Emmanuelle Kelodjoue
email: emmanuelle.kelodjoue-nguemegne@univ-grenoble-alpes.fr

Jérôme Goulian
email: jerome.goulian@univ-grenoble-alpes.fr

Didier Schwab
email: didier.schwab@univ-grenoble-alpes.fr

Performance of two French BERT models for French language on verbatim transcripts and online posts

Pre-trained models based on the Transformer architecture have achieved notable performances in various language processing tasks. This article presents a comparison of two pretrained versions for French in a three-class classification task. The datasets used are of two types: a set of annotated verbatim transcripts from face-to-face interviews conducted during a market study and a set of online posts extracted from a community platform. Little work has been done in these two areas with transcribed oral corpora and online posts in French.

Introduction

Opinion mining has recently undergone a change with the rise of deep learning and, especially, the use pre-trained Language Models [START_REF] Vaswani | Attention is all you need[END_REF]. The use of the latter such as ELMO [START_REF] Matthew E Peters | Deep contextualized word representations[END_REF] and BERT [START_REF] Devlin | Bert: Pre-training of deep bidirectional transformers for language understanding[END_REF] has led to significant improvements on a wide range of NLP tasks for the English language, from relation extraction to document classification [START_REF] Peng | Transfer learning in biomedical natural language processing: an evaluation of bert and elmo on ten benchmarking datasets[END_REF][START_REF] Tahmid Rahman Laskar | Contextualized embeddings based transformer encoder for sentence similarity modeling in answer selection task[END_REF]. French variants such as FlauBERT [START_REF] Le | Flaubert: Unsupervised language model pre-training for french[END_REF] and Camem-BERT [START_REF] Martin | Camembert: a tasty french language model[END_REF] were proposed later on.

In this work, we are interested in the classification of two types of data as being either in favour (motivation), either not in favour (barriers) or in favour on the condition that (condition) :

• Verbatim transcripts from face-to-face interviews conducted in the context of a market potential study of an innovative product using natural language processing methods (NLP).

• Online posts comes from a community platform called Yoomaneo. 1Since we work with French data, we propose to compare and analyse the performance of two pretrained versions for French. Additionally, since the collected data is small, we propose to augment the data with different augmentation techniques.

Contribution: This paper aims to compare and analyse the performances of two french BERT models on two different types of data.

2 Dataset : Constitution and Annotation

Dataset origin: Verbatim transcript

The dataset used to build and evaluate the French BERT models in this work comes from a set of 4367 verbatim. These verbatim were manually extracted from 75 transcripts2 of face-to-face interviews. 3 To use this dataset for our research task, we conduct a human evaluation. We gather 6 evaluators and create two subunits of 3 annotators and add one more4 to balance the evaluation of the two groups. We ask each group to review monthly 200 verbatim from the 4367.

Evaluation rules:

Only the verbatim whose classification obtained an interrater agreement according to the following rules were kept. Each verbatim of our initial corpus (4367) must be evaluated by at least 3 people. If a class (barrier, motivation or condition) results in an agreement greater than or equal to 50% for a verbatim and there is not a 50/50 on it, the selected verbatim and the assigned class is selected. On the other hand, if the interrater agreement is less than 50% or if there is 50/50 on two labels, the verbatim is eliminated from the corpus. 1578 out of 4367 verbatim transcripts have been evaluated, and only 839 verbatim transcripts obtained an agreement greater than or equal to 50%. The distribution of the corpus is given in Table 1.

Classes Number of verbatim

Dataset origin: Online posts

Yoomaneo is a free community platform open to all. It was created in 2020 by the company Ixiade. 5 Yoomaneo was created to build a database of individuals willing to participate in studies on Innovation. Ixiade is responsible for the recruitment of the participants of the studies, who are then invited to download the application. For our case, 755 responses or posts were extracted from Yoomaneo. These posts come from 4 different projects which focus on the evaluation of different innovative concepts in 3 different domains: health, well-being and electrical (2 projects).

Evaluation rules The collected posts were then given to 3 research fellows to evaluate. The evaluation procedure is similar to the one mentioned in section 2.1. Only the posts which received at least the same evaluation (same category when annotated) were kept. As a result, of the 755 evaluated, 433 were assigned to the motivation class, 112 to the barrier class, 97 to the condition class, 65 were deemed unclassifiable, and 48 received no agreement. The distribution of the corpus is given in Table 2.

