors use generalized colour moments for the definition of combined invariants to the affine transform of coordinates and contrast changes. Compared to colour moments these descriptors are invariant to light intensity shift and change and light colour change and shift [START_REF] Van De Sande | Evaluating color descriptors for object and scene recognition[END_REF].

Features based on global information

We also tested some global information features (colour, texture and global scene description).

To identify the different colours of each image, we used colour segmentation by region growing [START_REF] Fernandez-Maloigne | Advanced Color Image Processing and Analysis[END_REF] which is a two step algorithm: initialize the seeds and then grow region from seeds in order to obtain a segmented image. For the initialization of the seeds, we performed an analysis of greyscale histogram. This analysis was made in greyscale to save time in homogeneous areas. To convert colour images to greyscale we use again the equation ( 3) according to the NTSC standard.

grey = 0.299R + 0.587G + 0.114B (3)
The seeds are then the maxima of the greyscale histogram. The region growing was performed in CIE Lab 1976 colour space in order to use a perceptual distance. In our case, we consider the distance computed with ∆E and obtained with equation ( 4) (for two colours C 1 and C 2 ). Then on the segmented version, we retained only the average colour of different regions.

∆E = (L * 1 -L * 2 ) 2 + (a * 1 -a * 2 ) 2 + (b * 1 -b * 2 ) 2 (4)
To extract the textures of images, we use Wave Atom transform introduced by Ying and Demanet [START_REF] Demanet | Wave atoms and time upscaling of wave equations[END_REF] on greyscale images. These features can be considered as a variant of 2D wavelet packets with a parabolic wavelength scale and prove their efficiency on local oscillatory textures. Wave Atom transform is a multi-scale transform and yields information from different levels. It is an oriented decomposition where the number of coefficients for each orientation depends on the decomposition level. Before applying Wave Atom transform we resized all image to 256 * 256 with zero padding if it is needed. With this new size, we obtain 5 levels of decomposition and only retained the scales 4 and 5 due to the small size of the three other scales. On scale 4 we obtain a set of 91 orientations, each of them containing 2 4 * 2 4 (256) coefficients. Scale 5 contains 32 orientations and 1024 coefficients per orientation.

Our global scene description of the image is obtained using GIST introduced by Oliva and Torralba in 2001 [START_REF] Oliva | Modeling the shape of the scene: A holistic representation of the spatial envelope[END_REF]. This descriptor leads to a low dimensional representation of image. It is obtained with a set of perceptual dimensions (naturalness, openness, roughness, expansion, ruggedness) that represent the dominant spatial structure of a scene. These dimensions are estimated using spectral and coarsely localized information. For our study we compute GIST on images resized to 256 * 256 with zero padding to respect the recommendations provided by the authors.

Classification process

Traditionally, for CBIR task, an image is represented by a visual signature, which concentrates the usefull information of the content of the image into a smaller descriptor. For a recognition or retrieval task, two images are considered as visually close if their visual signatures are close too. There are different ways to obtain this visual signature [START_REF] Jégou | Aggregating local descriptors into a compact image representation[END_REF][START_REF] Sivic | Video Google: A text retrieval approach to object matching in videos[END_REF][START_REF] Perronnin | Fisher kernels on visual vocabularies for image categorization[END_REF], but the large majority of them depends on a visual codebook and visual words. We evaluate two different visual signatures methods: Bag of Visual Words (BoVW) [START_REF] Sivic | Video Google: A text retrieval approach to object matching in videos[END_REF] and VLAD [START_REF] Jégou | Aggregating local descriptors into a compact image representation[END_REF]. Here, the visual codebook is a set a visual words (a set of features) obtained by a K-Means algorithm. The idea is to resume an image database with K visual words (features). Then, after obtaining the signature, the decision process on emotion recognition uses a classification algorithm such as SVM for example.

Compact representation of features vectors with visual signature

The visual signature named Bag of Visual Words (BoVW) was initially proposed by Sivic and Zisserman [START_REF] Sivic | Video Google: A text retrieval approach to object matching in videos[END_REF] with applications on images and videos and is inspired by the method "bag of words" used in text categorization. An image is represented here by the histogram of occurrences of the various visual words in the codebook.

VLAD is another visual signature which describes the distance between each feature and its nearest visual word. VLAD can be seen as a simplification of the Fisher kernel [START_REF] Perronnin | Fisher kernels on visual vocabularies for image categorization[END_REF]. Let C = C 1 , . . . , C K a visual codebook composed of K visual words obtained with K-means algorithm, each local descriptor D is associated to its nearest visual word C i as shows the equation [START_REF] Ou | A study of colour emotion and colour preference. part i: Colour emotions for single colours[END_REF].

V k = Dn:N N (Dn)=W k (D n -W k ). ( 5
)
The idea of the VLAD descriptor is to accumulate, for each visual word C i , the differences D -C i of the vectors D assigned to C i . This characterizes the distribution of the vectors with respect to the center. Assuming the local descriptor to be d-dimensional, the dimension D of VLAD representation is

D = K * d.
Except for GIST, on all our descriptors the visual codebooks are obtained with a K-Means algorithm. The size of the K-Means codebook is obtained with the equation ( 6):

K = 4 √ N * d, (6)
where K is the number of visual words and N is the number of descriptors and d the size of vector of characteristics.

For VLAD we only compute K=64 visual words based on the results obtained by Jégou et al [START_REF] Jégou | Aggregating local descriptors into a compact image representation[END_REF].

In the particular case of GIST, we use PCA as advised by Oliva and Torralba [START_REF] Oliva | Modeling the shape of the scene: A holistic representation of the spatial envelope[END_REF]. To perform PCA we compute the principal components on the GIST descriptors from the full database considered. We select the K axes that preserve 99% of the initial information.

After computing the visual signature, we apply a L2-normalization to allow the comparison of the signatures coming from different images.

Classification with SVM

For emotion recognition, Liu et al.

