MD Guillaume Pineton De Chambrun
email: g-pinetondechambrun@chu-montpellier.fr

MD, PhD Aurélien Amiot

MD, PhD Guillaume Bouguen

MD Stéphanie Viennot

MD Romain Altwegg

MD, PhD Edouard Louis

MD Michael Collins

MD, PhD Mathurin Fumery

MD Florian Poullenot

MD Laura Armengol

MD, PhD Anthony Buisson

MD Vered Abitbol

MD, PhD David Laharie

MD, PhD Philippe Seksik

MD, PhD Stéphane Nancey

MD, PhD Pierre Blanc

MD, PhD Yoram Bouhnik

MD, PhD Benjamin Pariente

MD, PhD Laurent Peyrin- Biroulet

Celgene Abbvie

Ferring

Janssen

Laurent Peyrin-Biroulet

Efficacy of Tumor Necrosis Factor Antagonist Treatment in Patients With Refractory Ulcerative Proctitis

Keywords: , 5-aminosalycilic acids ACT, active ulcerative colitis trials ADA, adalimumab AZA, azathioprine PGA, physician global assessment SD, standard deviation TNFα, tumor necrosis factor alpha UC, ulcerative colitis inflammatory bowel disease, second-line treatment, immune suppression, trial, proctitis

INTRODUCTION

Ulcerative colitis (UC) is a chronic inflammatory bowel disease (IBD) characterized by intestinal inflammation limited to the colonic mucosa. [START_REF] Ordas | Ulcerative colitis[END_REF] In population-based studies, 25-55% of patients had ulcerative proctitis (UP) at diagnosis. [START_REF] Meucci | The natural history of ulcerative proctitis: a multicenter, retrospective study. Gruppo di Studio per le Malattie Infiammatorie Intestinali (GSMII)[END_REF] UP defined as a disease limited to the rectum is classified as E1 according to the Montreal classification. [START_REF] Satsangi | The Montreal classification of inflammatory bowel disease: controversies, consensus, and implications[END_REF] Although it is generally assumed that UP represents the benign end of the spectrum of UC, it is responsible for many distressing symptoms including increased stool frequency, tenesmus, urgency and bleeding, and clearly alters patients' quality of life. [START_REF] Meucci | The natural history of ulcerative proctitis: a multicenter, retrospective study. Gruppo di Studio per le Malattie Infiammatorie Intestinali (GSMII)[END_REF] Despite the significant benefits of aminosalicylates and corticosteroids, some patients with UP fail to improve and will require additional medical therapy.

Medical management of patients with UP refractory to standard therapies is challenging as there is very little evidence-based data regarding drug efficacy in this clinical situation. [START_REF] Gecse | Ulcerative proctitis: an update on the pharmacotherapy and management[END_REF] Several medications have been tested to treat refractory UP. [START_REF] De Chambrun | The treatment of refractory ulcerative colitis[END_REF] In a randomized controlled trial, azathioprine (AZA) was more effective than oral 5-aminosaliylates (5-ASA) to achieve steroid-free clinical and endoscopic remission. [START_REF] Ardizzone | Randomised controlled trial of azathioprine and 5aminosalicylic acid for treatment of steroid dependent ulcerative colitis[END_REF] Cyclosporin enemas and oral methotrexate have not proven to be significantly effective in inducing and maintaining long-term clinical response and remission. [START_REF] Ardizzone | Randomised controlled trial of azathioprine and 5aminosalicylic acid for treatment of steroid dependent ulcerative colitis[END_REF][START_REF] Oren | Methotrexate in chronic active ulcerative colitis: a doubleblind, randomized, Israeli multicenter trial[END_REF][START_REF] Sandborn | A placebo-controlled trial of cyclosporine enemas for mildly to moderately active left-sided ulcerative colitis[END_REF] A recent randomized, placebo-controlled, trial demonstrated that tacrolimus rectal ointment was more effective than placebo for the induction of clinical remission and mucosal healing (MH) in patients with UP. [START_REF] Lawrance | Efficacy of Rectal Tacrolimus for Induction Therapy in Patients With Resistant Ulcerative Proctitis[END_REF] Appendectomy has also been proposed as a treatment for patients with refractory UP. [START_REF] Bageacu | Appendicectomy as a potential therapy for refractory ulcerative proctitis[END_REF] Overall, these results remain difficult to interpret because of small sample size and the lack of well-designed published studies supporting their efficacy for refractory UP.

M A N U S C R I P T A C C E P T E D

Furthermore, patients with UC limited to the rectum are systematically excluded from randomized clinical trials on biologics. Topical administration of infliximab was found to be effective in one patient with chronic refractory UP. [START_REF] Molnar | Topically administered infliximab can work in ulcerative proctitis despite the ineffectiveness of intravenous induction therapy[END_REF] Only one French small retrospective observational study has investigated the efficacy of infliximab in patients with refractory UP. [START_REF] Bouguen | Infliximab for refractory ulcerative proctitis[END_REF] Regarding short-term outcome, 69% (9/13) patients presented a complete response to infliximab. To date, there is no data regarding efficacy of adalimumab, golimumab or other biologics in patients with refractory UP.

The aim of this study was therefore to evaluate the effectiveness of anti-TNF therapy in a large nationwide retrospective cohort study from the GETAID.

Data collection

The date of inclusion corresponded to the first administration of anti-TNF therapy. Patient files were retrospectively reviewed and demographic, biological, and endoscopic data were obtained from the medical records. The following characteristics were anonymously recorded for each included patient: gender, age at inclusion, date of diagnosis, duration of disease, smoking status, presence of extraintestinal manifestations, prior exposure to UC treatment including local and systemic steroids, local and oral 5-ASA, conventional immunosuppressants (thiopurines, methotrexate and cyclosporin), UP clinical activity before the start of anti-TNF based on Mayo clinical subscore (from 0 to 9) and endoscopic findings (Mayo endoscopic subscore and UCEIS) when available, main indication for introducing anti-TNF, type of anti-TNF (infliximab, adalimumab, golimumab), anti-TNF induction and

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 11 11
maintenance doses, type of response (no response, partial response and complete response), concomitant treatment with thiopurines, other ongoing drugs at commencement of anti-TNF, duration of anti-TNF treatment, optimization of the treatment, C-reactive protein levels (CRP) and endoscopic findings at inclusion and during follow-up. All data were encoded in an Excel® electronic database which was anonymized with attribution of a nonsignificant number for each patient.

Outcomes

The primary objective was to assess the primary clinical response of UP to anti-TNF treatment. Evaluation of the global clinical response to anti-TNF was based on the judgement of the referring physician and was graded as follows: no response, clinical response, and clinical remission. Clinical response was defined as significant improvement in UC-related symptoms as judged by the treating physician. Remission was defined as the complete disappearance of UC-related symptoms as judged by the treating physician. probability of anti-TNF retention among primary responders, and (7) the safety of anti-TNF treatment. The rate of anti-TNF optimization was also recorded, but was not considered to be a loss of clinical benefit. To determine safety, all adverse events, defined as any significant event that occurred from the date of inclusion to the last follow-up, were recorded in patients receiving at least one injection of any anti-TNF agents. Severe adverse events were defined as any adverse event that resulted in hospitalization or extension of the hospital stay, was fatal or life threatening, or led to a significant disability.

Statistical analysis

Descriptive statistics were used to analyze baseline characteristics. Medians with interquartile ranges (IQR) or means with standard deviations (SD) were calculated for continuous data, and percentages were computed for discrete data. Univariate and multivariate logistic regression were performed to identify predictive factors associated to clinical remission with anti-TNF treatment, expressed as odds ratios (OR) with 95% confidence intervals (CI). Variables with a p value below 0.1 were used for multivariate analysis. For multivariate analysis adjusted for sex and age at diagnosis, variables included were extraintestinal manifestations, the type of anti-TNF (subcutaneous vs intravenous), concomitant thiopurines, ongoing treatment with topical 5-ASA and topical steroids.