Classes

Data Augmentation

Data amplification involves all the techniques for amplifying the amount of data available by adding slightly modified copies of the original data [START_REF] Li | Data augmentation approaches in natural language processing: A survey[END_REF] or artificially generating data from the original data through transformations [START_REF] Taylor | Improving deep learning with generic data augmentation[END_REF] with the goal of increasing the size of the dataset. It has been used in various fields such image classification [START_REF] He | Deep residual learning for image recognition[END_REF]), speech recognition (Park et al., 2019), etc. In this work, 4 different popular augmentation methods have been implemented and adapted for text classification for the French language [START_REF] Bayer | A survey on data augmentation for text classification[END_REF]: synthetic noise [START_REF] Steven Y Feng | Genaug: Data augmentation for finetuning text generators[END_REF][START_REF] Belinkov | Synthetic and natural noise both break neural machine translation[END_REF], synonym replacement [START_REF] Wei | Eda: Easy data augmentation techniques for boosting performance on text classification tasks[END_REF][START_REF] Steven Y Feng | Genaug: Data augmentation for finetuning text generators[END_REF][START_REF] Coulombe | Techniques d'amplification des données textuelles pour l'apprentissage profond[END_REF], random trio techniques [START_REF] Steven Y Feng | Genaug: Data augmentation for finetuning text generators[END_REF] and backtranslation [START_REF] Mercadier | Classification automatique de textes par réseaux de neurones profonds: application au domaine de la santé[END_REF][START_REF] Marivate | Improving short text classification through global augmentation methods[END_REF], [START_REF] Steven Y Feng | Genaug: Data augmentation for finetuning text generators[END_REF], [START_REF] Wei | Eda: Easy data augmentation techniques for boosting performance on text classification tasks[END_REF], and [START_REF] Marivate | Improving short text classification through global augmentation methods[END_REF]. To our knowledge, most of the mentioned techniques have only been applied to English data reviews and not on the type of data this work used: verbatim transcripts and online posts.

Synthetic noise

For each verbatim transcript in our training dataset, we randomly delete, insert and swap characters according to a replacement percentage rate. We produce for a verbatim transcript 5%, 10%, and 15% noise variations.

Random trio techniques

For random trio techniques, we randomly remove a word which is not a stopword, insert a random synonym of a word into a random position in the verbatim transcript and swap the position of two words with a percentage rate of 5% (5% of the words are changed).

Replacement methods

Lexical replacement approach is a technique that replaces a word or words in a text with similar words. Most works [START_REF] Kolomiyets | Model-portability experiments for textual temporal analysis[END_REF][START_REF] Zhang | Character-level convolutional networks for text classification[END_REF] replace words in the original text with their synonyms using WordNet [START_REF] Esuli | Sentiwordnet: a high-coverage lexical resource for opinion mining[END_REF]. Since we deal with French data, we used the lexical resource DBnary [START_REF] Sérasset | Dbnary: Wiktionary as a lmf based multilingual rdf network[END_REF][START_REF] Sérasset | Dbnary: Wiktionary as linked data for 12 language editions with enhanced translation relations[END_REF]. DBnary is a large lexical resource which provides multilingual lexical data extracted from Wiktionary. The dataset contains extracts from 22 Wiktionary languages. We replace only adjectives, adverbs, verbs and nouns with a randomly chosen synonym of the same POS provided by DBnary. We use Stanza [START_REF] Qi | Stanza: A python natural language processing toolkit for many human languages[END_REF] for tagging.

Back-translation

Back-translation [START_REF] Sennrich | Improving neural machine translation models with monolingual data[END_REF] consists in translating a sentence from a source language to a target language. The sentence obtained after translation from the source language to the target language is then translated back into the source language. This approach makes it possible to obtain different variants of the same sentence. We use Deepl6 translation service web to produce those new data for our training dataset. We used all the languages provided by Deepl, approximately 25 languages. We divide our dataset into 3 subsets: train, dev and test (respectively 60%, 20%, 20%). We augment only the training set. Table 3 gives an example of verbatim transcripts generated using the different augmentation methods mentioned above. Table

Methods

Training Architecture. For our task, we append the relevant predictive layer on top of CamemBERT's and FlauBERT's architecture. We fine-tune all the different models to follow the process described by [START_REF] Devlin | Bert: Pre-training of deep bidirectional transformers for language understanding[END_REF] and followed by [START_REF] Le | Flaubert: Unsupervised language model pre-training for french[END_REF]. The classification head for FlauBERT consists of the following layers, a dropout, a linear layer followed by the activation function tanh, a dropout and another linear layer. To obtain the probabilities for each class, the softmax function was used. The dimensions of the inputs of the linear layers are respectively equal to the size of the Transformer. For CamemBERT, the classification heads are the same as the ones described in [START_REF] Martin | Camembert: a tasty french language model[END_REF].