[1] among others, use an SVM classifier with a linear kernel in its multiclass extension "One against one" for classification. They showed that this method gives the best results using their descriptors and databases, so we naturally choose to test our descriptors and databases with this classifier. The inputs of the classifier are the visual signatures according to the considered descriptor. We performed a two class classification: positive and negative emotions. We do not consider the "Neutal" class since, during our database assessment on SENSE, this class was given by observers which whether cannot decide about the nature of the emotion or really feel neutral when looking at the images. Moreover, the neutral images are rarely considerd in the literature [START_REF] Wei | Image Emotional Classification Based on Color Semantic Description[END_REF][START_REF] Machajdik | Affective image classification using features inspired by psychology and art theory[END_REF] due to the same restriction. On IAPS, some authors [START_REF] Bradley | Brain potentials in perception: Picture complexity and emotional arousal[END_REF][START_REF] Bradley | A multi-process account of startle modulation during affective perception[END_REF][START_REF] Keil | Large-scale neural correlates of affective picture processing[END_REF] list in their articles the images according to their hedonic valence that induces the three groups: Pleasant, Neutral and Unpleasant images, which respectively correspond to positive, neutral and negative. However, to perform a fair comparison between our results on the two databases in the rest of this paper we only keep positive and negative images. After classification for each descriptor we combined the results for the different descriptors using "Majority Voting" algorithm as shown on the Fig. 3.

Classification results

In this Section we present our results for local and global feature evaluation for emotional impact recognition. We firstly discuss our results on SENSE and IAPS, then we compare those from IAPS to some baselines from the literature. The configuration of the different image databases (learning and test sets) is given in the appendix.

Results on SENSE and IAPS and discussions

In Table 1, we summarize the results obtained after classification for each descriptor. In this table :   • WA4 and WA5 respectively means Wave Atoms Scale 4 and Wave Atoms Scale 5;

• CM denotes Colour Moments and CMI Colour Moment Invariants;

• OpSIFT means OpponentSIFT;

• We use the notation Dataset Visual codebook to resume the different configurations we have tested. Then in SENSE I configuration, the visual signatures of the images of SENSE are computed using the visual vocabulary from IAPS. The different configurations allow us to determine whether or not the results are dependent on the image database used to create the visual dictionary.

In [START_REF] Gbehounou | Image database indexing: Emotional impact evaluation[END_REF], we have studied the impact of the visual signature according to the nature of the features. We noticed that VLAD representation matches better for the local descriptors and BoVW for global ones. In general, on local features, VLAD outperformed BoVW by 10% and on global features underperformed them by 20%, interested reader may refer to [START_REF] Gbehounou | Image database indexing: Emotional impact evaluation[END_REF] for more details.

Then for the following results we use BOVW for global feature descriptors and VLAD for local feature descriptors.

One can easily see on Table 1 that the selected descriptors have a different behaviour whether the nature of emotion is positive or negative. However the average of correct classification for each nature of emotion remains higher than the random selection (50%). In general, when considering IAPS as test database or as visual codebook, the negative images are more easily classified.

It comes from the nature of images in IAPS since many of them are voluntarily modified to ensure a strong emotional response. For SENSE database, the average results are more consistent for negative and positive emotions with 55.55% and 54.16%. We can also conclude that the visual dictionary has little impact on the behaviour of descriptors for SENSE and IAPS. Those global average results prove that our choice to consider classic CBIR features for emotion evaluation gives interesting results.

When differentiating the descriptors, the results are less consistent. For example, SIFT have approximately the same results for negative and positive emotions with yet a higher classification rate for negative ones (63.28%). It is also the only descriptor which allows a classification significantly higher than random one for both positive and negative emotions whether the dataset and the visual dictionary. CSIFT and OpSIFT compete with SIFT for global recognition of emotions, but OpSIFT is less efficient for negative images with SENSE or using SENSE visual codebook. In spite of this less efficiency, it is the best descriptor for IAPS using IAPS codebook with 60.66% for negative images and 63.79% for positive ones. CSIFT gives the best negative estimation of all global and local descriptors with 77.75% in average and even 90% for SENSE using IAPS codebook. Colour descriptors tend to extract more negative images except for SENSE using SENSE dictionary. In this case, for CM and Colours, the classification rates for positive images are higher than 80%. The other descriptors give less reliable results on both positive and negative images with a very low score for WA4 on positive images on IAPS with the codebook obtained with SENSE. However WA4 and WA5 are complementary since WA4 tends to extract negative images and WA5 positive ones.

Regarding the obtained results, all the descriptors may enhance the classification rate since the misclassified images are different. However, it appears rather clearly that negative images will be more easy to extract than positive ones. To verify this hypothesis we performed a fusion based on Majority Voting. The results are presented in Table 2. In Table 2 we compare the classification rates before and after fusion with Majoriting Voting. As we think considering the previous results, there is a significant improvement after the fusion. For example, regardless the codebook used, the recognition of negative images is increased by 15% on average for the two datasets. Moreover, the best classification rates are obtained after merging using the dictionary built from IAPS. Before the fusion, 54.86% and 45.02% of positive images were respectively recognized on SENSE and IAPS against 64.58% and 46.55% after. If we generally consider these results after fusion, we see that they have especially been improved on our image database (SENSE), independently of visual dictionaries and emotions:

• ∼ +15% for negative images and ∼ +6% for positive ones;

• ∼ +17% with the codebook from IAPS and ∼ +3.7% with the codebook from SENSE.

Note that for IAPS, positive image average results (47.13% and 45.02%) are lower than a simple random selection (50%). There are two hypotheses for this: the construction of the database itself or the fact that negative images are easier to recognize. The proposed algorithm highlights the complementarity of the chosen features. In fact, we have also tested different fusion combinations and the better configuration is the fusion of all of the features to obtain the best classification of positive and negative images. We also prove that CBIR methods are effective for the emotional impact recognition.

Comparison with literature on IAPS

As stated in the introduction, we want to point out the difficulty of comparison of results on emotion recognition since the datasets vary and, even on IAPS, there is no consensus on the training set. Regarding the divergences induced by this disparity, the goal of this comparison is only to present the interval of the classification rates. We chose three results on IAPS to make the comparison:

• Wei et al. [START_REF] Wei | Image Emotional Classification Based on Color Semantic Description[END_REF] using a semantic description of the images for emotional classification of images. The authors chose a discrete modeling of emotions in 8 classes: "Anger", "Despair", "Interest", "Irritation", "Joy", "Fun", "Pride" and "Sadness". The classification rates they get are between 33.25% for the class "Pleasure" and 50.25% for "Joy."

