Enhancing brain-computer interfacing through advanced independent component analysis techniques

A Brain-computer interface (BCI) is a direct communication system between a brain and an external device in which messages or commands sent by an individual do not pass through the brain’s normal output pathways but is detected through brain signals. Some severe motor impairments, such as Amyothrophic Lateral Sclerosis, head trauma, spinal injuries and other diseases may cause the patients to lose their muscle control and become unable to communicate with the outside environment. Currently no effective cure or treatment has yet been found for these diseases. Therefore using a BCI system to rebuild the communication pathway becomes a possible alternative solution. Among different types of BCIs, an electroencephalogram (EEG) based BCI is becoming a popular system due to EEG’s fine temporal resolution, ease of use, portability and low set-up cost. However EEG’s susceptibility to noise is a major issue to develop a robust BCI. Signal processing techniques such as coherent averaging, filtering, FFT and AR modelling, etc. are used to reduce the noise and extract components of interest. However these methods process the data on the observed mixture domain which mixes components of interest and noise. Such a limitation means that extracted EEG signals possibly still contain the noise residue or coarsely that the removed noise also contains part of EEG signals embedded. Independent Component Analysis (ICA), a Blind Source Separation (BSS) technique, is able to extract relevant information within noisy signals and separate the fundamental sources into the independent components (ICs). The most common assumption of ICA method is that the source signals are unknown and statistically independent. Through this assumption, ICA is able to recover the source signals. Since the ICA concepts appeared in the fields of neural networks and signal processing in the 1980s, many ICA applications in telecommunications, biomedical data analysis, feature extraction, speech separation, time-series analysis and data mining have been reported in the literature. In this thesis several ICA techniques are proposed to optimize two major issues for BCI applications: reducing the recording time needed in order to speed up the signal processing and reducing the number of recording channels whilst improving the final classification performance or at least with it remaining the same as the current performance. These will make BCI a more practical prospect for everyday use. This thesis first defines BCI and the diverse BCI models based on different control patterns. After the general idea of ICA is introduced along with some modifications to ICA, several new ICA approaches are proposed. The practical work in this thesis starts with the preliminary analyses on the Southampton BCI pilot datasets starting with basic and then advanced signal processing techniques. The proposed ICA techniques are then presented using a multi-channel event related potential (ERP) based BCI. Next, the ICA algorithm is applied to a multi-channel spontaneous activity based BCI. The final ICA approach aims to examine the possibility of using ICA based on just one or a few channel recordings on an ERP based BCI. The novel ICA approaches for BCI systems presented in this thesis show that ICA is able to accurately and repeatedly extract the relevant information buried within noisy signals and the signal quality is enhanced so that even a simple classifier can achieve good classification accuracy. In the ERP based BCI application, after multichannel ICA the data just applied to eight averages/epochs can achieve 83.9% classification accuracy whilst the data by coherent averaging can reach only 32.3% accuracy. In the spontaneous activity based BCI, the use of the multi-channel ICA algorithm can effectively extract discriminatory information from two types of singletrial EEG data. The classification accuracy is improved by about 25%, on average, compared to the performance on the unpreprocessed data. The single channel ICA technique on the ERP based BCI produces much better results than results using the lowpass filter. Whereas the appropriate number of averages improves the signal to noise rate of P300 activities which helps to achieve a better classification. These advantages will lead to a reliable and practical BCI for use outside of the clinical laboratory

Proposals and Comparisons from One-Sensor EEG and EOG Human-Machine Interfaces

[Abstract] Human-Machine Interfaces (HMI) allow users to interact with different devices such as computers or home elements. A key part in HMI is the design of simple non-invasive interfaces to capture the signals associated with the user’s intentions. In this work, we have designed two different approaches based on Electroencephalography (EEG) and Electrooculography (EOG). For both cases, signal acquisition is performed using only one electrode, which makes placement more comfortable compared to multi-channel systems. We have also developed a Graphical User Interface (GUI) that presents objects to the user using two paradigms—one-by-one objects or rows-columns of objects. Both interfaces and paradigms have been compared for several users considering interactions with home elements.Xunta de Galicia; ED431C 2020/15Xunta de Galicia; ED431G2019/01Agencia Estatal de Investigación de España; RED2018-102668-TAgencia Estatal de Investigación de España; PID2019-104958RB-C42Xunta de Galicia; ED481A-2018/156This work has been funded by the Xunta de Galicia (by grant ED431C 2020/15, and grant ED431G2019/01 to support the Centro de Investigación de Galicia “CITIC”), the Agencia Estatal de Investigación of Spain (by grants RED2018-102668-T and PID2019-104958RB-C42) and ERDF funds of the EU (FEDER Galicia & AEI/FEDER, UE); and the predoctoral Grant No. ED481A-2018/156 (Francisco Laport