Parameters. As far as the hyperparameters are concerned, they are all fixed at the time of learning, with a batch size of 8 for all the architectures. The number of epochs is set to 5 and the learning rate to 5e-5 for the first epoch, then decreasing linearly. The AdamW (Kingma and Ba, 2014) optimizer is used.

7 http://www.gutenberg.org.

Results and Analysis

In this section, we present the results on our two test data. We compare the performance of FlauBERT with its competitor (CamemBERT). The metrics used to measure the performance of each method were the F1-score and the accuracy (F-micro). The F-score is used as metric since our data are imbalanced in order to observe the real performance of the model. The results are evaluated according to the amplification method used and the architecture used. Our baseline is the model without amplification.

FlauBERT

For FlauBERT, we use the 3 model sizes: FlauBERT BASE CASED (BC), FlauBERT BASE UNCASED (BU) and FlauBERT LARGE (L). Table 6 presents the size of data on which each model was trained. Table 7 presents the final accuracy and F1 on test set for the verbatim transcripts. The results show that FlauBERT BU performs better than the CASED model and the LARGE model, with an accuracy score of 0.714 and F1 score of 0.682. Overall, Back-translation and noise injection perform better for all the 3 models, with an average accuracy greater than 0.60. Huge improvement is observed with the F1 score for all the models, except for the case where FlauBERT LARGE is combined with random trio and Noise Injection. One reason may be that too much injection and replacement of words might have altered the semantic sense of the training data when augmenting it. Table 8 presents the results on the test set for online posts. The results show that FlauBERT L performs slightly better than the CASED model and the LARGE model, with an accuracy score greater than 0.80 for all the amplification methods. The best score is obtained with synonym replacement and FlauBERT L with an accuracy score of 0.829 and F1 of 0.733.

By comparing the results, we observe that the amplification methods combined with the different FLauBERT models improve the classification task for both test data. Nevertheless, the results are more significant on the online post data, with an accuracy above 0.80. This might be because they are somewhat similar to reviews or critics. Verbatim transcripts are quite particular since they come from oral dialogue which has been transcribed and revised. The classification models have somewhat more difficulties to classify those type of data compare to online posts, even though the accuracy is quite good (> 0.70 on verbatim transcripts test data). Random trio and synonym replacement are respectively the ones which produced the best score for the test data for verbatim transcripts and test data for online posts.

In the next section, we present the results obtained when using CamemBERT model.

CamemBERT

For CamemBERT, we used three model sizes which were introduced in Martin et Table 11 show that CamemBERT LARGE performs better than the BASE model, with an accuracy score of 0.868 and F1 score of 0.801. Random trio is the best performing method, follow by the back-translation method (acc.: 0.853) and synonym replacement (acc.: 0.783).

By comparing the results, we observe that augmentation methods used in this work clearly improved the performances for both CamemBERT and FlauBERT. Overall, CamemBERT performances are better than FlauBERT. Synonym replacement combined with CamemBERT LARGE is the best performing duo on verbatim and online posts test data. We also noted that performances on post online are better than on verbatim transcripts. One reason may be the type of data the pre-trained model were trained on. CCNET corpus were crawled from internet, so they may be more similar or linguistically closer to online posts than verbatim transcripts. A linguistic analysis of the data used to trained CamemBERT model may be interesting to conduct in order to explore the lingusitic similarities or differences with our datasets. In conclusion, the results are promising and clearly open up work prospects.

Conclusion

We have presented a work where we sought to compare the performances of two BERT models for French language on a three-class classification task . Firstly, we show that simple augmentation techniques used for text classification can be implemented and adapted for the datasets used in this work. Overall, we also obseved that Camem-BERT model was better than FlauBERT for this task and the best amplification method was synonym replacement. For future works, we would like to use other pretrained language models for French such as XLNET, BERT multilingual, etc. In this paper, we just focus on comparing two French Variants. We also think exploring the linguistic features of our dataset in the training of the model may be interesting with the goal of evaluating their impact on the performance. Finally, we also think that trying to other amplification methods such as replacement via a language model may be interesting.

The data used in this work comes from a private enterprise, and we have not received their consent to share the dataset.

  al. (2019): Camem-BERT BASE O for the model trained on the OS-CAR corpus, CamemBERT BASE C for the model trained on the CCNET corpus and CamemBERT LARGE trained of the CCNET corpus.