Proportion of patients with sustained clinical remission and anti-TNF failure (defined as the occurrence of anti-TNF withdrawal for loss of response or intolerance and/or colectomy) over time were described using Kaplan-Meier survival analysis. A p value of < 0.05 was considered to be significant.

M A N U S C R I P T A C C E P T E D

RESULTS

Patient characteristics

One-hundred and four patients (51 female and 53 male) with refractory UP treated with anti-TNFα from 16 GETAID centers were included in the study, with a median follow-up of 24 (IQR: 12.9-51.2) months. The baseline demographic and clinical characteristics of the patients are presented in table 1. Mean age at diagnosis was 34±11.9 years. Anti-TNF therapy was started after a median follow-up of 46 (IQR:19.8-110.5) months from the diagnosis of UP.

Fifty percent (52/104) of the patients were treated with infliximab, 39% (41/104) with adalimumab and 11% (11/104) with golimumab. Fifty-three (55/104) percent of patients were concomitantly treated with topical or oral 5-ASA or steroids at the start of anti-TNF therapy. Anti-TNF was associated with a thiopurine in 38 % (40/104) of the patients. Patients were initially treated with the recommended dose of anti-TNF for induction. Following initiation of anti-TNF, 47% (49/104) of patients had an intensification of the anti-TNF agent after a median duration of follow-up of 6 (IQR: 3-13.6) months; 17 patients had a dose increase, 24 a shortening of the injection interval, and 8 both dose increase and interval shortening.

Short-term outcomes

Following a median duration of follow-up of 3 (IQR:1.6-7.0) months between anti-TNF initiation and clinical evaluation, 77% (80/104) of patients had a primary clinical response to the anti-TNF agent and 50% (52/104) achieved clinical remission (Figure 1). Corticosteroidfree remission was achieved in 45% (n=47/104) of the patients. The mean Mayo clinical subscore before the start of anti-TNFα was of 5.9 ± 1.9 points (n=99). At 3 months after anti-

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 14 14
TNF start 42% (33/78) of the patients had a MAYO clinical subscore < 2. In patients with clinical scores available at baseline and 3 months after anti-TNFα start (n = 76), we observed a significant decrease in the Mayo clinical subscore (5.9 ± 1.9 vs. 2.5 ± 2.6, p < 0.001) between baseline and week 12 evaluation and 58% of the patients presented at least a clinical response defined by a decreased in the Mayo clinical subscore of 3 or more points with bleeding score of 0 or 1. Among patients with an available CRP at baseline and 3 months after anti-TNF treatment initiation (n=49), there was a significant decrease in the mean CRP level (11.6±21.4 at inclusion vs. 4.7±4.6 at the end of the anti-TNF induction period, p=0.028) (Supplementary Table 1).

Factors associated with short-term outcomes

In univariate analysis, extraintestinal manifestations, ongoing topical steroids at baseline and ongoing topical 5-ASA at baseline were significantly associated with the absence of primary clinical remission (Table 2). Concomitant treatment with thiopurines at baseline was significantly associated with primary clinical remission (Table 2). In a multivariate analysis adjusted for sex and age at diagnosis and including as variables extraintestinal manifestations, the type of anti-TNF (subcutaneous vs intravenous), concomitant thiopurines, ongoing treatment with topical 5-ASA and topical steroids, extraintestinal manifestations (OR=0.24; 95%CI:0.08-0.7; p=0.009), ongoing topical steroids at baseline (OR=0.14; 95%CI:0.03-0.73; p=0.019) and ongoing topical 5-ASA at baseline (OR=0.21; 95%CI:0.07-0.62; p=0.007) were independently associated with the absence of primary clinical remission (Table 2).

Endoscopic findings

M A N U S C R I P T A C C E P T E D

A baseline colonoscopy was available in 82% (85/104) patients with a median delay before anti-TNF start of 0.9 (IQR: 0.1-2.16) months. A follow-up colonoscopy was available in 61% (63/104) of patients after a median follow-up of 11.7 (IQR: 5.5-17.4) months. Among these patients, 60% (38/63) had mucosal healing (Mayo endoscopic subscore of 0 or 1) (Figure 1). Among these patients, there was a significant decrease in the Mayo endoscopic subscore (2.4±0.6 vs. 1.3±1.1, n=46, p<0.001) and in the UCEIS index (4.9±1.4 vs. 2.3±2.3, n=42, p<0.001), between baseline and follow-up colonoscopies (Supplementary Table 1).

Long-term outcomes

Among the overall population (n=104), after a median follow-up of 23.6 months (IQR:12.9-57.9), 64% (67/104) were in clinical remission at last follow up. Among these 104 patients, the cumulative probability of sustained clinical remission was 87.6%±3.4% at one year, 74.7%±4.8% at two years, and 56.4%±6.2% at 5 years (Figure 2a). When considering only patients with an initial response to anti-TNF therapy (n=80), the cumulative probability of sustained clinical remission, irrespective of the treatment given, was 90.5%±3.4% at one year, 77.9%±5.3% at two years, and 55.8%±7.4% at five years (Figure 2b). During follow-up, 9% (9/104) of patients were hospitalized for a flare of their UP and 4% (4/104) underwent a coloproctectomy with ileal pouch-anal anastomosis.

Among the 24 patients with primary non response to anti-TNFα, 75% (18/24) of the patients were switch to another ant-TNFα agent and 46% (11/24) were eventually treated with vedolizumab with achievement of clinical remission in 22% (4/18) and 82% (9/11) of the cases, respectively. Among patients with an initial response to anti-TNFα, 19% (15/80) had a switch to another anti-TNFα and 11% (9/80) were eventually treated with vedolizumab

M A N U S C R I P T A C C E P T E D

during follow-up with achievement of clinical remission in 53% (8/15) and 56% (5/9) of the cases, respectively.

At the end of the follow-up period, 61% (63/104) of the patients were still on anti-TNF at last follow up. Among the 80 patients with a primary clinical response to anti-TNF, 34% (27/80) stopped the first anti-TNF agent for secondary loss of response, intolerance or surgery. In these patients (n=80), the cumulative probability of first anti-TNF failure-free survival (no withdrawal for secondary loss of response, intolerance and/or surgery) was 94.6%±2.6% at 6 months, 80.6%±4.9% at one year, and 69.6%±5.9% at two years. Optimization of anti-TNF therapy during follow-up was performed in 43.7% of the patients (35/80). Failure of first anti-TNF therapy defined as optimization, intolerance, loss of response or surgery was observed in 57.5% (46/80) of the patients during follow-up.

Safety of anti-TNF therapy

There were missing data for 8 patients. Overall, 22% (21/96) of the patients presented side effects after starting anti-TNF therapy (Table 3). Three patients had an infusion reaction leading to anti-TNF withdrawal, five patients had skin manifestations, four patients had an infection, one patient presented alopecia, and 9 patients had other side effects such as arthralgia, headache, abnormal liver enzymes or weight gain.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

17

DISCUSSION

The management of refractory UP remains challenging in the era of biologics. These patients are excluded from clinical trials on biologics and available studies on the effectiveness of anti-TNF therapy in a real-life setting are of small sample size. [START_REF] Bouguen | Infliximab for refractory ulcerative proctitis[END_REF] As UP represents about one third of all cases of UC, 5-ASA treatment is often insufficient in moderate to severe UC and azathioprine has modest efficacy in this indication. [START_REF] Mallet | Azathioprine for refractory ulcerative proctitis: A retrospective multicenter study[END_REF] Further evidence regarding the potential of anti-TNF therapy in treating these patients is eagerly awaited.