Incorporation of a language model into a brain computer interface based speller

Brain computer interface (BCI) research deals with the problem of establishing direct communication pathways between the brain and external devices. The primary motivation is to enable patients with limited or no muscular control to use external devices by automatically interpreting their intent based on brain electrical activity, measured by, e.g., electroencephalography (EEG). The P300 speller is a widely practised BCI set up that involves having subjects type letters based on P300 signals generated by their brains in response to visual stimuli. Because of the low signal-to-noise ratio (SNR) and variability of EEG signals, existing typing systems use many repetitions of the visual stimuli in order to increase accuracy at the cost of speed. The main motivation for the work in this thesis comes from the observation that the prior information provided by both neighbouring and current letters within words in a particular language can assist letter estimation with the aim of developing a system that achieves higher accuracy and speed simultaneously. Based on this observation, in this thesis, we present an approach for incorporation of such information into a BCI-based speller through Hidden Markov Models (HMM) trained by a language model. We then describe filtering and smoothing algorithms in conjunction with n-gram language models for inference over such a model. We have designed data collection experiments for offline and online decision-making which demonstrate that incorporation of the language model in this manner results in significant improvements in letter estimation and typing speed

Novas estratégias de pré-processamento, extração de atributos e classificação em sistemas BCI

Orientador: Romis Ribeiro de Faissol AttuxTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: As interfaces cérebro-computador (BCIs) visam controlar um dispositivo externo, utilizando diretamente os sinais cerebrais do usuário. Tais sistemas requerem uma série de etapas para processar e extrair atributos relevantes dos sinais observados para interpretar correta e eficientemente as intenções do usuário. Embora o campo tenha se desenvolvido continuamente e algumas dificuldades tenham sido superadas, ainda é necessário aumentar a capacidade de uso, melhorando sua capacidade de classificação e aumentando a confiabilidade de sua resposta. O objetivo clássico da pesquisa de BCI é apoiar a comunicação e o controle para usuários com comunicação prejudicada devido a doenças ou lesões. Aplicações típicas das BCI são a operação de cursores de interface, programas de escrita de texto ou dispositivos externos, como cadeiras de rodas, robôs e diferentes tipos de próteses. O usuário envia informações moduladas para a BCI, realizando tarefas mentais que produzem padrões cerebrais distintos. A BCI adquire sinais do cérebro do usuário e os traduz em comunicação adequada. Esta tese tem como objetivo desenvolver uma comunicação BCI não invasiva mais rápida e confiável baseada no estudo de diferentes técnicas que atuam nas etapas de processamento do sinal, considerando dois aspectos principais, a abordagem de aprendizado de máquina e a redução da complexidade na tarefa de aprendizado dos padrões mentais pelo usuário. A pesquisa foi focada em dois paradigmas de BCI, Imagética Motora (IM) e o potencial relacionado ao evento P300. Algoritmos de processamento de sinais para a detecção de ambos os padrões cerebrais foram aplicados e avaliados. O aspecto do pré-processamento foi a primeira perspectiva estudada, considerando como destacar a resposta dos fenômenos cerebrais, em relação ao ruído e a outras fontes de informação que talvez distorçam o sinal de EEG; isso em si é um passo que influenciará diretamente a resposta dos seguintes blocos de processamento e classificação. A Análise de Componente Independente (ICA) foi usada em conjunto com métodos de seleção de atributos e diferentes classificadores para separar as fontes originais relacionadas à dessincronização produzida pelo fenômeno de IM; esta foi uma tentativa de criar um tipo de filtro espacial que permitisse o sinal ser pré-processado, reduzindo a influência do ruído. Além disso, os resultados dos valores de classificação foram analisados considerando a comparação com métodos padrão de pré-processamento, como o filtro CAR. Os resultados mostraram que é possível separar os componentes relacionados à atividade motora. A proposta da ICA, em média, foi 4\% mais alta em porcentagem de precisão de classificação do que os resultados obtidos usando o CAR, ou quando nenhum filtro foi usado. O papel dos métodos que estudam a conectividade de diferentes áreas do cérebro foi avaliado como a segunda contribuição deste trabalho; Isso permitiu considerar aspectos que contemplam a complexidade da resposta cerebral de um usuário. A área da BCI precisa de uma interpretação mais profunda do que acontece no nível do cérebro em vários dos fenômenos estudados. A técnica utilizada para construir grafos de conectividade funcional foi a correntropia, esta medida foi utilizada para quantificar a similaridade; uma comparação foi feita usando também, as medidas de correlação de Spearman e Pearson. A conectividade funcional relaciona diferentes áreas do cérebro analisando sua atividade cerebral, de modo que o estudo do grafo foi avaliado utilizando três medidas de centralidade, onde a importância de um nó na rede é medida. Também, dois tipos de classificadores foram testados, comparando os resultados no nível de precisão de classificação. Em conclusão, a correntropia pode trazer mais informações para o estudo da conectividade do que o uso da correlação simples, o que trouxe melhorias nos resultados da classificação, especialmente quando ela foi utilizada com o classificador ELM. Finalmente, esta tese demonstra que os BCIs podem fornecer comunicação efetiva em uma aplicação onde a predição da resposta de classificação foi modelada, o que permitiu a otimização dos parâmetros do processamento de sinal realizado usando o filtro espacial xDAWN e um classificador FLDA para o problema do speller