Table 1 :

 1 Number of verbatim per categories.

	Barriers	189
	Motivation	407
	Condition	243

Table 2 :

 2 Number of verbatim per categories.

		Number of verbatim
	Barriers	112
	Motivation	433
	Condition	97

Table 3 :

 3 Example of a verbatim transcript and its variations using our augmentation methods. Changes are bolded.

	4 Experimental Setup
	We chose 4 data augmentation techniques and 2
	Pretrained Models (FlauBERT and CamemBERT)
	for this experimental work.
	4.1 Data splitting and augmentation
	Methods	Training Testing
	Original	503	168
	Synthetic Noise	1981	168
	Random trio	8024	168
	Synonym replacement 6822	168
	Back-translation	11 236	168

Table 4 :

 4 Overview of the augmented datasets for the verbatim dataset.

Table 5 :

 5 Overview of the augmented datasets for the online posts dataset.4.2 Pretrained Models and FinetuningModel description. FlauBERT[START_REF] Le | Flaubert: Unsupervised language model pre-training for french[END_REF] is a French BERT model. It was trained on 71 GB of French text corpus. The corpus consists of 24 subcorpora covering diverse topics and writing styles from formal and well-written text (e.g. Wikipedia and books).

	Testing

7

CamemBERT is also a language model for French based on the RoBERTa

[START_REF] Liu | Roberta: A robustly optimized bert pretraining approach[END_REF]

architecture pretrained on the French corpus OSCAR (Suárez et al., 2019) (138 GB) and CCNET

[START_REF] Wenzek | Ccnet: Extracting high quality monolingual datasets from web crawl data[END_REF]

(135 GB). Both FlauBERT and CamemBERT were trained on the masked Language Modeling (MLM) task.

Table 6 :

 6 pre-trained model size for FlauBERT[START_REF] Le | Flaubert: Unsupervised language model pre-training for french[END_REF].

	TAD			Verbatim transcripts
		FlauBERT Base Cased FlauBERT Base Uncased FlauBERT Large
		accuracy	F1	accuracy	F1	accuracy	F1
	0 -Baseline	0.482	0.217	0.500	0.267	0.589	0.538
	1 -BT	0.667	0.604	0.690	0.650	0.690	0.657
		+0.18	+0.39	+0.19	+0.38	+0.10	+0.12
	2 -SR	0.589	0.574	0.649	0.607	0.690	0.641
		+0.11	+0.36	+0.15	+ 0.34	+0.10	+0.10
	3 -RT	0.595	0.558	0.714	0.683	0.583	0.411
		+0.11	+0.34	+0.21	+0.42	-0.01	-0.13
	4 -NI	0.673	0.591	0.685	0.641	0.625	0.514
		+0.19	+0.37	+0.18	+0.37	+0.04	-0.02
	Table 7: FlauBERT: F1 and accuracy score for verbatim
	transcripts test data.

Table 8 :

 8 FlauBERT: F1 and accuracy score for online posts test data.

  Table 10 presents the final accuracy and F1 on test set for online posts. The results show that CamemBERT LARGE performs better than the BASE model, with an accuracy score of 0.756 and

	Model	Parameter Architecture Training corpus
	CamemBERT BASE O 110M	Base	corpus OSCAR (135 GB )
	CamemBERT LARGE 335M	Large	corpus CCNet (135 GB )
	CamemBERT BASE C 110M	Base	corpus CCNet (135 GB )

Table 9 :

 9 Pre-trained models size for CamemBERT[START_REF] Martin | Camembert: a tasty french language model[END_REF].

	TAD			Verbatim transcripts
		CamemBERT B (OSCAR) CamemBERT B (CCNet) CamemBERT L (CCNet)
		accuracy	F1	accuracy	F1	accuracy	F1
	0 -Baseline	0,482	0,217	0,607	0,458	0,494	0,318
	1 -BT	0,696	0,640	0,732	0,687	0,673	0,611
		+0,21	+0,42	+0,13	+0,47	+0,18	+0,39
	2 -SR	0,714	0,663	0,702	0,653	0,649	0,581
		+0,23	+0,45	+0,10	+0,44	+0,15	+0,36
	3 -RT	0,714	0,648	0,655	0,594	0,756	0,720
		+0,23	+0,43	+0,05	+0,38	+0,26	+0,50
	4 -NI	0,685	0,642	0,667	0,621	0,714	0,687
		+0,20	+0,43	+0,06	+0,16	+0,22	+0,37

Table 10 :