• Liu et al.

[1] proposing a system based on colour, texture, shape features and a set of semantic descriptors based on colours. Their results on IAPS are 54.70% in average after a fusion with the Theory of evidence and 52.05% with MV fusion. For their classification, they held four classes by subdividing the dimensional model Valence/Arousal into four quadrants; those defined by the intersection of the axes.

• Machajdik et al. [START_REF] Machajdik | Affective image classification using features inspired by psychology and art theory[END_REF] using colour, texture, composition and content descriptors. They chose a discrete categorization in 8 classes: "Amusement", "Anger", "Awe", "Contentment", "Disgust", "Excitement", "Fear" and "Sad". The average rates of classification are between 55% and 65 %. The lowest rate is obtained for the class "Contentement" and the highest for the class "Awe". The results are from the best feature selections implemented during their work.

If we compare our results with those three, we can conclude that our method is really relevant. Our classification rates are in the high average on IAPS: 54.44% and 55.30% before fusion; 58.82% and 62.18% after. Moreover, our approach allows us to compete with the best scores from the literature even outperform them in terms of classification rate.

Conclusions and future works

In this paper, we propose an evaluation of different standard CBIR features for emotion prediction on low and high semantic images. The emotional impact of images is the result of many parameters both intrinsic and extrinsic. On the one hand, colours, textures or shapes are intrinsic parameters. On the other hand, culture, state of mind and experience of the viewer can be considered as extrinsic. Our goal in this work is to model the intrinsic ones using local and global features, and to deal with the large variability of images. So we have tested our algorithm on two databases: one low semantic (SENSE) and the other more semantic (IAPS). Whether they are local or global, the different descriptors have proven their efficiency for emotional impact recognition on both databases. Moreover, the compact representation of local features using VLAD seems to focus their emotional response and give very promising results for SIFT based descriptors.

One of the important perspective in our study will be evaluations of saliency for different emotions. For this purpose, we plan to hold new psychovisual tests with an eye tracker. We can then assess visual attention of observers based on the emotional impact of images. Another interesting perspective is to use another algorithm of combining, for example Evidence Theory that gives best results compared to Majority Voting on the emotion recognition solution proposed by Liu et al. [1].

[1] E. Liu, N.and Dellandréa, L. Chen, Evaluation of features and combination approaches for the classification of emotional semantics in images, in: International Conference on Computer Vision Theory and Applications, 2011.

Fig. 1 :

 1 Fig. 1: Russel's emotions modeling. The axe Unpleasant/Pleasant corresponds to the arousal and the second one to the valence.

Fig. 2 :

 2 Fig. 2: Some images from SENSE.

Fig. 3 :

 3 Fig. 3: Algorithm of classification fusion. Concerning "Majority Voting" the final class is the class predicted by a maximum of classifiers.

Table 1 :

 1 Classification rates after classification for each descriptor. SENSE I configuration corresponds to the results obtained where the visual signatures of the images of SENSE are computed using the visual vocabulary from IAPS. For SENSE S configuration the visual signatures are obtained using SENSE visual codebook. For IAPS I and IAPS S the visual signatures of the images of IAPS are respectively computed using the visual vocabularies from IAPS and SENSE.

	Descriptors	Configuration Test database Visual codebook IAPS I emotions SENSE S SENSE I IAPS S Nature of	Average
		Colours	Negative	40%	70%	85.25%	78.69%	68.49%
	Global descriptors	WA4 WA5	Positive Negative Positive Negative Positive	80.21% 50% 30.21% 30% 50%	43.75% 50% 52.08% 60% 65.62%	27.59% 77.05% 20.69% 57.38% 41.38%	29.31% 68.85% 32.76% 44.26% 58.62%	45.22% 61.48% 33.94% 47.91% 53.91%
		GIST	Negative	90%	40%	42.62%	62.3%	58.73%
			Positive	27.08%	61.46%	56.90%	37.93%	45.84%
		CM	Negative	10%	80%	40.98%	60.66%	47.91%
			Positive	88.54%	54.17%	68.97%	51.72%	65.85%
	Local descriptors	CMI SIFT CSIFT	Negative Positive Negative Positive Negative	70% 57.29% 70% 56.25% 80%	60% 58.33% 70% 52.08% 90%	60.66% 55.17% 52.46% 51.72% 73.77%	86.89% 27.59% 60.66% 53.45% 67.21%	69.39% 49.60% 63.28% 53.38% 77.75%
			Positive	50%	54.17%	53.45%	50%	51.91%
		OpSIFT	Negative	60%	60%	65.57%	60.66%	61.56%
			Positive	47.92%	52.08%	48.28%	63.79%	53.02%
		Average	Negative	55.55%	64.44%	61.75%	65.58%	61.83%
			Positive	54.16%	54.86%	47.13%	45.02%	50.29%

Table 2 :

 2 Comparison of correct average classification rates on SENSE and IAPS before and after fusion with Majority Voting.

			Before fusion After fusion
		Negative	55.56%	60%
	SENSE S	Positive	54.17%	57.29%
		Average	54.87%	58.65%
		Negative	64.44%	90%
	SENSE I	Positive	54.86%	64.58%
		Average	59.65%	77.29%
		Negative	61.75%	75.41%
	IAPS S	Positive	47.13%	41.38%
		Average	54.44%	58.40%
		Negative	65.58%	77.05%
	IAPS I	Positive	45.02%	46.55%
		Average	55.30%	61.80%

It is the size of the database when we received it.


Pol Johannes Van Der

Jean-Paul Rameshkoumar

David Virapin

Bernard Zozime

Johannes Van Der Pol
email: johannes.van-der-pol@u-bordeaux.fr

Keywords: knowledge diffusion, collaboration network, patents, publications, bibliometrics, dynamic network

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

A preliminary analysis of knowledge flows: the case of structural composite materials in aeronautics $ ,$$

Introduction

Innovations are the driving force behind growing economies and prosperous firms. Achieving innovation is hence at the center of any business strategy. With the growing complexity of new technologies, a single firm can no longer master all the technologies needed for the production of a single product. Accessing knowledge held by other firms becomes of vital importance for firms in order to innovate. Accessing different knowledge sources has proven to be beneficial for the firm [START_REF] Mcevily | Embedded ties and the acquisition of competitive capabilities[END_REF], for innovation [START_REF] Kogut | Knowledge of the firm, combinative capabilities, and the replication of technology[END_REF], [START_REF] Tsai | Knowledge transfer in intraorganizational networks: Effects of network position and absorptive capacity on business unit innovation and performance[END_REF] as well as survival and growth [START_REF] Watson | Modeling the relationship between networking and firm performance[END_REF].