We first demonstrated that anti-TNF therapy, either intravenously or subcutaneously, can induce a clinical response in 77% of patients. These results are in line with previous reports. Indeed, in a small retrospective study on infliximab efficacy in patients with UP, 85% of patients experienced clinical improvement. [START_REF] Bouguen | Infliximab for refractory ulcerative proctitis[END_REF] The ACT (infliximab), ULTRA (adalimumab), and golimumab (PURSUIT) trials in patients with pancolitis or left-sided colitis treated with infliximab demonstrated short-term clinical response in about 63%-69% of patients whatever disease extension. [START_REF] Rutgeerts | Infliximab for induction and maintenance therapy for ulcerative colitis[END_REF][START_REF] Sandborn | Subcutaneous golimumab induces clinical response and remission in patients with moderate-to-severe ulcerative colitis[END_REF][START_REF] Sandborn | Adalimumab induces and maintains clinical remission in patients with moderate-to-severe ulcerative colitis[END_REF] Moreover, in our study, clinical response was accompanied by a significant drop in CRP levels. Similar changes were in CRP levels were reported in the previous retrospective study on infliximab in patients with UP. [START_REF] Bouguen | Infliximab for refractory ulcerative proctitis[END_REF] Interestingly, no difference in clinical efficacy was observed in our study between the three anti-TNF for patients with UP, as it has already been demonstrated in population-based studies and network meta-analysis for patients with UC. [START_REF] Stidham | Systematic review with network meta-analysis: the efficacy of anti-tumour necrosis factor-alpha agents for the treatment of ulcerative colitis[END_REF] Importantly, UP patients treated with anti-TNF in our study are truly refractory patients with previous use of topical and oral 5-ASA and corticosteroids in a large majority of patients and previous failure of thiopurines in almost two thirds of them.

M A N U S C R I P T A C C E P T E D

Few studies have investigated other immunosuppressants to treat patient with UP. A recent retrospective multicenter study assessing the efficacy of AZA in patients with refractory UP demonstrated that 71% (10/14) of patients achieved short term response and 21% (3/14) steroid-free clinical remission. Also, In this study, after a median follow-up of 46.2 (26.4-47.8) months, only 5 patients receiving AZA out of 25 had treatment success at the end of follow-up. [START_REF] Mallet | Azathioprine for refractory ulcerative proctitis: A retrospective multicenter study[END_REF] Another multicenter, randomized, double-blind, placebo-controlled, induction trial compared the efficacy of a tacrolimus rectal ointment (3ml of tacrolimus at 0.5mg/ml) administrated twice a day for 8 weeks with rectal placebo in patients (n=21) with refractory UP. In this study, 73% (8/11) of the patients treated with tacrolimus achieved clinical response. Clinical remission and mucosal healing were achieved in 45% and 73% of the patients treated with tacrolimus. [START_REF] Lawrance | Efficacy of Rectal Tacrolimus for Induction Therapy in Patients With Resistant Ulcerative Proctitis[END_REF] It is well established that anti-TNF agents are able to induce mucosal healing in patients with UC. [START_REF] Peyrin-Biroulet | Selecting Therapeutic Targets in Inflammatory Bowel Disease (STRIDE): Determining Therapeutic Goals for Treat-to-Target[END_REF] Mucosal healing is associated with better outcomes and is now a therapeutic goal in our practice. [START_REF] Peyrin-Biroulet | Selecting Therapeutic Targets in Inflammatory Bowel Disease (STRIDE): Determining Therapeutic Goals for Treat-to-Target[END_REF] In our study, we observed mucosal healing (Mayo endoscopic subscore of 0 or 1) in 60% of the patients with available endoscopic assessment. Moreover, there was a significant decrease in the Mayo endoscopic subscore and UCEIS from baseline to follow-up colonoscopies. ACT 1 and 2 studies reported the same rate of mucosal healing at week 8 in patents with UC treated with infliximab 5mg/kg (62% and 60%, respectively). [START_REF] Rutgeerts | Infliximab for induction and maintenance therapy for ulcerative colitis[END_REF] The previous retrospective study on infliximab in 13 patients with UP reported mucosal healing in only two of the seven patients (28%) with follow-up colonoscopies. [START_REF] Bouguen | Infliximab for refractory ulcerative proctitis[END_REF] Long-term follow-up is required to assess the sustained efficacy of medical treatment in refractory UP. The median follow-up in our study was 24 months. In patients with an initial response to anti-TNF, the probability of first anti-TNF failure-free survival at two years was

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 19 19
70%. More importantly, among the whole cohort, at the end of the follow-up, 64% of the patients with refractory UP were in clinical remission, with 61% still receiving an anti-TNF agent. These data are in accordance with previous studies on the long-term outcome of patients treated with infliximab for refractory UC, with a sustained clinical response rate of 68% after a median follow-up of 33 months. [START_REF] Ferrante | Long-term outcome after infliximab for refractory ulcerative colitis[END_REF] Previous studies have identified several clinical or biological factors influencing response to anti-TNF in UC, such as severity of the disease, younger age, duration of colitis or extensive colitis. [START_REF] Zampeli | Predictors of response to anti-tumor necrosis factor therapy in ulcerative colitis[END_REF] In our study, we found that extraintestinal manifestations, ongoing topical steroids and 5-ASA at baseline were significantly associated with the absence of clinical remission in patients with refractory UP. Another recent study also identified extraintestinal manifestation as a risk factors for colectomy in patients with UC on thiopurine treatment. [START_REF] Canas-Ventura | Risk of colectomy in patients with ulcerative colitis under thiopurine treatment[END_REF] In our cohort combination therapy with thiopurines was associated with clinical remission in univariate analysis only, probably because of lack of statistical power.

Regarding ongoing treatment with topical 5-ASA or steroids, this may emphasize that the fact that patients on topical treatments at anti-TNF initiation might present more refractory UP.

In the first retrospective study on UP, only one patient relapsed after infliximab induction and underwent proctocolectomy. [START_REF] Bouguen | Infliximab for refractory ulcerative proctitis[END_REF] In our cohort, 4% of patients underwent proctocolectomy with ileo-anal anastomosis. This colectomy rate is lower than those reported in patients with left-sided or extensive UC (17%), as expected given the limited disease extent. [START_REF] Ferrante | Long-term outcome after infliximab for refractory ulcerative colitis[END_REF] Very little is known about the switch to another anti-TNF agent in patients with refractory UP. Our cohort provides interesting data showing that more than two thirds of the patients with anti-TNF primary non-response were switched to a second The strengths of our study are the large number of patients included, the nationwide character of the study and the duration of follow-up which allowed us to look at predictors of short and long-term efficacy. Moreover, the availability of data on CRP, an objective biomarker of intestinal inflammation, improved the strength of the assessment of anti-TNF efficacy in these patients. Limitations of our study are its retrospective character with absence of comparator group and the absence of systematic assessment of mucosal healing. Moreover, we were not able to collect data on fecal calprotectin, anti-TNF trough level or disease extension during follow-up.

In conclusion, our data support the use of anti-TNF monoclonal antibodies in patients with refractory UP with 50% of patients achieving clinical remission and 64% showing sustained clinical remission at the end of follow-up. Moreover, our study also demonstrated that anti-TNF agents are able to induce mucosal healing in 60% of patients with refractory UP.

Regarding follow-up, about half of the patients were still on anti-TNF therapy at 2 years.