 10 CamemBERT: F1 and accuracy score for Verbatim transcripts test data.

	F1 score of 0.720. Random trio is the best per-
	forming method (acc.: 0.756) follow by the back-
	translation method (acc.: 0.732) and synonym re-
	placement (acc.: 0.714).
	TAD			Online Posts
		CamemBERT B (OSCAR) CamemBERT B (CCNet) CamemBERT L (CCNet)
		accuracy	F1	accuracy	F1	accuracy	F1
	0 -Baseline	0,674	0,269	0,752	0,484	0,674	0,269
	1 -BT	0,783	0,68	0,814	0,755	0,822	0,771
		+0,11	+0,41	+0,06	+0,27	+0,15	+0,50
	2 -SR	0,767	0,672	0,845	0,759	0,868	0,801
		+0,09	+0,40	+0,09	+0,27	+0,19	+0,53
	7 -RT	0,744	0,666	0,853	0,780	0,775	0,708
		+0,07	+0,40	+0,10	+0,30	+0,10	+0,44
	8 -NI	0,744	0,580	0,806	0,731	0,806	0,624
		+0,07	+0,31	+0,05	+0,25	+0,13	+0,36

Table 11 :

 11 CamemBERT: F1 and accuracy score for Online Posts test data.

https://www.yoomaneo.com/

434 081 tokens.

The interviews were conducted as part of different market potential studies catering various innovative products in the field of electricity, health, electrical goods, gerontology, automatism and pastry.

 4 We called him the common annotator since his role is to fill the empty space left by one of the six initials annotators.

https://www.ixiade.com/

https://www.deepl.com/fr/translator 4 and 5 gives an overview of the training size per augmentation method.


Brousseau Christian
email: christian.brousseau@univ-rennes1.fr

APPLICATION OF THE MULTIRESOLUTION WAVELET REPRESENTATION TO NON-COOPERATIVE TARGET RECOGNITION

Keywords: High resolution radar, non-cooperative target recognition, radar cross section, wavelet, multiresolution representation. I

In this paper, the problem of efficient representation of large database of target radar cross section is investigated in order to minimize memory requirements and recognition search time, using wavelet representation. Synthetic RCS of large aircrafts, in the HF-VHF frequency bands, are used as experimental data. Many parameters are evaluated like mother wavelet, decomposition level, and classification parameters. Criteria used to determine the efficiency of multiresolution representations are compression scores, false identification rate and search time.

INTRODUCTION

Requirements for future air defence radar systems are detection, localization, but also identification of aircrafts. With the increasing resolution of modern radar systems, it is theoretically possible to store much information, according to aspect, elevation, pulsewidth, etc., of a complex target and use them in the field of target identification.

The advantage of the increasing resolution of radar systems is the opportunity to have more details characteristic of a specific target. The disadvantage is that these detailed characteristics require more and more computer memory to be stored, computer resources and increase the search time to NCTR (Non-Cooperative Target Recognition) association.

It is therefore important to develop efficient methods to decrease the size of representations of high resolution data of radar targets. One way to compress these representations is to use multiresolution signal decomposition to analyze the RCS (Radar Cross Section) information content [START_REF] Nelson | Iterative wavelet transformation and signal discrimination for HRR radar target recognition[END_REF] - [START_REF] Baras | Adaptive classification based on compressed data using learning vector quantization[END_REF].

In this paper, we investigate the problem of efficient representation of a large database of radar range profiles in order to minimize memory requirements and recognition search time, using time-frequency representation.

The paper is organized as follows. In a first step, the used synthetic RCS database of large aircrafts, in the HF-VHF frequency bands, is described. In a second step, after a brief review of the wavelet transform theory, the method of applying the wavelet transform to radar signal processing and the procedure to establish the compressed database will be described. In a third step, the identification algorithm and the data processing algorithm are presented. Finally, in a fourth step, the efficiency of multiresolution representations using wavelet transform are discussed regarding some criteria, like compression scores, false identification rate and search time.

II. DESCRIPTION OF SYNTHETIC RCS DATABASE

A. Introduction

The synthetic RCS database has been developed during the MOSAR project [START_REF] Barès | A multifrequency HF -VHF radar system for aircraft identification[END_REF][START_REF] Barès | Aircraft identification using RCS measurements in the low VHF band[END_REF] with the support of the French Ministry of Defence (DGA). The objectives of the MOSAR project are to improve knowledge of frequency response of targets in resonance region by measurements, and to test the efficiency of recognition methods. These studies led to:

• Development of a coherent, pulsed, quasi-monostatic, multifrequency, HF-VHF radar using the 20-80 MHz frequency band and the horizontal and vertical polarizations. • Development and validation of a simulated RCS database using numerical models of aircraft in the 20-80 MHz frequency band. • Development and the tests of NCTR algorithms.