Working under the Schumpeterian hypothesis that innovations are achieved through the recombination of existing technologies, diversity is the key to new innovations [START_REF] Dosi | Innovation, organization and economic dynamics: selected essays[END_REF], [START_REF] Cowan | Structural holes, innovation and the distribution of ideas[END_REF]. By recombining knowledge held in different firms new knowledge is created. Cooperations started to appear between firms, changing the business landscape by a profound reconsideration of strategic decisions. Firms now focus on the identification of efficient partners in order to absorb and recombine as much relevant information as possible. Empiric analyses show that the number of cooperations has increased steadily over the last two decades paolo [START_REF] Paolo Saviotti | On the dynamics of generation and utilisation of knowledge: The local character of knowledge[END_REF]. During this same period we can observe that cooperation has evolved from (predominantly) dyadic cooperation to multilateral cooperations. Firms evolve in networks, an interconnection of cooperating firms with a common goal [START_REF] Pippel | The impact of r&d collaboration networks on the performance of firms: a meta-analysis of the evidence[END_REF]. In networks knowledge flows between firms, allowing them to learn from one another. The manner in which firms benefit from the network depends in part on the structure of the network since the structure defines how fast and efficient knowledge flows through the network [START_REF] Verspagen | The small worlds of strategic technology alliances[END_REF]. The evolution of these networks has been studied in the past by many researchers Ahuja (2000), [START_REF] Verspagen | The small worlds of strategic technology alliances[END_REF], [START_REF] Buchmann | The evolution of innovation networks: The case of a german automotive network[END_REF], [START_REF] König | Recombinant knowledge and the evolution of innovation networks[END_REF]), ven der Valk et al. (2011). We hypothesize that there is a correlation between the evolution of the structure of a collaboration network and that of the technology life-cycle. More precisely, the life-cycle of a technology is defined by a research and a development stage. The structure of the network differers according to the stage of the cycle. A first stage requires the absorption of knowledge from fundamental research and knowledge from other sectors. The second stage is defined by a diffusion of the new technology. In order to verify this hypothesis we analyze the structure and evolution of the knowledge network relative to structural composite materials. The first aim of this chapter is hence to analyze how a collaboration network evolves when a new technology is being developed. Since we focus on an existing sector, firms already have collaborative links with other firms. Firms hence need to make the strategic decision to either collaborate with historic partners or collaborate with new firms. The importance of social capital in network evolution has been intensively studied. We present here an example of two firms developing a same technology which took opposite decisions in terms of collaboration. We will show how one strategy resulted in a 10-year technological delay in development. The second aim of this paper is hence to consider the impact of social capital as a collaborator selection mechanism on innovation performance. This chapter is organized as follows. In a first section we will present the technology under analysis: Structural Composite Materials (SCM). We will then present the data and methodology. Section 3 provides an analysis of the IPC network, section 4 correlates section 3 with the evolution of the collaboration network. Section 5 analyzes the impact of social capital on innovative performance. Section 6 concludes.

Structural Composite Materials

Structural Composite Materials (SCM) were first developed by chemists in the early 20th century and have since been used in sport equipment and the automotive industry. It caught the attention of civil aircraft manufacturers during the late 70s. During this period, research programs focusing on the optimization of energy consumption were launched by the European Union and the american government. The aim of these programs was to exploit composite materials in order to increase energy efficiency for aircrafts by the means of weight reduction. This makes SCM the perfect candidate for a study to analyze how a network is structured in order to absorb an existing technology from other sectors and develop it for its own needs.

The aerospace sector has a particular structure, it is organized as a production chain. An aircraft being a multi-technological product, each part of the airplane is developed in a different part of the network (see chapter 4 for more details).

In the value chain that makes up the sector, a small number of firms occupies a strategic (central) position, these firms assemble intermediary products before sending them to either the final assembler (Airbus, Boeing etc.) or to other firms that use intermediary goods for larger parts. Firms with these specific positions in the value chain are called "pivot firms" [START_REF] Frigant | Les territoires de l'aéronautique: Eads, entre mondialisation et ancrage[END_REF]. These firms have to master all the technologies of the downstream firms in order to complete their part of the aircraft.

The introduction of a new technology such as SCM, can only succeed if the value chain adapts to the technology. Indeed, the introduction of SCM alter the structure of an aircraft in many dimensions. Pivot firms have to adjust their production methods and hence so do the downstream firms. Integrating SCM in the aerospace industry hence implies a thorough understanding of the core and linkage technologies [START_REF] Prencipe | Technological competencies and product's evolutionary dynamics a case study from the aero-engine industry[END_REF]) by all the actors implicated in aeronautical programs.

Data and methodology

In order to generate the collaboration network around the SCM technology in aeronautics we need to identify all firms working with SCMs. We call this first step "Technology Framing".

Technology framing

We used patent and publication data to generate our network. Patents were extracted from Orbit while publications were extracted from Scopus. In order to extract all relevant patents and publication we started by framing the technologies involved in the production of SCM. The framing process is an iterative process based on discussions with engineers and executives from the aerospace sector. We conducted an initial search for relevant IPC codes by identifying parts of the aircraft that can be made out of SCM. A detailed search was then conducted in order to identify what specific products and technologies are involved in the creation of composite materials (resins, matrices). We then discussed these codes and terms with engineers who would confirm or infirm the relevance. New codes and terms were identified based upon these discussions and then discussed again. This process allows us to frame the technology and build up a query that extracts patents beyond the scope of keywords which would result in false positives and unidentified patents and publications.