M A N U S C R I P T A C C E P T E D

TABLES AND FIGURE LEGENDS

  study was performed in 15 French and one Belgium referral center affiliated with the Groupe d'Etude Thérapeutique des Affections Inflammatoires du tube Digestif (GETAID). All consecutive patients with a diagnosis of UC based on clinical, biological and morphological criteria according to European guidelines, and with an active UP according to treating physician (maximal extension of macroscopic endoscopic lesions <20 cm from the anal verge) refractory to conventional therapies (topical and oral 5-ASA, topical and systemic corticosteroids and/or thiopurines) who were treated with at least one injection of a monoclonal anti-TNFα antibody (infliximab, adalimumab, golimumab) from October 2006 to February 2017 were included in the study. The study protocol was approved by the Montpellier University institutional review board. All authors had access to the study data, reviewed and approved the final manuscript.

  Clinical outcomes were collected by each local investigators from retrospective notes in each patient chart. Definitions of primary outcomes were clearly defined in study protocol and explained to each local investigator before data collection. Secondary outcomes were: (1) clinical response and remission during the induction phase (first 3 months), (2) changes in the Mayo clinical subscore (retrospectively calculated from physician notes) between anti-TNF therapy initiation and week 12, (3) Mucosa healing during follow-up (defined as a Mayo endoscopic subscore of 0 or 1) among patients who underwent endoscopic assessment, (4) changes in the Mayo endoscopic subscore or UCEIS index prospectively assessed before anti-TNF initiation and during the first follow-up colonoscopy, (5) coloproctectomy during follow-up, (6) the identification of predictive factors of anti-TNF efficacy, (6) the cumulative

  during follow-up with achievement of clinical remission in 22% of the cases.Moreover, half of these patients eventually received vedolizumab during follow-up with achievement of clinical remission in 82% of patients.

Figure 1 :

 1 Figure 1: Efficacy of anti-TNFα therapy in patients with refractory ulcerative proctitis.

Figure 2 :

 2 Figure 2: Sustained clinical remission during follow-up in patients with ulcerative proctitis

Table 1 : Baseline characteristics of patients with refractory ulcerative proctitis

 1 ASA, 5-aminosalycilates; ADA, adalimumab ; Anti-TNF, anti-tumor necrosis factor alpha monoclonal antibodies; GOL, golimumab ; IFX, infliximab ; IQR, interquartile range; n, number of patients; UC, ulcerative colitis; UCEIS, ulcerative colitis endoscopic index of severity.

	n = 104

Table 2 : Predictive factors associated with primary clinical remission in patients with ulcerative proctitis treated with anti-TNF (n=104)

 2 Variables included in the multivariate analysis are sex, age at diagnosis, extraintestinal manifestations, type of anti-TNF (subcutaneous vs intravenous), concomitant thiopurines, ongoing treatment with topical 5-ASA, ongoing treatment with Topical steroids and ongoing treatment with oral steroids. Abbreviations

	Univariate analysis	Multivariate analysis α

: 5-ASA, 5-aminosalycilic acid; ADA, adalimumab; Anti-TNF, anti-tumor necrosis factor alpha monoclonal antibodies; CI, confidence interval; GOL, golimumab; IFX, infliximab; IV, intravenous; OR, odds ratio; SC, subcutaneous.

Table 3 : Adverse events in patients with ulcerative proctitis treated with anti-TNF

 3

	n=104

ACKNOWLEDGEMENTS

We thank the Association François Aupetit for its financial support.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

• Management of refractory ulcerative proctitis is challenging as patients with ulcerative colitis limited to the rectum are systematically excluded from randomized clinical trials investigating efficacy of biologics.

• We investigated the effectiveness of tumor necrosis factor (TNF) antagonists in a large cohort of patients with refractory ulcerative proctitis.

Findings:

• In a retrospective study of 104 patients with refractory ulcerative proctitis, anti-TNF therapy induced clinical remission in 50% and mucosal healing in 60%.

• About two thirds of the patients were still receiving anti-TNF therapy at 2 years.

Implications for patient care:

• Anti-TNF agents might be a good therapeutic option for patients with ulcerative proctitis.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

Supplementary Table 1: Changes in biological and endoscopic parameters with anti-TNF therapy

Biological parameter


BRGM Christophe Tournassat

Stéphane Gaboreau

Coupling clay swelling properties to hydro-geochemical conditions: a reactive transport modeling approach

The mineralogical and chemical properties of clays have been the subject of longstanding study for the long-term disposal of nuclear wastes in geological repositories. The low permeability of clay materials, including shales, provides at least part of the safety functions for radionuclide contaminants confinement. From a geochemical and mineralogical point of view, the high adsorption capacity of clay minerals adds to the effect of low hydraulic conductivities by greatly increasing the retardation of radionuclides and other contaminants, making clays ideal where isolation from the biosphere is desired. While their low permeability and high adsorption capacity are widely acknowledged, it is clear nonetheless that there is a need for an improved understanding of how the chemical and mineralogical properties of shales impact their macroscopic properties. It is at the pore-scale that the chemical properties of clay minerals become important since their electrostatic properties can play a large role. The negative electrostatic potential field at the clay mineral surfaces results in the presence of porosity domains where electroneutrality is not achieved: cations are attracted by the surfaces while anions are repulsed from them, resulting in the presence of a diffuse ion swarmor diffuse layer. Numerical methods for modeling macroscopic properties of clay media with the consideration of the presence of a diffuse ion swarm have met a growing interest in diverse communities in the past years. In this presentation we will highlight the complex interplays of mineralogical, chemical and microstructural characteristics of clay materials that are ultimately responsible for a remarkable array of coupled macro-scale properties, including swelling. A coupling scheme for predicting swelling pressure as a function of chemical conditions will be presented in the framework of a reactive transport modeling approach.


domain: math info info.info-mo spi

text:
Amel Borgi
email: amel.borgi@insat.rnu.tn

Rim Kalai
email: rym.kalai@gmail.com

Hayfa Zgaya
email: hayfa.zgaya@univ-lille2.fr

Attributes regrouping in Fuzzy Rule Based Classification Systems: an intra-classes approach

Keywords: Fuzzy rule based classification systems, supervised learning, automatic generation of fuzzy rules, ensemble learning methods, attributes regrouping, intra-classes correlation

Fuzzy rule-based classification systems (FRBCS) are able to build linguistic interpretable models, they automatically generate fuzzy if-then rules and use them to classify new observations. However, in these supervised learning systems, a high number of predictive attributes leads to an exponential increase of the number of generated rules. Moreover the antecedent conditions of the obtained rules are very large since they contain all the attributes that describe the examples. Therefore the accuracy of these systems as well as their interpretability degraded. To address this problem, we propose to use ensemble methods for FRBCS where the decisions of different classifiers are combined in order to form the final classification model. We are interested in particular in ensemble methods which split the attributes into subgroups and treat each subgroup separately. We propose to regroup attributes by correlation search among the training set elements that belongs to the same class, such an intra-classes correlation search allows to characterize each class separately. Several experiences were carried out on various data. The results show a reduction in the number of rules and of antecedents without altering accuracy, on the contrary classification rates are even improved.

I. INTRODUCTION

One of the most used tools in supervised machine learning is Fuzzy Rule Based Classification Systems (FRBCS) [START_REF] Antonelli | A fast and efficient multi-objective evolutionary learning scheme for fuzzy rulebased classifiers[END_REF][START_REF] Dehzangi | Efficient fuzzy generation: A new approach using data mining principles and rule weighting[END_REF][START_REF] Elkano | Fuzzy Rule-Based Classification Systems for multi-class problems using binary decomposition strategies: On the influence of n-dimensional overlap functions in the Fuzzy Reasoning Method[END_REF][START_REF] Ishibuchi | Distributed representation of fuzzy rules and its application to pattern classification[END_REF][START_REF] Ishibuchi | Efficient fuzzy partition of pattern space for classification problems[END_REF][START_REF] Riza | frbs: Fuzzy Rule-Based Systems for Classification and Regression in R[END_REF]. These systems are very powerful since, on the one hand, they provide an easily interpretable model composed by linguistic if-then rules, and on the other hand, they are able to deal with imprecise and noisy data.