P300, buscando a melhor resposta para cada usuário. O modelo de predição utilizado foi Bayesiano e confirmou os resultados obtidos com a operação on-line do sistema, permitindo otimizar os parâmetros tanto do filtro quanto do classificador. Desta forma, foi visto que usando filtros com poucos canais de entrada, o modelo otimizado deu melhores resultados de acurácia de classificação do que os valores inicialmente obtidos ao treinar o filtro xDAWN para os mesmos casos. Os resultados obtidos mostraram que melhorias nos métodos do transdutor BCI, no pré-processamento, extração de características e classificação constituíram a base para alcançar uma comunicação BCI mais rápida e confiável. O avanço nos resultados da classificação foi obtido em todos os casos, comparado às técnicas que têm sido amplamente utilizadas e já mostraram eficácia para esse tipo de problema. No entanto, ainda há aspectos a considerar da resposta dos sujeitos para tipos específicos de paradigmas, lembrando que sua resposta pode variar ao longo de diferentes dias e as implicações reais disso na definição e no uso de diferentes métodos de processamento de sinalAbstract: Brain-computer interfaces (BCIs) aim to control an external device by directly employing user's brain signals. Such systems require a series of steps to process and extract relevant features from the observed signals to correctly and efficiently interpret the user's intentions. Although the field has been continuously developing and some difficulties have been overcome, it is still necessary to increase usability by enhancing their classification capacity and increasing the reliability of their response. The classical objective of BCI research is to support communication and control for users with impaired communication due to illness or injury. Typical BCI applications are the operation of interface cursors, spelling programs or external devices, such as wheelchairs, robots and different types of prostheses. The user sends modulated information to the BCI by engaging in mental tasks that produce distinct brain patterns. The BCI acquires signals from the user¿s brain and translates them into suitable communication. This thesis aims to develop faster and more reliable non-invasive BCI communication based on the study of different techniques that serve in the signal processing stages, considering two principal aspects, the machine learning approach, and the reduction of the complexity in the task of learning the mental patterns by the user. Research was focused on two BCI paradigms, Motor Imagery (MI) and the P300 event related potential (ERP). Signal processing algorithms for the detection of both brain patterns were applied and evaluated. The aspect of the pre-processing was the first perspective studied to consider how to highlight the response of brain phenomena, in relation to noise and other sources of information that maybe distorting the EEG signal; this in itself is a step that will directly influence the response of the following blocks of processing and classification. The Independent Component Analysis (ICA) was used in conjunction with feature selection methods and different classifiers to separate the original sources that are related to the desynchronization produced by MI phenomenon; an attempt was made to create a type of spatial filter that pre-processed the signal, reducing the influence of the noise. Furthermore, some of the classifications values were analyzed considering comparison when used other standard pre-processing methods, as the CAR filter. The results showed that it is possible to separate the components related to motor activity. The ICA proposal on average were 4\% higher in percent of classification accuracy than those obtained using CAR, or when no filter was used. The role of methods that study the connectivity of different brain areas were evaluated as the second contribution of this work; this allowed to consider aspects that contemplate the complexity of the brain response of a user. The area of BCI needs a deeper interpretation of what happens at the brain level in several of the studied phenomena. The technique used to build functional connectivity graphs was correntropy, this quantity was used to measure similarity, a comparison was made using also, the Spearman and Pearson correlation. Functional connectivity relates different brain areas activity, so the study of the graph was evaluated using three measures of centrality of graph, where the importance of a node in the network is measured. In addition, two types of classifiers were tested, comparing the results at the level of classification precision. In conclusion, the correntropy can bring more information for the study of connectivity than the use of the simple correlation, which brought improvements in the classification results especially when it was used with the ELM classifier. Finally, this thesis demonstrates that BCIs can provide effective communication in an application where the prediction of the classification response was modeled, which allowed the optimization of the parameters of the signal processing performed using the xDAWN spatial filter and a FLDA classifier for the problem of the P300 speller, seeking the best response for each user. The prediction model used was Bayesian and confirmed the results obtained with the on-line operation of the system, thus allowing to optimize the parameters of both the filter and the classifier. In this way it was seen that using filters with few inputs the optimized model gave better results of acuraccy classification than the values initially obtained when the training ofthe xDAWN filter was made for the same cases. The obtained results showed that improvements in the BCI transducer, pre-processing, feature extraction and classification methods constituted the basis to achieve faster and more reliable BCI communication. The advance in the classification results were obtained in all cases, compared to techniques that have been widely used and had already shown effectiveness for this type of problemsDoutoradoEngenharia de ComputaçãoDoutora em Engenharia Elétrica153311/2014-2CNP