Two queries were constructed, one for publications and one for patents. The results in figure 1 show the evolution of the number of patents and publications identified. A total number of 9000 patents and 12000 publications were identified worldwide between 1980 and 2014. The analysis was initiated in 1980 since it is the point at which SCM caught the attention of aircraft manufacturers. We checked patents and publication before 1980 and confirmed the latter. 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007

Data treatment

The collaboration network. We used the previously described query to extract patents and publications. The Orbit database uses algorithms to extract and translate data from patents, this results in terms that get lost in translation and textual mistakes. In addition to this, names on patents often do not match names on publication. For example, we observe the name "Airbus SA" on a patent, "Airbus S.A". on a publication, even mistakes like "Aerhjbus" appear in the data. We used Intellixir to clean any mismatches or textual mistakes. Intellixir is a browser based tool for patent and publication analysis. It has a feature that automatically cleans the data. A final treatment was conducted by hand to clean any remaining problems.

Once the data was cleaned all firm names were extracted from the patents and publications to generate a network. A link was created between two firms that co-wrote or co-deposited a patent. A link resulting from a publication was hence treated as a link resulting from a patent. A date was added to each link, which was the priority date for patents and the publication date for publications.

From this data we create two series of temporal networks, a first using a 5-year window [START_REF] Powell | Network dynamics and field evolution: The growth of interorganizational collaboration in the life sciences1[END_REF], [START_REF] Buchmann | The evolution of innovation networks: The case of a german automotive network[END_REF], a second using a cumulative method. Each method adds specific information about the evolution of the network. The 5-year window allows us to put an end date on a collaboration. This method allows us to track the number of active firms in the network and how they are connected, allowing us to track more precisely when the network starts to decline. It paints a precise picture of the behavior of firms and the interest they have for the technology. For example, if the technology has become obsolete this will be visible by a decline in the number of firms present in the network and an absence of new firms. From a purely practical point of view it allows us to delete bankrupt firms, or firms which changed their name from our dataset. The cumulative network keeps the history of the network, this allows us to observe if old firms work more intensively together or if the evolution is defined by new entrants. It allows us to see where a particular technology was fostered and how it spreads through the network (by bridging structural holes for example). For the purpose of knowledge collaborative behavior we will use the 5-year window network. For the purpose of knowledge flows we will focus on the cumulative network, even if the collaboration is over firms still have a social link with each other and collaborations hence last longer than the time they work together [START_REF] Dahl | Knowledge flows through informal contacts in industrial clusters: myth or reality?[END_REF]. Since this network shows the origins of technologies. Even if a collaboration does not exist anymore, and the firms has exited the network, the knowledge still exists and is still exploitable. For the purpose of identifying knowledge (creation and flow) we use IPC codes present on patents. For the specific analysis of the flow of knowledge we will use patent citations to identify which firm is influenced by which firm. This will allow us to track when a firm starts working on a specific technology and who the firm learned from In addition, since we have dynamic data, it will allow us to see if some firms are leaders and other followers.

The knowledge network. In order to identify the life-cycle of the technology we use IPC codes present on the patents. Whenever two or more IPC codes are present on the same patent a link is created between them. The International Patent Classification (IPC) classifies patented technologies according to different technological fields. The system itself is crescendo is nature. The more digits, the more precise the codes become from a technological point of view. A 4-digit level defines a broad definition of technologies, for instance B64C defines "Aeroplanes; helicopters". The 7-digit level goes one step further into detail by specifying for B64C1, " Fuselages; Constructional features common to fuselages, wings, stabilizing surfaces, or the like". Going a step further, at the 9-digit level we will find "Floors" for code B65C1/18. We use 3 different digit levels for our analysis, the 4, 7 and 9 digit levels.

In order to obtain a 4-digit network, all IPC codes are reduced to their 4-digit format. For example B64C001/23 is a 9-digit code, in order to obtain the corresponding 4-digit code, one simply reduced the code to 4-digits: B64C. The same goes for the 7-digit code which would be B64C001 in this example. Just as for the collaboration network we use a 5-year window and a cumulative method.

The technology life-cycle

In the early phases of the technology life-cycle patents are deposited using codes that refer to the core elements of the technology. This should result, as the number of patents increases, in the appearance of a cluster interconnecting all the core-technologies. This core is reinforced as the number of patents increases since the same technologies are used. From a structural point of view:

Hypothesis 1:. We should hence observe an increase in the clustering coefficient of the network during this research phase.

Once the research phase has reached its peak the development stage starts. This stage is defined by the incorporation of the technology for new applications. These applications are less densely connected than the core technologies since they have specific applications. In the knowledge network this means that new nodes are added to the previously build cluster. From a structural point of view Hypothesis 2:. this results in a decrease of the clustering coefficient since the nodes are added to the periphery of the network and will not interconnect with other IPC codes relative to other applications. The average distance (as well as the diameter of the network) should increase due to these new nodes.

In theory then, hypothesis 3:. the network should have the structure of a core-periphery network.

I will start by checking for the presence of a core-periphery structure before proceeding to the analysis of the evolution of the clustering coefficient and the average distance.

Core-periphery check

Checking for a scale-free structure is done by fitting a function to the cumulative degree distribution of a network. A CP network has a small number of highly connected nodes (the core) and a large number of (relatively) less connected nodes (the periphery). This can be observed directly when we represent the degree distribution of the network. Which is simply a plot with the number of nodes with degree k on the y-axis and the degree on the x-axis. This distribution is then transforms into a cumulative degree distribution as can be seen in figure 5. A function is fitted to the CFD in order to check for a core-periphery structure. The most sought-after (and found) structure is represented by a power law which has the form:

p(k) = c • k -α .
In a log-log plot this non-linear function becomes linear. We also check for another form which is the log-normal function. The functions are fitted using a maximum likelihood estimation. As previously a 5-year window and a cumulative method are used. Figure 7 shows the results for the 4-digit network. Even though the p.value for the window configuration shows that the power law fit is statistically significant, this is only the case for part of the distribution. Indeed we can see that the straight line starts towards the end of the distribution. We hence cannot confirm that the distribution follows a power law. However the loglinear distribution is both signification and represents almost the complete distribution. This confirms the presence of a core-periphery structure at the 4-digit level. The log-linear form shows a small decrease in the fraction of nodes when the density is decreased by a factor of 1 at the beginning of the distribution. This remains the case until a density of 20 showing that the network is quite densely connected. Almost all nodes have at least 3 links.