The aim of a FRBCS is to construct a linguistic model which will be used to predict the class of new objects. In the literature, several methods have been proposed to generate fuzzy rules automatically from numerical data [START_REF] Dehzangi | Efficient fuzzy generation: A new approach using data mining principles and rule weighting[END_REF][START_REF] Ishibuchi | Distributed representation of fuzzy rules and its application to pattern classification[END_REF][START_REF] Riza | frbs: Fuzzy Rule-Based Systems for Classification and Regression in R[END_REF]. The big challenge of these systems is how to deal with high dimensional datasets. Indeed, a high number of predictive attributes leads to an exponential increase of the number of generated rules. Moreover it produces large premises, since they contain all the attributes that describes the observations. An important number of generated rules has a direct impact on training time as well as on storage capabilities It also has consequences on the transparency and the interpretability of the obtained results. Moreover it may affect the accuracy of the learning algorithms and their predictive capacity.

Thereby, reducing the number of rules and the number of antecedents without altering too much the classification performances appears as a key to improve FRBCS. To overcome this problem, several approaches have been proposed. A first possible approach is to select relevant rules. Many methods have been proposed in the literature to reduce rules number and to remove the useless. In [START_REF] Nozaki | Selecting fuzzy rules with forgetting in fuzzy classification systems[END_REF], authors have suggested to reduce the number of rules by forgetting the weak ones. Other methods of rules selection based on genetic algorithm have been studied [START_REF] Ishibuchi | Fuzzy rule selection by multiobjective genetic local search algorithms and rule evaluation measures in data mining[END_REF][START_REF] Ishibuchi | Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning[END_REF][START_REF] Villar | A genetic algorithm for feature selection and granularity learning in fuzzy rule-based classification systems for highly imbalanced data-set. Information Processing and Management of Uncertainty in Knowledge-Based Systems[END_REF]. They explicitly consider a trade-off between the number of fuzzy if-then rules and the classification accuracy. Moreover, Multi-Objective Evolutionary Algorithms have also been used to design FRBS with a trade-off between the accuracy and the interpretability of the model [START_REF] Fazzolari | A multi-objective evolutionary method for learning granularities based on fuzzy discretization to improve the accuracy-complexity trade-off of fuzzy rule-based classification systems: D-MOFARC algorithm[END_REF][START_REF] Rudziński | A multi-objective genetic optimization of interpretability-oriented fuzzy rule-based classifiers[END_REF]. The second possible approach is feature selection which aim to remove the non-significant and redundant attributes. Indeed, since recent classification systems aim to deal with larger problems, the issue of feature selection is becoming increasingly important [START_REF] Biagetti | Multivariate direction scoring for dimensionality reduction in classification problems[END_REF][START_REF] Crippa | Multi-class ECG beat classification based on a Gaussian mixture model of Karhunen-Loève transform[END_REF][START_REF] Dhir | Extraction of independent discriminant features for data with asymmetric distribution[END_REF][START_REF] Lee | An efficient fuzzy classifier with feature selection based on fuzzy entropy[END_REF][START_REF] Phong | An application of feature selection for the fuzzy rule based classifier design based on an enlarged hedge algebras for high-dimensional datasets[END_REF][START_REF] Verleysen | On the effects of dimensionality on data analysis with neural networks. Int. work-conf. on artificial and natural neural networks[END_REF][START_REF] Villacampa | Feature Selection and Classification Methods for Decision Making: A Comparative Analysis[END_REF].

Another interesting solution is to decompose the set of attributes into subgroups and treat each subgroup separately. Based on the concept of ensemble learning methods, the learning problem which contains a big number of attributes is decomposed into sub-problems of lower complexity. Different classifiers are thus constructed with a different projection of the feature set. Each classifier generates his local rule base and the different rule bases are then combined to form the final classification model [START_REF] Slima | Regroupement d'attributs par règles d'association dans les systèmes d'inférence floue[END_REF][START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF].

The main issue of these methods is how to determine the attributes that will appear together in the same group, and consequently in the same if-then rules. In [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF], a linear correlation search method was used to determine the related attributes: the attributes which are linearly correlated are grouped together and used by a classifier to construct the fuzzy if-then rules.

In this context, we study the attributes regrouping by correlation search among the training set elements that belong to the same class, it corresponds to an intra-classes correlation search. Thus, we propose a supervised learning method by automatic generation of fuzzy classification rules, the so called SIF-INTRA approach that allows reducing the number of rules without deteriorating classification accuracy, on the contrary it is even improved. In [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF], the proposed approach called SIFCO is based on a correlation search among the components of all the training set elements, without any distinction. However, in our work, the linear correlation search is an intra-classes one: the training set elements are gathered together according to their class, and a linear correlation search is done among the components of the elements of each class considered separately. Thus, we may characterize each class and gather discriminating information for a further classification. As in [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF], we perform an ensemble methodology by combining several simple classification models: each model, here a FRBCS, uses a subset of the initial attributes, and solves a part of the original task. This is done in order to obtain a better composite global model, a set of classifiers, with more accurate and reliable decisions than a complex single model. This paper is organized as follows. In section 2, we remind the classical process of FRBCS. Then, in section 3, we introduce the basic concepts of ensemble learning method and the SIFCO approach for regrouping attributes [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF]. In section 4, we describe our proposed method of attributes regrouping by intra-classes correlation search. The tests and results obtained by computer simulations with different databases are provided in section 5. Finally, section 6 concludes this study.

II. FUZZY RULE BASED CLASSIFICATION SYSTEMS

A FRBCS is a supervised learning approach. It consists of two main phases: the learning phase and the classification phase. During the learning phase, fuzzy rules are automatically generated from the training data. In the classification phase, the above constructed rule base is used to classify new objects.

In the literature, several approaches have been proposed for automatically generating fuzzy if-then rules from numerical data [START_REF] Angelov | Evolving fuzzy classifiers using different model architectures[END_REF][START_REF] Elkano | Fuzzy Rule-Based Classification Systems for multi-class problems using binary decomposition strategies: On the influence of n-dimensional overlap functions in the Fuzzy Reasoning Method[END_REF][START_REF] Hefny | Effective Method for Extracting Rules from Fuzzy Decision Trees based on Ambiguity and Classifiability[END_REF][START_REF] Ishibuchi | Distributed representation of fuzzy rules and its application to pattern classification[END_REF][START_REF] Nguyen | Fuzzy If-Then rules classifier on ensemble data[END_REF]. The generation of fuzzy rules can be made by partitioning the training examples into fuzzy subsets by using membership functions and then constructing a fuzzy rule for each fuzzy grid [START_REF] Ishibuchi | Distributed representation of fuzzy rules and its application to pattern classification[END_REF][START_REF] Ishibuchi | Efficient fuzzy partition of pattern space for classification problems[END_REF][START_REF] Ishibuchi | Fuzzy rule selection by multiobjective genetic local search algorithms and rule evaluation measures in data mining[END_REF][START_REF] Ishibuchi | Rule weight specification in fuzzy rule-based classification systems[END_REF][START_REF] Ishibuchi | Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning[END_REF]. This method is also known as fuzzy grid-type partition. Another way to generate fuzzy rules is the use of decision trees [START_REF] Hefny | Effective Method for Extracting Rules from Fuzzy Decision Trees based on Ambiguity and Classifiability[END_REF][START_REF] Pal | Fuzzy rule extraction from ID3type decision trees for real data[END_REF]. Neural networks have also been used to construct neurofuzzy classification models [START_REF] Mitra | Neuro-fuzzy rule generation: survey in soft computing framework[END_REF].