Multi-channel extraction methods for event-related potentials

Event-related potentials (ERPs) are neural activities that are generated in response to an event. In recent decades, multi-channel EEG recordings have been increasingly adopted in ERP studies. In this thesis, to extract an ERP-of-interest, single-trial multi-channel extraction methods have been developed. The developed methods are data-driven and thus avoid human intervention during ERP analyses. For this reason, they are also practical for real-time applications such as brain-computer interface (BCI)

Spatio-Temporal Approaches to Denoising and Feature Extraction in Rapid Image Triage

Ph.DDOCTOR OF PHILOSOPH

Probabilistic Graphical Models for ERP-Based Brain Computer Interfaces

An event related potential (ERP) is an electrical potential recorded from the nervous system of humans or other animals. An ERP is observed after the presentation of a stimulus. Some examples of the ERPs are P300, N400, among others. Although ERPs are used very often in neuroscience, its generation is not yet well understood and different theories have been proposed to explain the phenomena. ERPs could be generated due to changes in the alpha rhythm, an internal neural control that reset the ongoing oscillations in the brain, or separate and distinct additive neuronal phenomena. When different repetitions of the same stimuli are averaged, a coherence addition of the oscillations is obtained which explain the increase in amplitude in the signals. Two ERPs are mostly studied: N400 and P300. N400 signals arise when a subject tries to make semantic operations that support neural circuits for explicit memory. N400 potentials have been observed mostly in the rhinal cortex. P300 signals are related to attention and memory operations. When a new stimulus appears, a P300 ERP (named P3a) is generated in the frontal lobe. In contrast, when a subject perceives an expected stimulus, a P300 ERP (named P3b) is generated in the temporal – parietal areas. This implicates P3a and P3b are related, suggesting a circuit pathway between the frontal and temporal–parietal regions, whose existence has not been verified. Un potencial relacionado con un evento (ERP) es un potencial eléctrico registrado en el sistema nervioso de los seres humanos u otros animales. Un ERP se observa tras la presentación de un estímulo. Aunque los ERPs se utilizan muy a menudo en neurociencia, su generación aún no se entiende bien y se han propuesto diferentes teorías para explicar el fenómeno. Una interfaz cerebro-computador (BCI) es un sistema de comunicación en el que los mensajes o las órdenes que un sujeto envía al mundo exterior proceden de algunas señales cerebrales en lugar de los nervios y músculos periféricos. La BCI utiliza ritmos sensorimotores o señales ERP, por lo que se necesita un clasificador para distinguir entre los estímulos correctos y los incorrectos. En este trabajo, proponemos utilizar modelos probabilísticos gráficos para el modelado de la dinámica temporal y espacial de las señales cerebrales con aplicaciones a las BCIs. Los modelos gráficos han sido seleccionados por su flexibilidad y capacidad de incorporar información previa. Esta flexibilidad se ha utilizado anteriormente para modelar únicamente la dinámica temporal. Esperamos que el modelo refleje algunos aspectos del funcionamiento del cerebro relacionados con los ERPs, al incluir información espacial y temporal.DoctoradoDoctor en Ingeniería Eléctrica y Electrónic