The core is much more densely connected than the scale-free network identified in chapter 4. The core is hence surrounded by a periphery that is itself (relatively) densely connected as shown in figure 7. We hence conclude that the 4-digit network has a core-periphery structure. Both in the 5-year window case and the cumulative method. The same conclusion is valid for the 7-digit network even though the window shows that the core-periphery structure appears towards the end of the period. The 9-digit network structure also has a core-periphery structure when we consider the cumulative method. The window method does not show proof of a core-periphery network. We deduce from these results that hypothesis 3 is verified. The P.values for all configurations are provided in the annex.

Clustering and average distance

Now that we have established that the structure of the network is indeed a core-periphery structure. We now turn to the analysis of the structure of the network.

Figure 8 shows that the clustering coefficient in the 4-digit configuration is high from the start due to a relatively small number of nodes. In figure 8 we see that the number of technological combinations is exhausted towards the end of the period (i.e the number of links stabilizes in the +1 method).

In addition this core is very densely connected (density =0.95) hence 95% of all possible links are present. The clustering coefficient is decreasing over the whole period in the additional configuration. Figure 2 shows the densely connected core of the IPC network at the 4-digit level. The combination of these technologies make perfect sense since the technology under study is a combination of aircraft technologies and the development of composite materials. Around this core we find C-section codes relative to chemistry, G-section codes relative to physics and H, mechanical engineering. The construction of the core is clear.

In the 5 year window case we also see this decline even though there is an increase in the later stages. Since the last 2 years are defined by a decrease in the number of deposits (due to patent deposit times) in the later period clustering goes up. Even the newer patents still have the core IPC codes present, the lower number of patents hence result in the same core but lower number of peripheral technologies which results in an increase in clustering. This can be seen in figures 3. The number of new nodes as well as the number of links is sharply reduced in the last periods.

The 7 and 9-digit network reveal more interesting information. We can observe a clear increase in the clustering coefficient from the beginning of the period to 1993 for the 7-digit network and 1995 for the 9-digit network. These dates coincide with the point at which the collaboration network enters the small world zone. From that point on the clustering coefficient declines until it increases again for the same reason as we previously discussed for the 4-digit network.

The peak is observable both in the cumulative network and the 5-year window even though the window networks are more hectic. These points seem to confirm our hypothesis that there is a link between the evolution of the IPC network and the collaboration network. In order to further investigate that the evolution of both networks are rules by an evolution from research stage to development stage, [START_REF] March | Exploration and exploitation in organizational learning[END_REF]. If this is indeed the case we should observe some variation of a core-periphery structure.

Network structure and the technology life-cycle

A network can evolve in two dimensions, the number of links and the number of nodes. Figure 2 shows the evolution of different network indicators from the cumulative network and from the 5-year window network. The growth rate of the number of nodes shows that new firms appeared in the network each year. This growth rate is however not homogenous. Two phases can be distinguished in the evolution of the network. A first phase spanning from 1980 to 1995, highlights a high volatility in the number of firms present in the network and in the other network indicators. This phase is the research phase in the life-cycle of the technology, during which firms identify relevant partners to collaborate with. The number of collaborations decreases over time. Collaborations rely on trust and mutual understanding [START_REF] Floréan | The emergent prerequisites of managerial learning in small firm networks[END_REF] which take time to emerge between partners [START_REF] Prencipe | Inter-project learning: processes and outcomes of knowledge codification in project-based firms[END_REF]. When no previous interaction has allowed for the emergence of trust, firm use referrals to identify reliable collaborators [START_REF] Hanakia | The dynamics of r and d network in the it industry[END_REF]. This results in the creation of strong ties between firms which cooperate multiple times [START_REF] Granovetter | The strength of weak ties: A network theory revisited[END_REF] and reduces, over time, the number of cooperations between firms since they will have a tendency to collaborate with the same firms [START_REF] Hanaki | The dynamics of r&d network in the it industry[END_REF]. The number of links in the 5 year window network shows indeed a large number of collaborations in this early stage in the evolution of the network. Remarkably the clustering coefficient stays high and stable over this period of time. Implying that the number of links increases faster than the number of nodes and that firms work together in close clusters. This can be easily understood since an airplane is made up from a different parts that require different technologies [START_REF] Prencipe | Technological competencies and product's evolutionary dynamics a case study from the aero-engine industry[END_REF], each technology is fostered in its own cluster.

If we look at the 5-year window we observe that the number of firms in the network starts a significant decline in 1995, accompanied by a significant decline in the number of new collaborations in the network. This marks the beginning of the development stage.

The technologies developed by different firms are now diffusing though the network to be integrated in intermediary and final products. The intermediary product are assembled by firms with a strategic position inside the production chain called pivot firmTalbot (2013). The downstream firms which researched the technology now exit the network while the pivot firms develop the technology further. This results in the a stabilization of the network indicators in the cumulative network implying that firms are working with firms with which they have established strong links in the past.

The network ends with a low centrality and high clustering coefficient, clearly showing that the network is build from interconnected clusters.

Typology of the network structure

The interest in the global structure of a network is motivated by questions related to the efficiency of a network in terms of knowledge diffusion. Research on innovation network has resulted in the identification of several typologies, mainly small worlds [START_REF] Watts | Networks, dynamics, and the small-world phenomenon 565 1[END_REF], [START_REF] Gulati | The rise and fall of small worlds: Exploring the dynamics of social structure[END_REF][START_REF] Tomasello | The rise and fall of r&d networks[END_REF], [START_REF] Baum | Where do small worlds come from?[END_REF]), scale free networks [START_REF] Barabási | Emergence of scaling in random networks[END_REF] and nested split graphs [START_REF] König | Recombinant knowledge and the evolution of innovation networks[END_REF]. Small worlds are of particular interest since theoretical models show that this structure is particularly efficient when it comes to the diffusion of information though a network. A small world network is characterized by a low average distance and a high clustering. The clustering assures that firms have enough access to diverse and new knowledge to innovate. The low average distance ensure that the knowledge is quickly transferred to the rest of the network. Following [START_REF] Watts | Collective dynamics of 'small-world' networks[END_REF], [START_REF] Baum | Where do small worlds come from?[END_REF] and [START_REF] Gulati | The rise and fall of small worlds: Exploring the dynamics of social structure[END_REF] we check the structure of our network for a small world structure. [START_REF] Gulati | The rise and fall of small worlds: Exploring the dynamics of social structure[END_REF] method compares the structure of an empirical network to that of a random network. We compute the clustering (C) and average distance (L) of our network, we then approximate the clustering (Cr) and average distance (Lr) of a random graph with the same number of links and edges. The clustering and average distance of both graphs are then compared. The idea is that we want an empirical clustering coefficient higher than the clustering in the random graph. However we want an average distance approximatively identical. For a graph to be a small world we hence want:

C Cr >> 1 and L Lr ≈ 1 (1)
Figure 10 shows the results for our network for each year. We observe that the network converges towards a small world structure which it reaches around 1997, at the beginning of the development phase where knowledge flow intensifies. The network keeps it small world structure for about 10 years. During these years knowledge diffusion takes place. The technologies developed by the downstream firms are diffused to the pivot firms which include them for further development. The observed decline is the result of the technology reaching maturity, firm may from that point on have turned their attention to a new generation of composite materials which might be outside of the scope of our query.

Our results are hence different from those found by Gulati et al. [START_REF] Gulati | The rise and fall of small worlds: Exploring the dynamics of social structure[END_REF] who observed a network that kept the small world property at each point in time. Our result is due the fact that we analyze a network for one specific technology. At the genesis of the network small clusters forms in which different parts of the technologies are developed. These clusters interconnect over time reducing the average distance between firms, resulting in the observed convergence towards the small world structure. One could argue that the convergence is the result of the increase in the number of firms in the network, resulting in a higher average distance. Figure 11 shows indeed that each year new firms are added to the network, while the clustering coefficient shows a steady increase.

The indicators used here are adjusted for network size in order to compensate for network size. Additionally, new firms enter the network even when the network diverges from the small world property. The convergence is hence the result of the propensity of firms to interconnect rather than the addition of new firms.

Micro-meso analysis

We will now turn our attention to a specific part of the network. In the aerospace sector, two major competing actors are of interest: Airbus and Boeing. As we discussed before, these firms need to be able to learn all technologies related to SCM in order to include them into the production of the final product. Based on what we previously discussed we can imagine two diverging strategies in terms of knowledge absorption for these firms. Either they decide to cooperate with firms from other sectors that have experience in the field or they cooperate based on social capital, i.e they pick firms based on their whether or not they have previously cooperated. In this section we will show how these two strategies lead to different results in terms of innovate performance.

Network position

Boeing was present in the network since the 1980's while Airbus entered the market a couple of years later (this is why all graphs start in 1985). A first clue giving away the diverging strategies can be observed in Figure 5. When Boeing entered the market and until 1998, it has a clustering coefficient of 0. The clustering coefficient measures the number of collaborators of Boeing that work together. A clustering of 0 hence means that none of the collaborators of Boeing have worked together. At the complete opposite we find Airbus which entered with a clustering of 1. Where Boeing took the risk of collaborating with firms specialized in composite materials1 , Airbus chose to cooperate with a cluster of its historical partners. The strong links the firm has created in the aerospace sector have highly influenced its absorption strategy.

These observations are reinforced by the study of the citation network of both firms. Figure 7 shows the firms cited by Boeing and Airbus and the firms citing Boeing and Airbus. We observe here that the European company is largely influenced by the firms it has previously collaborated with while

Boeing has a larger variety in its inspirations. At the center of this graph we find firms that inspired both firms. Above Airbus we find firms that inspired only Airbus, underneath Boeing we find firms that only inspired Boeing. The larger the arrow the higher the number of citations between two firms. We hence observe that Boeing has a large variety of inspirations with a low frequency while Airbus tends to cite more frequently the same firms. These firms are often previous collaborators. Theory on preferential attachment [START_REF] Barabási | Emergence of scaling in random networks[END_REF] suggest that firms might motivate their decision to cooperate with a specific firms if they have previously worked together. Firms who know each other have the advantage of cooperating more efficiently because they know how the other operates.

Boeing ignored these benefits and chose to identify specialists, with the risk it would lose in efficiency during the cooperation because of a lack of social capital.

Towards the second phase of the evolution of the network we observe that both firms have very similar positions in terms of centrality. The betweenness centrality measures the relative position of a firm on all the paths connecting all other firms. This means that a high betweenness centrality is synonymous with a position through which many information flows may be captured. Fig-

ure 5 shows that both firms converge to a similar level of centrality as can be observed for the other indicators. This implies that both firms had an identical position for the absorbing of new technologies which is expected considering their position in their respective value chain.

The number of cooperations marks however a point of divergence. Airbus has accelerated the number of firms with which it collaborates from 1997 onwards. Boeing on the other hand has been much more conservative, ending with less than half the collaborations of Airbus. We observe two different strategies resulting in nearly identical network positions. The resulting innovative performance is however not the same as we will show in the next subsection.

The race for innovation

By extracting IPC codes from Boeing and Airbus' patents we are able to track when firms deposit patents in specific IPCs that are at the core of SCMs technology. Two of these core IPCs are: B64C1 ("Fuselages, Wings, stabilizing surfaces, or the like"2 ) and B29C70 ("Shaping composites"). From the patents we create a network connecting IPC codes with Airbus and Boeing. If there is a link between Boeing and B64C1 that means that Boeing has deposited a patent using this code. The results are shown in figure 6, the thicker the link between the IPC and the firm the more deposits using the IPC were identified.

In the center of the graph we find IPC that were used by both firms, the most relevant IPC codes are found here. From a dynamic perspective we can observe when a firms first deposits a patent in one of those relevant IPC codes. We hence created a dynamic network that allowed us to observe when a firm deposits its fist patent in a certain technology. This representations can show how far a head (or far behind) a firm is compared to another. In our case we observed that Boeing deposited in the 2 IPC codes 10 years before Boeing did, showing clearly that Airbus has a technological lag compared to Boeing. This lag can be explained by the previously identified strategy of Airbus, who decided to research the technology with historical partners. This decision was made even though the identified partners might not have been the most specialized firms in the sector.