In this section, we briefly describe the fuzzy grid-type partition approach that we use in this work [START_REF] Ishibuchi | Distributed representation of fuzzy rules and its application to pattern classification[END_REF][START_REF] Ishibuchi | Rule weight specification in fuzzy rule-based classification systems[END_REF][START_REF] Ishibuchi | Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning[END_REF].

A. Learning phase with a simple fuzzy grid

We consider an n-dimensional classification problem, with m labelled examples X p = (X p 1, X p 2… X p n), p=1, 2… m, the set of these examples is the training set denoted as TS. We denote the C classes as y1, y2… yC. X p i is the value of the i th attribute of the p th example. The generation of fuzzy ifthen rules from numerical data includes two main phases [START_REF] Ishibuchi | Distributed representation of fuzzy rules and its application to pattern classification[END_REF][START_REF] Ishibuchi | Rule weight specification in fuzzy rule-based classification systems[END_REF]. At first, a fuzzy partition of the pattern space into fuzzy subspaces is performed. So, each numerical attribute is partitioned into K fuzzy subsets {A1, A2, … AK} , where each subset is defined by a membership function. Thus, we obtain a fuzzy grid (see Fig. 1). Then, a fuzzy if-then rule is constructed for each subspace of the fuzzy grid. The fuzzy partition can be made by several approaches, such as the simple fuzzy grid [START_REF] Ishibuchi | Distributed representation of fuzzy rules and its application to pattern classification[END_REF], the efficient fuzzy partition [START_REF] Ishibuchi | Efficient fuzzy partition of pattern space for classification problems[END_REF] or the supervised fuzzy partition [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF]. Fig. 1 represents an example of simple fuzzy grid where all the attributes are partitioned into the same number (K=5) of fuzzy subsets. Thus, the number of fuzzy rules generated is equal to 5 2 . In general, if we consider an n-dimensional problem with K fuzzy subsets for the fuzzy partition, then we obtain K n fuzzy rules. A triangular membership function is used in Fig. 1 [START_REF] Ishibuchi | Distributed representation of fuzzy rules and its application to pattern classification[END_REF][START_REF] Ishibuchi | Efficient fuzzy partition of pattern space for classification problems[END_REF][START_REF] Ishibuchi | Fuzzy rule selection by multiobjective genetic local search algorithms and rule evaluation measures in data mining[END_REF][START_REF] Ishibuchi | Rule weight specification in fuzzy rule-based classification systems[END_REF]. Note that the membership function could have different shapes as triangular, trapezoidal, Gaussian, etc.

Let's consider a bi-dimensional pattern classification problem (with 2 attributes X1 and X2). A fuzzy rule, labeled Rij K and corresponding to the fuzzy subspace Ai K ×Aj K , is written as follows:

Rij K : If X1 is Ai K and X2 is Aj K then X= (X1, X2) belongs to yij with CF=CFij i=1… K and j=1… K
where X= (X1, X2) is a 2-dimentional pattern, K is the number of fuzzy subsets on each axis of the pattern space, yij corresponds to one among the C class labels, CF is the certainty factor which reflects the validity of the rule.

The conclusion and the certainty degree of each rule are determined as follows [START_REF] Ishibuchi | Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning[END_REF]:

1. For each class yt (t=1,2,...,C), calculate the compatibility grade of each training example X p belonging to this class, with the antecedent part of the fuzzy rule.

= ∑ ( 1 ) × ( 2 ) ∈ (1)
where µi k and µj k are membership functions respective to Ai K and Aj K .

2. Find the class ya that has the maximum value of the compatibility grade βyt and assigns this class to yij

= max { 1 , 2 , … , } (2)
3. CFij is calculated as follows:

= | -| ∑ =1 ℎ = ∑ ( -1) ⁄ ≠ (3)
The rule base generated by the above procedure is denoted by SR={Rij K , i=1,2,…,K and j=1,2,…,K}

B. Classification phase: fuzzy inference

In the classification phase, an inference system uses the rule base SR generated in the learning phase to classify new objects. Let X'=(X'1, X'2) be a new observation. The steps, below, describe the inference method adopted in this paper [START_REF] Ishibuchi | Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning[END_REF].

1. For each class yt, calculate αyt (for t=1,2,…, C) as:

= max { 1 ′ × 2 ′ × / = , } (4)
2. Find the class ya which maximizes αyt:

= max { 1 , 2 , … , } (5)
If two or more classes take the maximum value, then X' cannot be classified, else X' is assigned to ya. Moreover, if there is no fuzzy rule with μi(X'1)×μj(X'1)×CFij≠0 the example X' cannot be classified.

The extension of this approach to n attributes is straightforward.

III. REGROUPING ATTRIBUTES IN FRBCS

FRBCS with grid-type partition suffer from the explosion of the rules' number when the number of attributes is high. An interesting way to overcome this problem is the use of the regrouping attributes approach. It is based on the concept of ensemble learning machines.

Ensembles of learning machines constitute one of the main current themes in machine learning research, and have been applied to various real problems. They correspond to a set of supervised learning machines whose decisions are combined to make the final decision. Taking into account the opinions of several experts rather than one single opinion (which cannot always be the best one) can improve the performance of the overall system [START_REF] Ren | Ensemble classification and regression-recent developments, applications and future directions[END_REF][START_REF] Valentini | Ensembles of learning machines[END_REF]. Several algorithms based on this concept have been developed, like Bagging, Boosting and Stacking [START_REF] Cao | Combining interpretable fuzzy rule-based classifiers via multi-objective hierarchical evolutionary algorithm[END_REF][START_REF] Breiman | Bagging predictors[END_REF][START_REF] Freund | Boosting a weak learning algorithm by majority[END_REF][START_REF] Prudhomme | Maps ensemble for semi-supervised learning of large high dimensional dataset[END_REF][START_REF] Ren | Ensemble classification and regression-recent developments, applications and future directions[END_REF][START_REF] Valentini | Ensembles of learning machines[END_REF]. The following steps describe the process of these methods:

• information, which may correspond to the examples, the attributes or the class variable, is distributed between different learners,

• each learner performs the learning phase using its own information,

• the decisions of the different learners are combined to make the final decision and classify a new observation.

In this paper, we focus on the regrouping attributes approach proposed in [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF] in the context of FRBCS. This method, called SIFCO, combines different classifiers by giving to each one a different projection of the set of initial attributes. The idea is to consider different classifiers, and to give to each classifier a different projection of the training set elements. This is done by decomposing the initial set of attributes into subsets of correlated components; each classifier, here a FRBCS, uses a subset of attributes and generates his local rule base. Thus, the correlated attributes will appear in the same premise. Such an approach, inspired by Vernazza, allows considering the eventual discrimination power of the union of simultaneous selected features [START_REF] Cao | Combining interpretable fuzzy rule-based classifiers via multi-objective hierarchical evolutionary algorithm[END_REF][START_REF] Vernazza | Image classification by extended certainty factors[END_REF]. Then the different rule bases are combined to form the final model or the global rule base. In opposition to a feature selection, the idea here is to preserve all attributes. The advantage, as mentioned in [START_REF] Verleysen | On the effects of dimensionality on data analysis with neural networks. Int. work-conf. on artificial and natural neural networks[END_REF], is to exploit the redundancy of information in order to reduce noise on each variable. Another objective is to improve the prediction ensured by the diversity of built learners for each group [START_REF] Prudhomme | Maps ensemble for semi-supervised learning of large high dimensional dataset[END_REF].