B. Description of synthetic RCS database

To study aircraft RCS, several possibilities exist. One can perform:

• Anechoic chamber measurements on real aircrafts or scaled models. • In-flight measurements with a radar system.

• Simulations using a computational model. Anechoic chamber measurements are not well suited to collect data at various angle aspects of a target but they are useful to validate numerical models. To perform in-flight measurements, it is necessary to use a calibrated radar system and to wipe out propagation effects. The simulation of RCS behaviour, using a computational model, is a very attractive scheme but the model must be validated.

To be able to use a small computer like a PC, the analysis has been made with the free Numerical Electromagnetic Code NEC2 which is based on the Method of Moments (MoM). In this case, the aircraft structure is considered as Perfect Electric Conducting (PEC) body. An example of wiregrid model is presented at Fig. 1.

The synthetic database is constituted of eight aircrafts: Airbus A320, BAe 146-200, Boeing 727-200, 737-200, 737-300, 747-200, 757-200 and Fokker 100. For each aircraft, RCS has been determined as a function of frequency and angle aspect, using the following parameters:

• Frequency band: 20 to 100 MHz with a 1 MHz frequency step, • Azimuth angle: -10° to +190° with a step of 2°,

• Elevation angle: 0° to 90° with a step of 1°,

• Polarization: HH, HV, VH, VV.

Then, the range profile is estimated using an inverse Fourier transform from the RCS frequency response. The synthetic database is finally constituted of around 300 000 range profiles, on eight aircrafts [START_REF] David | Simulations and measurements of radar cross section of a Boeing 747 -200 in the 20 -60 MHz frequency band[END_REF][START_REF] David | Validation of heavy aircraft RCS simulations at very high frequencies[END_REF]. Fig. 2 shows an example of estimated range profile.

III. APPLICATION OF WAVELET TRANSFORM TO DATABASE

COMPRESSION

Wavelet transforms have been found useful in a variety of applications. This is because they provide the analyst with an approximation of the signal and a detail of the signal as well. For a complete description of wavelet analysis, the reader should refer to [START_REF] Mallat | A wavelet tour of signal processing[END_REF] and [START_REF] Mallat | A theory for multiresolution signal decomposition : The wavelet representation[END_REF]. A brief summary of how the wavelets were used is presented here. The Discrete Wavelet Transform (DWT) of finite sequences analyzes a signal S by decomposing it into approximation A i and details D i parts by quadrature filter systems [START_REF] Mallat | A theory for multiresolution signal decomposition : The wavelet representation[END_REF], where i is the decomposition level. Fig. 3 presents the scheme of the filter systems. An example of wavelet functions used in this paper for the DWT is shown in Fig. 4.

The approximation and detail parts are respectively obtained by a low-pass filter and a high-pass filter. At each level, filtering process is followed by decimation by 2 that decreases the data size. Fig. 5 presents an example of range profile and its wavelet decomposition computed in five levels.

The approximations and details at each level are preprocessed from the original signal and placed in the training data set.

IV. DATA PROCESSING ALGORITHM

A. Introduction

To test the efficiency of database compression using multiresolution representation, many criteria can be used:

• Compression scores,

• Probability of false classification (Pfc) as a function of Signal to Noise Ratio (SNR), • Minimum SNR to obtain a Pfc lower than 1 %,

• Search computational time (Sct) for a fixed SNR.

To determine these parameters, processing steps are the following: Loading of complete target database, selection of wavelet function, computation of compressed database on several decomposition levels, estimation of Pfc and Sct as a function of SNR.

B. Compression scores

The notion behind compression is based on the concept that the regular signal component can be accurately approximated using the following elements: a small number of approximation coefficients (at a suitably chosen level) and some of the detail coefficients.

The compression procedure contains three steps [START_REF] Misiti | Wavelet toolbox 4 -Users's guide[END_REF]:

• Decompose: Choose a wavelet, choose a level N, and compute the wavelet decomposition of the signal s at level N. • Threshold detail coefficients: For each level from 1 to N, a threshold is selected and thresholding is applied to the detail coefficients. • Reconstruct: Compute wavelet reconstruction using the original approximation coefficients of level N and the modified detail coefficients of levels from 1 to N.