Bayesian machine learning applied in a brain-computer interface for disabled users

A brain-computer interface (BCI) is a system that enables control of devices or communication with other persons, only through cerebral activity, without using muscles. The main application for BCIs is assistive technology for disabled persons. Examples for devices that can be controlled by BCIs are artificial limbs, spelling devices, or environment control systems. BCI research has seen renewed interest in recent years, and it has been convincingly shown that communication via a BCI is in principle feasible. However, present day systems still have shortcomings that prevent their widespread application. In part, these shortcomings are caused by limitations in the functionality of the pattern recognition algorithms used for discriminating brain signals in BCIs. Moreover, BCIs are often tested exclusively with able-bodied persons instead of conducting tests with the target user group, namely disabled persons. The goal of this thesis is to extend the functionality of pattern recognition algorithms for BCI systems and to move towards systems that are helpful for disabled users. We discuss extensions of linear discriminant analysis (LDA), which is a simple but efficient method for pattern recognition. In particular, a framework from Bayesian machine learning, the so-called evidence framework, is applied to LDA. An algorithm is obtained that learns classifiers quickly, robustly, and fully automatically. An extension of this algorithm allows to automatically reduce the number of sensors needed for acquisition of brain signals. More specifically, the algorithm allows to perform electrode selection. The algorithm for electrode selection is based on a concept known as automatic relevance determination (ARD) in Bayesian machine learning. The last part of the algorithmic development in this thesis concerns methods for computing accurate estimates of class probabilities in LDA-like classifiers. These probabilities are used to build a BCI that dynamically adapts the amount of acquired data, so that a preset, approximate bound on the probability of misclassifications is not exceeded. To test the algorithms described in this thesis, a BCI specifically tailored for disabled persons is introduced. The system uses electroencephalogram (EEG) signals and is based on the P300 evoked potential. Datasets recorded from five disabled and four able-bodied subjects are used to show that the Bayesian version of LDA outperforms plain LDA in terms of classification accuracy. Also, the impact of different static electrode configurations on classification accuracy is tested. In addition, experiments with the same datasets demonstrate that the algorithm for electrode selection is computationally efficient, yields physiologically plausible results, and improves classification accuracy over static electrode configurations. The classification accuracy is further improved by dynamically adapting the amount of acquired data. Besides the datasets recorded from disabled and able-bodied subjects, benchmark datasets from BCI competitions are used to show that the algorithms discussed in this thesis are competitive with state-of-the-art electroencephalogram (EEG) classification algorithms. While the experiments in this thesis are uniquely performed with P300 datasets, the presented algorithms might also be useful for other types of BCI systems based on the EEG. This is the case because functionalities such as robust and automatic computation of classifiers, electrode selection, and estimation of class probabilities are useful in many BCI systems. Seen from a more general point of view, many applications that rely on the classification of cerebral activity could possibly benefit from the methods developed in this thesis. Among the potential applications are interrogative polygraphy ("lie detection") and clinical applications, for example coma outcome prognosis and depth of anesthesia monitoring

EEG Signal Processing in Motor Imagery Brain Computer Interfaces with Improved Covariance Estimators