As represented in Fig. 2, SIFCO method is composed of 3 phases [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF]:

• a pre-treatment phase (attributes regrouping phase)

• a learning phase • a classification phase Fig. 2. Diagram describing the different steps of SIFCO [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF] For the pre-treatment phase, the authors proposed to regroup the attributes using linear correlation search among the training set elements [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF]. Each group of high correlated attributes is treated separately by a FRBCS to generate a local rule base. During the learning phase the method described in section 2.1. was used to construct the local rule bases. In the classification phase the inference method described in section 2.2. was applied to classify a new object using the global rule base (union of all the local bases).

IV. PROPOSED APPROACH: INTRA-CLASSES ATTRIBUTES REGROUPING IN FUZZY RULE BASED CLASSIFICATION SYSTEMS

We have drawn on the work of [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF] and we belief that the regrouping attributes approach proposed in [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF] can be very interesting if the information about the class attribute is taken into account in the process of the determination of the related attributes.

For that purpose, we proceed to the attributes regrouping by correlation search among the training set elements that belong to the same class, it corresponds to an intra-classes correlation search. In [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF], the authors have proposed to regroup attributes by using a correlation search among the components of all the training set elements, without any distinction. However, in our work, the linear correlation search is an intra-classes one: the training set elements are gathered together according to their class, and a linear correlation search is done among the components of the elements of each class considered separately. Thus, we may characterize each class and gather discriminating information for a further classification.

On the first step we rely on the class as a criterion for splitting the initial training set TS into several subsets. This step leads to a partitition of TS into C (total number of classes) training subsets denoted by TS1, TS2, ..., TSC, such as TSt contains all the training examples of the class yt. The second step consists in computing, for each subset TSt, the correlation matrix R t = (r t i,j)n×n, with n the number of attributes. We denote by r t i,j the coefficient of linear correlation between the components Xi and Xj of the TSt vectors (t=1,2,...,C).

{ }

C t where R ,..., 2 , 1 1 ... ... r .. . ... 1 r r ... r 1 t n 1, t 2,1 t n 1, t 1,2 t ∈                 =
Next step in attributes regrouping consists of thresholding each matrix Rt with a prefixed threshold denoted θ, same threshold being used for all the matrices. As in [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF], we use the following procedure to decide if two attributes Xi and Xj are correlated: if | r t i,j | < θ then Xi and Xj are not correlated and r t i,j is set to 0 else Xi and Xj are correlated and r t i,j is set to 1 For each thresholded matrix Rθ t obtained from R t , we extract the largest subsets of correlated components, these subsets form a partition P t of the components set {X1, X2, ..., Xn}. All the subsets, obtained from the different matrices, are regrouped by the union operator to obtain a final set of correlated components subsets. As a same correlated components subset can be found from two or more different training subsets, we use the union operator to eliminate such redundancies. It should be noted that this final set is not necessarily a partition of {X1, X2, ..., Xn}.

Each subset of correlated components will be treated separately by a FRBCS. Fig. 3 and Fig. 4 summarize these different steps of our approach SIF-INTRA.

In order to illustrate this procedure, let us consider an example of a 5-dimensional classification problem with 2 classes y1 and y2, and a training set TS containing m labeled patterns X p = (X p 1, X p 2… X p n), p=1, 2… m. TS is decomposed into 2 subsets: TS1 containing the observations of class y1 and TS2 containing the observations of class y2. Then we compute the correlation matrix R1 among the examples of TS1, and R2 among the examples of TS2. We obtain, for example, the following correlation matrices:

                = 1 0

R

with a threshold θ=0.7, we obtain the following thresholded matrices:

                = 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 Rθ                 = 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 2

Rθ

So, for the training subset TS1, the partition P 1 of the initial set of attributes obtained from Rθ 1 is: P 1 ={{X1,X2,X3}, {X4,X5}}, it contains the largest subsets of correlated components. For the training subset TS2, the obtained partition P 2 of the initial set of attributes obtained from R2 1 is: P 2 ={{X1,X2},{X3},{X4,X5}}. The final set of correlated attributes obtained through the union of all these subsets is: {{X1,X2,X3}, {X4,X5},{X1,X2},{X3}}.

Each of these four groups of attributes will be treated separately by a FRBCS, so the correlated components will be brought together in the premises of the rules. Thus the number of attributes present in the premises of the generated rules is smaller than the total number of attributes describing the learning examples. Thereby our method allows to reduce the size of the premises of the rules generated compared with FRBCS without grouping of attributes. Moreover, having less attributes in each group than the total number of attributes allows reducing the number of rules comparing to a single FRBCS that treats all the attributes. This is confirmed by the experimental tests.

In our example, and with simple fuzzy grids divided into K=5 fuzzy subsets, a single FRBCS handling all the attributes {X1,X2,X3,X4,X5} would lead to at most 5 5 = 3125 rules. With a FRBCS treating each group of attributes we will obtain at most only 180 rules (125+25+25+5) as explained below:

• a FRBCS with {X1,X2,X3} will lead to 5 3 = 125 rules • a FRBCS with {X4,X5} will lead to 5 2 =25 rules • a FRBCS with {X1,X2} will lead to 5 2 =25 rules • a FRBCS with{X3} will lead to 5 1 rules

V. EXPERIMENTATION AND RESULTS

We implemented our intra-classes regrouping attributes approach in a so called SIF-INTRA system. As SIFCO, SIF-INTRA is composed of 3 phases: the pre-processing phase, the learning phase and the classification phase (see Fig. 2). In the pre-processing phase, we used our method of regrouping attributes based on an intra-classes correlation search (described in section 4): this point is different from the work of [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF] as the authors used a correlation search among all the examples, without distinction of classes. The learning and the classification phases are kept the same as in [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF]. We tested our system with well-known data bases that differ in terms of their attributes number, instances number and number of classes (Table 1). To evaluate the generalization performance of our method, we used the 10fold cross-validation technique [START_REF] Kohavi | A study of cross-validation and bootstrap for accuracy estimation and model selection[END_REF]. Different parameters values were tested, for the correlation threshold (θ): 0.5, 0.8, 0.9, 0.95, and for the fuzzy grid size (K): 3, 4, 5, 6.

Let us begin by analyzing the influence of the threshold, with a fuzzy grid size K=3. Experimental results are presented in Table 2, every cell contains the good classification rates followed in brackets by the number of generated rules, and in braces by the size of the premises. The best classifications rates are highlighted in bold. "Imp" refers to the impossibility of generating the fuzzy rule base due to the explosion of the rules' number (in our experiments, we note this problem from a number of rules about 10 5 ).

For Iris, Lupus and Wine data sets, the classification accuracy degrades or remains the same with the increase of the correlation threshold. For a high threshold, the number of subsets of correlated attributes is less than the one determined with a low threshold: the correlated attributes are those strongly correlated. Thus, we can lose information on the weak correlation of certain attributes. This is not the case for the Vehicle base: with a lower correlation threshold, information about the correlation of some discriminating attributes is lost and the classification rates are worse. To understand whether weak or strong correlations should be favoured a detailed analysis of the nature of data should be performed in a future work.

For the Vehicle base, we note the impossibility of generating a rule base with low correlation thresholds (0.5 and 0.8). This is due to a very large number of correlated attributes regrouped together.

We also notice that the number of generated rules (in brackets) decreases with the increase of the correlation threshold. This decrease is very important in the case of the Vehicle base: a difference of about 36116 between a threshold of 0.9 and a threshold of 0.95. This is due to the decrease in the number of correlated attributes in the subsets of correlated components found with a higher threshold. For the two data sets Iris and Wine, we obtain the same results with the two different correlation thresholds 0.9 and 0.95, and for the Lupus data, the same results are obtained whatever the correlation threshold is. It means that these thresholds lead to the same groups of correlated attributes that is to say to the same grouping of attributes in the premises. The rule bases are then identical, hence the same classification results.