Two parameters can be calculated to estimate the compression scores [START_REF] Misiti | Wavelet toolbox 4 -Users's guide[END_REF]:

• The retained energy E defined as:

2 100 (%) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ × = C CC E (1)
Where C are the coefficients of original signal, CC, the coefficients of current decomposition, and ||.||, the vector norm.

• The number of zeros NZ defined as: Where m i is the number of classification error, and n i , number of element in the class i.

NZ (%) =
The nearest neighbour algorithm [START_REF] Cover | Nearest neighbour pattern classification[END_REF] is used to recognize the target. It is a simple algorithm and is useful to use it to test the efficiency of database compression using multiresolution representation.

The distance used to find the nearest neighbour is the Euclidean distance d T k,r,s between the RCS magnitudes:

∑ = - = n i T i s r k i s r k T A A d 1 2 , , , , (4)
Where A T is the magnitude of unknown aircraft T, A k,r,s , the magnitude of database element (aircraft k, azimuth angle r, elevation angle s), i, the sample number, and n, the number of sample.

Then, minimal distances to each aircraft are computed and the nearest neighbour k T for the measure T is extracted like:

( ) s r k T s r k T d k , , , min arg = (5)

D. Signal to Noise Ratio

To see the effect of random noise, zero-mean white Gaussian noise has been added to the signal. The Signal to Noise Ratio is defined as: Where s i is the sampled signal, N, the length of the signal, and σ 2 , the variance of Gaussian noise.

E. Search computational time

In computing, to estimate the search computational time (Sct), a standard parameter is the number of MFLOPs. It's an acronym meaning "Million FLoating point OPerations". With this parameter, it is very easy to make a comparison between performances of different processing algorithms.

V. WAVELET APPLICATION TO TARGET RECOGNITION

A. Introduction

The multiresolution aspect of the wavelet decomposition is a solution to "compress" database because the target signature on each decomposition levels correspond to the measured signals with multiresolution radar. By the reduction of the number of samples, the use of low resolution decomposition level decreases the search computational time.

To evaluate the performances due to the use of decomposition levels with lower resolution, some parameters must be determined: Mother wavelets, optimum decomposition level, and classification parameter.

B. Selection of mother wavelets

Previous work [START_REF] Nelson | Iterative wavelet transformation and signal discrimination for HRR radar target recognition[END_REF] has shown that there is no statistically significant difference in performance of the classifier when different wavelets are chosen. To confirm this result, some tests have been realized using a great number of mother wavelets applied to compression techniques. The original signal is decomposed at level N and an adaptive threshold is applied on detail coefficients on each level from 1 to N [START_REF] Donoho | Threshold selection for wavelet shrinkage of noisy data[END_REF][START_REF] Birge | From model selection to adaptive estimation[END_REF]. The signal is then reconstructed using the approximation coefficients of level N and the modified detail coefficients of levels 1 to N. Fig. 6 shows an example of an original range profile and its compressed one. Differences between these range profiles can be observed.

Tab. I presents a resume of obtained results with different wavelets as a function of compression scores (retained energy E, number of zeros NZ). We can observe that the efficiency are very similar (80 % < NZ < 90 %, E > 95 %), but better performances are obtained with a hard threshold (retained energy is largest) due to a better agreement between original and compressed range profiles. A compromise must be found between E and NZ. This means that the simplest wavelet to implement will do as good a job as any other wavelet, at least for the high resolution radar target recognition problem. Finally, Fig. 8 presents the minimum SNR to obtain a probability of false classification Pfc lower than 1 %, as a function of decomposition level. We observe an important increase of the SNR for a level decomposition larger to 2. This characteristic can be used to make de-noising procedure on measured radar signals.

C. Determination of optimum decomposition level

Determination of the optimum decomposition level is a sensitive parameter because the resolution decrease has a smoothing effect on the target signature and eliminates the identifiable scatterers. Fig. 5 presents an example of range profile and its wavelet decomposition computed in five levels.

In theory, a maximum possible number J of scales can be considered for a signal composed of N = 2 J samples. In practice, the maximum decomposition level can be chosen using a criterion characterizing the smoothing effect on scatterers.

To evaluate the maximum decomposition level, a similarity measure, like intercorrelation, between the original set of vector samples and the approximations on each level resampled on the finest resolution can be realized (Fig. 9). We can observed a good correlation, larger than 0.9, for a maximum decomposition level equal to 4.

D. Selection of the classification parameter

NCTR association can be made on the different decomposition levels using the "approximation" signatures but also on the "detail" signatures. But in this case, the classification time gain is the same than previously due to the same size of data vectors. Fig. 13 presents the variation of the minimum SNR to obtain a Pfc lower than 1 %, as a function of decomposition level for a classification using detail or approximation signals.