Boeing's strategy however paid off, it positioned itself as gatekeeper between two sectors and it took the risk of collaborating with firms it has no connection with. Their knowledge absorption strategy was hence more efficient.

Conclusion and Discussion

This document has shown that the evolution of the collaboration network for a specific technology is correlated with the life-cycle of the technology. In the research stage of the technology, small clusters form in which different aspects of the technology are researched. Over time these clusters interconnect resulting in a convergence towards a small world structure at which point the development stage starts and the technologies start to diffuse. On a micro level we showed that a firm using social capital to find its collaborators fell 10 years behind a competitor who chose to cooperate with firms that had experience with the technology from another sector. The cumulative method is on the left, the window method is on the right. A p.value higher or equal to 0.1 shows a good fit.

q q q q q q q q q q q q q q q q q q q q q qq qq q q q q q q q q q qq q q q q q q q q q q q q q q q 4-digit p.value(pl)= 0 p.value(ln)= 0.9 q q q q q q q q q q q q q q q q q q q q q qqq q q q q qq q q q q q q q q q q q q q q q q q q q q q 1 2 5 10 20 50 100 p.value(pl)= 0.4 p.value(ln)= 1 q q q q q q q q q q q q q q q q qq qq qq qq q qq qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 4-digit Power Law fit-1996 Frequency Density log linear power p.value(pl)= 0 p.value(ln)= 0.2 q q q q q q q q q q q q q q q q q q qq q q q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 1 2 5 p.value(pl)= 0.8 p.value(ln)= 0.5 q q q q q q q q q q q q q q qq qq qq qqq qqq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q 4-digit Frequency Density log linear power p.value(pl)= 0 p.value(ln)= 0.4 q q q q q q q q q q q q q q q q qq qq qq q q q qqq qq q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q q q 1 2 5 The cumulative method is on the left, the window method is on the right. A p.value higher or equal to 0.1 shows a good fit.

q q q q q q q q q q q q q q q q qq qq q qq q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq qq q q q q q qq q q q q q q qq q q q q q q q q q q q q q q q q q 7-digit Frequency Density log linear power p.value(pl)= 0.7 p.value(ln)= 0.1 q q q q q q q q q q q q q q q q qq q q q q q q qq qq q q q q q q q q q qq q q q q q q q q q q qq qq qq q q q q q q q q qq q q q q qq q q q q q q q q q q q q q q q q q 1 2 5 p.value(pl)= 0.5 p.value(ln)= 0 q q q q q q q q q q q q q q qq qq qq q qq qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q qq q q q q q q q q q q q q q q q 7-digit Power Law fit-1996 Frequency Density log linear power p.value(pl)= 0 p.value(ln)= 0.1 q q q q q q q q q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q qq q q q q qq q qq q q q q q q q q q q q q q q q q 1 2 5 p.value(pl)= 0.7 p.value(ln)= 0 q q q q q q q q q q q q qq qq qq qq qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q qq q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q 7-digit Power Law fit-2014 5e-04 Frequency Density log linear power p.value(pl)= 0 p.value(ln)= 0.4 q q q q q q q q q q q q q q q qq q q q qq qq qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q 1 2 5 Figure 6: Power law fit to the IPC network at the 9 digit level. The cumulative method is on the left, the window method is on the right. A p.value higher or equal to 0.1 shows a good fit. q q q q q q q q q q q q q q q qq q q q qq q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 1 2 5 p.value(pl)= 0.7 p.value(ln)= 0.6 q q q q q q q q q q q q q q q qq qq q q qq q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 1 2 5 p.value(pl)= 0 p.value(ln)= 0 q q q q q q q q q q qq qq qq qq qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q qqq q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 1 5 10 50 100 500 1000 p.value(pl)= 0.4 p.value(ln)= 0.7 q q q q q q q q q q q q q qq q q q qq q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 1 2 5 p.value(pl)= 0.3 p.value(ln)= 0 q q q q q q q q q qqq qqqq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q qq q q q q q q q qq q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q 1 10 100 1000 10000 p.value(pl)= 0.1 p.value(ln)= 0.1 q q q q q q q q q q q q qq q q q qq q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q 1 5 10 50 100 500 1000 1980 1984 1988 1992 1996 2000 2004 2008 2012

Figure 1 :

 1 Figure 1: Distribution of the number of patents and publications over time.

  1. B29C: SHAPING OR JOINING OF PLASTICS; SHAPING OF SUB-STANCES IN A PLASTIC STATE, IN GENERAL; AFTER-TREATMENT OF THE SHAPED PRODUCTS 2. B32B: LAYERED PRODUCTS, i.e. PRODUCTS BUILT-UP OF STRATA OF FLAT OR NON-FLAT, e.g. CELLULAR OR HONEYCOMB, FORM 3. B64C: AEROPLANES; HELICOPTERS 4. B64D: EQUIPMENT FOR FITTING IN OR TO AIRCRAFT; FLY-ING SUITS; PARACHUTES; ARRANGEMENTS OR MOUNTING OF POWER PLANTS OR PROPULSION TRANSMISSIONS IN AIR-CRAFT

Figure 2 :Figure 3 :Figure 4 :

 234 Figure 2: The technology core, representing a 95% interconnection rate

22Figure 5 :

 5 Figure5: Power law fit to the IPC network at the 7 digit level. The cumulative method is on the left, the window method is on the right. A p.value higher or equal to 0.1 shows a good fit.

  (pl)= 0.1 p.value(ln)= 0.5

  (pl)= 0 p.value(ln)= 0.1

Figure 7 :

 7 Figure 7: The full 4-digit IPC network for structural composite materials in aeronautics

Figure 11 :Figure 12 :Figure 14 :

 111214 Figure 11: New firms in the network each year

Power Law fit-1985

	0.500 1.000
	0.050 0.100
	0.005 0.010
	0.001
	1	2	5	10	20	50	100	200

We refer here to firms that have worked with composite materials in other sectors

Titles given by WIPO in the international patent classification

$ A first version of this paper was presented at the 4th Global Techmining Conference $$ This project was made possible by support from the VIA-INNO project of the Groupe de Recherche en Economie Thorique et Applique (GREThA). The project also received financial support from the "Initiative d'Excellence" of the university of Bordeaux