For the four data sets, the number of attributes (in braces) present in the premises of the generated rules is smaller than the total number of attributes describing the learning examples. Thus, our method allows to reduce the size of the premises of the rules generated compared with FRBCS without grouping of attributes.

Our method SIF-INTRA is strongly inspired by Fuzzy Rule Based Systems with simple fuzzy grid [START_REF] Ishibuchi | Distributed representation of fuzzy rules and its application to pattern classification[END_REF] denoted by SIF in Table 3, as well as SIFCO method [START_REF] Soua | An ensemble method for fuzzy rule-based classification systems[END_REF]. Therefore, we give Table 3 as a comparative table between our method and these two approaches (rate of good classification followed in brackets by the rules' number). For each method, Table 3 shows the best results obtained with different values of the parameter K [START_REF] Slima | Regroupement d'attributs par règles d'association dans les systèmes d'inférence floue[END_REF][START_REF] Cao | Combining interpretable fuzzy rule-based classifiers via multi-objective hierarchical evolutionary algorithm[END_REF][START_REF] Breiman | Bagging predictors[END_REF][START_REF] Biagetti | Multivariate direction scoring for dimensionality reduction in classification problems[END_REF].

For Iris and Lupus data sets, SIF-INTRA allows a slight improvement of classification results compared to SIF, the number of rules is also lower. Moreover SIF-INTRA is able to process the two datasets Wine and Vehicle that can't be dealt with SIF (referred by "Imp" in Table 3). The reason is an important number of attributes that lead to a huge number of rules.

Let us now compare the two linear correlation methods: the intra-classes correlation search ensured by SIF-INTRA and the correlation search among all classes without distinction processed by SIFCO. SIF-INTRA generally outperforms SIFCO method, except with Lupus data where SIF-INTRA leads to a small deterioration of classification rates. Nevertheless the classification rates are generally similar, except with Vehicle data where we note a significant improvement of 24% with an important reduction in the rules number when using SIF-INTRA. In general, the number of generated rules is less important with the intra-classes method than with the linear correlation search upon all classes, and this for the same fixed parameters values (except for Wine data set). Indeed, in the case of the intra-classes method, the subsets of correlated attributes used to build the premises are more numerous but smaller (smaller number of attributes in each subset) than those obtained by SIFCO. So the number and size of the rules are reduced with Iris, Lupus and Vehicle data. In the case of Wine data, we notice an important increase of the number of rules with SIF-INTRA: the obtained subsets of correlated attributes remain in this case too large. In all cases, it would be interesting to consider a post treatment that eliminates the neutral rules and optimizes the whole rule base.

A linear correlation search among the vectors of each class separately allows to access to more discriminating information: each class is characterized by its own matrix and correlated attributes. However, if the linear correlation is done among the attributes of all the training set vectors, without any distinction of classes, as in SIFCO, some discriminating information may be lost and classification rates are worse. Nevertheless, we have to note, in consideration to this last method (correlation search upon all classes), that its results remain satisfying, and that its complexity is weaker than the intra-classes method complexity (less matrices to treat and less rules to generate). As the attributes subsets are treated separately, one may use, in future work, distributed approaches for modelling the overall system and for parallelizing tasks when possible.

VI. CONCLUSION

In this paper, we propose a supervised regrouping attributes approach based on intra-classes correlation search. Our main goal is to take into account the class of the labelled data while detecting the correlations between the attributes. Each obtained group of attributes is then used by a classical FRBCS to generate a local rule base, thus, the correlated attributes will appear in the same premises. Then, the different rule bases are combined to form the final model.

The proposed approach reduces complexity compared to classical FRBCS: the number of rules and the number of antecedent conditions are reduced, and thus, comprehensibility is improved. Moreover our method handles fairly high-dimensional data (such as Wine and Vehicle), unlike classical FRBCS that cannot provide classification results. It was shown through computer simulations that this complexity reduction is done without deteriorating classification accuracy, on the contrary it is even improved.

These encouraging results lead us to complete computer simulations with other datasets and real data. We also plan to continue the experimentation tests on data bases with larger dimensionality. Moreover, it would be interesting to study more precisely the choicie of the threshold in order to find the relevant value for each data base.

In this paper, we propose an intra-classes correlation search, it would be interesting to study a different method of attributes regrouping to characterize a class versus all others, known as OAA (One-Against-All) or OVA (One-Vs-All) approaches [START_REF] Rifkin | In Defense of One-Vs-All Classification[END_REF][START_REF] Yang | An Improvement of Oneagainst-all Method for Multi-class Support Vector Machine[END_REF]. Another attractive perspective consists in reducing the number of rules in SIF-INTRA by introducing rules' selection methods.

As further work, one may also study other methods to find dependencies within data sets in order to regroup dependent attributes. We have already begun such a study by using Association Rules, more precisely a frequent itemsets mining algorithm was used to detect associations between the attributes [START_REF] Slima | Regroupement d'attributs par règles d'association dans les systèmes d'inférence floue[END_REF]. In the same vein, it would be interesting to extend our approach SIF-INTRA to handle symbolic features. Indeed, in this work SIF-INTRA is limited to data with numerical features since it uses linear correlation to find dependencies between attributes. We have already started work in this direction using three methods to find associations between symbolic features: the chi-squared independence test, the Cramer V coefficient and the symmetrical uncertainty factor [START_REF] Borgi | Ensemble learning methods and attribute grouping for rule generation "Ensembles d'apprentissage et regroupement d'attributs pour la génération de règles[END_REF].

Fig. 1 .

 1 Fig. 1. Simple fuzzy grid

Final set of correlated components subsets

			TS
		Splitting the Training Set TS
	TS 1 Examples	...	TS t Examples	...	TS C Examples
	of class y 1		of class y t		of class y C
	Matrix		Matrix		Matrix
	processing		processing		processing
	P 1	...	P t	...	P C
			Union operator
	t } P t ={subsets of correlated components obtained from R θ R θ t : thresholded matrix computed from TS t
	Fig. 3. Attributes regrouping steps in SIF-INTRA
	TS t
			Computing the
		correlation matrix
	Correlation matrix			Correlation
	R t	Thresholding the		threshold θ
		correlation matrix
	Thresholded matrix
	R θ	t
		Finding the correlated
			components
	P

t Matrix processing Fig. 4. Matrix processing in SIF-INTRA

TABLE 1 .

 1 DESCRIPTION OF THE USED DATA SET

	Data Base	Number of	Number of	Number of
		instances	attributes	classes
	Iris	150	4	3
	Lupus	87	3	2
	Wine	178	13	3
	Vehicle	846	18	4

TABLE 2 .

 2 SIF-INTRA: INFLUENCE OF THE CORRELATION THRESHOLD

	θ	0.5	0.8	0.9	0.95
	Iris	96.66	95.33	94.66	94.66
		(97.5)	(21.9)	(12)	(12)
		{3.29}	{1.44}	{1}	{1}
	Lupus	78.08	78.08	78.08	78.08
		(11)	(11)	(11)	(11)
		{1.75}	{1.75}	{1.75}	{1.75}
	Wine	90.48	88.82	88.82	88.82
		(1435.8)	(44.7)	(39)	(39)
		{4.72}	{1.15}	{1}	{1}
	Vehicle			52.24	53.16
		Imp	Imp	(36652.8)	(536)
				{10.45}	{4.97}

TABLE 3 .

 3 COMPARISON BETWEEN SIF, SIFCO AND SIF-INTRA

		SIF	SIFCO	SIF-INTRA
	Iris	96	92.67	96.66
		(46)	(30)	(24)
	Lupus	77.01	79.31	78.08
		(11)	(12)	(9)
	Wine	Imp	93.26 (60)	93.82 (3289.3)
	Vehicle	Imp	43.5 (94514)	54 (1459.7)