Minimum SNR (dB)

Better results are obtained with the approximation signals.

A 1 dB difference is approximately observed for a fixed probability of false classification.

VI. COMMENTS AND CONCLUSION

The objective of this paper is to evaluate the efficiency of multiscale algorithm to minimize the computational search time to NCTR association. The wavelet transform is one solution to this problem, because it is suitable to the representation of radar returns as a function of decomposition levels corresponding to signals measured by a multiresolution radar system.

No significant difference in performance of the classifier is observed when different wavelets are chosen. This means that the simplest wavelet to implement will do as good a job as any other wavelet, at least for the high resolution radar target recognition problem.

NCTR procedure can be made on the different decomposition levels using the "approximation" or the "detail" signatures. A same decrease of the estimated probability of false classification can be observed but better results are obtained with the approximation signals. To have the same probability of false classification, signal to noise ratio must be increased by a factor of 1 to 11 dB as a function of the decomposition level. In this case, the computational search time is respectively decreased by a factor of 1.9 to 10.

ACKNOWLEDGMENT

The author thanks THALES Air Systems and the French Ministry of Defence for their support to this study.

Figure 1 .

 1 Figure 1. Example of modeling aircraft using a wiregrid model -Airbus A320.

Figure 2 .

 2 Figure 2. Example of estimated range profile -Airbus A320 -HH Polarisation.

Figure 3 .

 3 Figure 3. Filter systems of the wavelet transform (where S is the signal, A i , the approximations, D i , the details, and i, the decomposition level).

Figure 4 .Figure 5 .

 45 Figure 4. Example of wavelet functions used in 1-D discrete wavelet transforms -Daubechies family wavelets [10].

  100 × Number of zeros of the decomposition Number of coefficients (2) C. Probability of false classification Probability of false classification Pfc is defined for M target classes as:

Figure 6 .

 6 Figure 6. Example of original range profile and compressed range profile using Haar wavelet and hard threshold until decomposition level 4.

  Thus, in the next sections, three wavelets have been chosen: Haar, Daubechies 2 and biorthogonal 3.1. Fig.7presents an estimation of Pfc as a function SNR for different wavelets. Results are very similar whatever the wavelet families.

Figure 7 .Figure 8 .

 78 Figure 7. Probability of false classification Pfc as a function SNR for three different wavelets (Haar, Daubechies 2, biorthogonal 3.1) using an adaptative hard threshold and a decomposition until level 4.

Figure 9 .Figure 10 .

 910 Figure 9. Intercorrelation between the original set of vector samples and the approximations as a function of level decomposition.

Fig. 10

 10 Fig. 10 and 11 present respectively, the results of Pfc as a function of SNR, and the minimum SNR to obtain a Pfc lower than 1 %, as a function of decomposition level.Smoothing effects on target signature as a function of decomposition level increases the probability of false classification Pfc and to preserve a maximum Pfc of 1 %, SNR must be increased of 11 dB. In compensation, search time (Sct) is decreased by a factor of 10 (Fig.12).

Figure 11 .Figure 12 .

 1112 Figure 11. Variation of minimum SNR to obtain a Pfc < 1 % as a function of level decomposition, using Haar wavelet and approximation signals.

Figure 13 .

 13 Figure 13. Variation of minimum SNR to obtain a Pfc < 1 % as a function of level decomposition, using Haar wavelet and approximation and details signals.

TABLE I .

 I COMPRESSION SCORES AS A FUNCTION OF WAVELETS AND THRESHOLD UNTIL DECOMPOSITION LEVEL 4.

		Number of zeros (NZ)	Retained energy (E)
	Wavelet	Hard	Soft	Hard	Soft
		threshold	threshold	threshold	threshold
	Haar	89.06	89.06	95.99	89.24
	Daubechies 2	88.3	88.3	95.65	82.84
	Daubechies 6	84.89	84.89	98.67	91.33
	Daubechies 10	82.37	82.37	98.2	82.37
	Biorthogonal 3.1	88.3	88.3	99.53	96.83
	Biorthogonal 5.5	84.89	84.89	97.88	92.71
	Reverse biorthogonal 2.4	85.47	85.47	98.13	90.16
	Reverse biorthogonal 5.5	84.89	84.89	98.24	92.83
	Coiflets 4	81.21	81.21	99.33	95.98
	Symlets 2	88.3	88.3	95.65	82.84
	Symlets 6	84.39	84.39	98.5	91.7