Desde hace unos años hasta la actualidad, el desarrollo en el campo de los interfaces cerebro ordenador ha ido aumentando. Este aumento viene motivado por una serie de factores distintos. A medida que aumenta el conocimiento acerca del cerebro humano y como funciona (del que aún se conoce relativamente poco), van surgiendo nuevos avances en los sistemas BCI que, a su vez, sirven de motivación para que se investigue más acerca de este órgano. Además, los sistemas BCI abren una puerta para que cualquier persona pueda interactuar con su entorno independientemente de la discapacidad física que pueda tener, simplemente haciendo uso de sus pensamientos. Recientemente, la industria tecnológica ha comenzado a mostrar su interés por estos sistemas, motivados tanto por los avances con respecto a lo que conocemos del cerebro y como funciona, como por el uso constante que hacemos de la tecnología en la actuali- dad, ya sea a través de nuestros smartphones, tablets u ordenadores, entre otros muchos dispositivos. Esto motiva que compañías como Facebook inviertan en el desarrollo de sistemas BCI para que tanto personas sin discapacidad como aquellas que, si las tienen, puedan comunicarse con los móviles usando solo el cerebro. El trabajo desarrollado en esta tesis se centra en los sistemas BCI basados en movimien- tos imaginarios. Esto significa que el usuario piensa en movimientos motores que son interpretados por un ordenador como comandos. Las señales cerebrales necesarias para traducir posteriormente a comandos se obtienen mediante un equipo de EEG que se coloca sobre el cuero cabelludo y que mide la actividad electromagnética producida por el cere- bro. Trabajar con estas señales resulta complejo ya que son no estacionarias y, además, suelen estar muy contaminadas por ruido o artefactos. Hemos abordado esta temática desde el punto de vista del procesado estadístico de la señal y mediante algoritmos de aprendizaje máquina. Para ello se ha descompuesto el sistema BCI en tres bloques: preprocesado de la señal, extracción de características y clasificación. Tras revisar el estado del arte de estos bloques, se ha resumido y adjun- tado un conjunto de publicaciones que hemos realizado durante los últimos años, y en las cuales podemos encontrar las diferentes aportaciones que, desde nuestro punto de vista, mejoran cada uno de los bloques anteriormente mencionados. De manera muy resumida, para el bloque de preprocesado proponemos un método mediante el cual conseguimos nor- malizar las fuentes de las señales de EEG. Al igualar las fuentes efectivas conseguimos mejorar la estima de las matrices de covarianza. Con respecto al bloque de extracción de características, hemos conseguido extender el algoritmo CSP a casos no supervisados. Por último, en el bloque de clasificación también hemos conseguido realizar una sepa- ración de clases de manera no supervisada y, por otro lado, hemos observado una mejora cuando se regulariza el algoritmo LDA mediante un método específico para Gaussianas.The research and development in the field of Brain Computer Interfaces (BCI) has been growing during the last years, motivated by several factors. As the knowledge about how the human brain is and works (of which we still know very little) grows, new advances in BCI systems are emerging that, in turn, serve as motivation to do more re- search about this organ. In addition, BCI systems open a door for anyone to interact with their environment regardless of the physical disabilities they may have, by simply using their thoughts. Recently, the technology industry has begun to show its interest in these systems, mo- tivated both by the advances about what we know of the brain and how it works, and by the constant use we make of technology nowadays, whether it is by using our smart- phones, tablets or computers, among many other devices. This motivates companies like Facebook to invest in the development of BCI systems so that people (with or without disabilities) can communicate with their devices using only their brain. The work developed in this thesis focuses on BCI systems based on motor imagery movements. This means that the user thinks of certain motor movements that are in- terpreted by a computer as commands. The brain signals that we need to translate to commands are obtained by an EEG device that is placed on the scalp and measures the electromagnetic activity produced by the brain. Working with these signals is complex since they are non-stationary and, in addition, they are usually heavily contaminated by noise or artifacts. We have approached this subject from the point of view of statistical signal processing and through machine learning algorithms. For this, the BCI system has been split into three blocks: preprocessing, feature extraction and classification. After reviewing the state of the art of these blocks, a set of publications that we have made in recent years has been summarized and attached. In these publications we can find the different contribu- tions that, from our point of view, improve each one of the blocks previously mentioned. As a brief summary, for the preprocessing block we propose a method that lets us nor- malize the sources of the EEG signals. By equalizing the effective sources, we are able to improve the estimation of the covariance matrices. For the feature extraction block, we have managed to extend the CSP algorithm for unsupervised cases. Finally, in the classification block we have also managed to perform a separation of classes in an blind way and we have also observed an improvement when the LDA algorithm is regularized by a specific method for Gaussian distributions