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Clasificación de señales EEG usando LDA y QDA aplicado a una Interface Cerebro – Computador basada en P300

Classification of EEG signals using LDA and= QDA applied to a Brain – Computer Interface based on P300

Franklin Cabezas1 *, Fermí= ;n Cabezas1

1 Facul= tad de Ingeniería Eléctrica y Electrónica, Universidad Nacion= al de Ingeniería, Av. Túpac Amaru 210, Lima, Perú.=

Recibido (Received= ): 22/12/2018           &= nbsp;          Aceptado (Accepted): 17/02/2018<= /o:p>

RESUME= N

Se han empleado diferentes técnicas de Machine Learning<= /span> con la finalidad de identificar las voluntades de pacientes con enfermedades neurodegenerativas. Para tal fin se empleó una base de datos de señales electroencefalográficas (= EEG) las cuales fueron filtradas y procesadas. La determinación de las voluntades de los pacientes se consiguió a través de la identificación de las ondas cerebrales P300, estas señales se presentan en el cerebro como respuesta a un estímulo inesperado y en= tre sus muchas aplicaciones se encuentra la implementación de la llamada Interface Cerebro – Computador.

La etapa de pre procesamiento de las señale= s se consiguió mediante el filtrado de las mismas, empleando un Filtro Digital Butterworth de Sexto Orden, así = como mediante técnicas de Submuestreo, Windsorizing y Escalamiento. Adicionalmente, para efe= ctos de reducción de dimensionalidad de las señales, se empleó la técnica de Análisis de Componentes Principales (PCA). Finalmente, para efectuar la clasificación de señales y determinar si estas contienen o no ondas P300, se emplearon las técnicas de Análisis Discriminan= te Lineal (LDA), Análisis Discriminante Cuadrático (QDA) y Coeficiente de Correlación de Pearson.
Los resultados obtenidos muestran que las técnicas propuestas consig= uen determinar eficientemente las voluntades de los pacientes, alcanzando una t= asa de clasificación de 86% al usar LDA. Estos resultados fueron validad= os con los datos proporcionados en la base de datos.

Palabras Clave: P300, Machine Learning, Interface Cerebro – Computador, Enfermedades Neurodegenerativas

 

ABSTRACT<= /o:p>

 

Different Machine Learning techniques have been used in order to identify t= he wishes of patients with neurodegenerative diseases. For this purpose, a database of electroencephalographic (EEG) signals was u= sed, which were filtered and processed. The determination of the wills of patien= ts was achieved through the identification of P300 brain waves, these signals = are presented in the brain in response to an unexpected stimulus and among its = many applications is the implementation of the

so-called<= /span> Brain Computer Interface.

The stage of pre-processing of= the signals was achieved by filtering them, using a = Sixth Order Butterworth Digital Filter, as well as by Subsampling, Windsorizing and Scaling techniques. Additionally, for reducing the dimensionality of the signals, the technique of Principal Component Analysis (PCA) was used. Finally, to p= erform the classification of signals and determine if they contain P300 waves or n= ot, the techniques of Linear Discriminant Analysis (LDA), Quadratic Discriminan= t Analysis (QDA) and Pearson’s Correlation Coefficient were = used. The results obtained show that the proposed techniques efficiently determine the wills of patients, reaching a classification rate of 86% when using LDA. These results were validated with the data provi= ded in the database.

Keywords: = P300, Machine Learning, Brain – Computer Interface, Neurodegenerative Disea= ses

______________________________________________________________= _________________________________________________________=

 


1.      = INTRODUCCIÓ= N

 

      Cada a&ntil= de;o millones de personas en el mundo se ven afectadas por diversos males neurodegenerativos que conllevan a severas discapacidades motrices.


*Corresponding author:
E-mail: fcabezash@uni.pe  

 

      Enfermedades tales como la esclerosis lateral a= miotrófica, la esclerosis múltiple o la enfermedad de Huntington, conllevan a limitaciones permanentes de las vías nerviosas, las cuales est&aacut= e;n designadas al control de los músculos implicados en la ejecuci&oacut= e;n voluntaria de los movimientos. Como consecuencia de estos males, muchas de estas personas quedan prácticamente aisladas de su entorno.

      En el Perú, aproximadamente 700.000 personas sufren alguna enfermedad neurodegenerativa, cifra que representa más del 2% de la población nacional [1].

 

      En los últimos 30 años se ha venido desarrollando una tecnolog&iacut= e;a llamada Interface Cerebro – Computador (BCI), la cual utiliza señales cerebrales para establecer una ruta de comunicación e= ntre una persona y un dispositivo externo. Esta tecnología permite a los pacientes comunicarse, desplazarse o activar y/o controlar dispositivos de = su entorno.

 

      Entre las m= uchas señales cerebrales, existen un grupo que pueden ser empleadas como señales de control en sistemas BCI, tales como: Potenciales evocados visuales, potenciales corticales lentos, ritmos sensor= iomotores y los potenciales evocados cognitivos. La onda P300 es un potencial evocado= que se manifiesta aproximadamente 300 ms después de la presentació= ;n de un estímulo inesperado, sea este visual, audible o somatosensorial, en la Figura 1 se observa una típica onda P300.

Figura 1. Onda P300 [1].

 

            Farwell y Donchin (1988) = fueron los primeros en emplear el P300 como señal de control en una Interfaz Cerebro – Computador. Describieron el sistema de deletreo P300, una matriz de 6 x 6 que contenía las letras del alfabeto y otros símbolos que se mostraban en una pantalla de computadora, lo que permitía a los pacientes formar palabras y comunicarse.

 

      En este tra= bajo se empleó la base de datos generada por Hoffman= n et al. [2] quienes emplearon un paradigma P300 de seis opciones, que se probó utilizando una población de cinco personas discapacitad= as y cuatro personas sanas. En su experimentación emplearon seis imágenes que destellaban en una pantalla de forma aleatoria con un intervalo de estímulo de 400 ms. Se probaron configuraciones de electrodos que consistían en cuatro, ocho, dieciséis y treint= a y dos. Para clasificar las señales cerebrales se emplearon el Análisis Discriminante Lineal Bayesiano (BLDA) y el Análisis Discriminante Lineal de Fisher (FLDA).

 

      En la Figur= a 2 se observa una recreación de la experimentación realizada por Hoffman et al. para la adquisición de las señales electroencefalográficas.<= o:p>

Figura 2. Paciente contando mentalmente el número de destellos de la imagen solicitada mientras sus seña= les cerebrales son registradas.

 

2.      METODOLOGÍA=

 

      Dado que las señales cerebrales presentan un alto nivel de ruido, es necesario aplicar distintas técnicas de pre procesamiento:

 

      Extracci&oa= cute;n de componente referencial: Entre el grupo de electrodos empleados para capt= ar las señales cerebrales de los participantes, dos de ellos fueron ubicados en la región de las apófisis mastoides, esta región permite captar con mayor sensibilidad ciertos ruidos biológicos. Por tanto a cada señal cerebral se le sustrajo el promedio de las señales medidas por estos dos electrodos.=

 

      Filtrado: D= ado que los electrodos, además de captar las señales de interés, captan también abundantes señales ruidosas, es necesario restringir la banda de frecuencias a un intervalo en el cual sea más probable encontrar las ondas P300. Por ello, se eligió co= mo banda de interés el rango comprendido entre 0.1 y 12Hz.

Para restringir= las señales a esta banda se diseñó y empleó un Filt= ro Digital Butterworth Pasa Banda de Sexto Orden.<= o:p>

 

      Extracci&oa= cute;n de segmentos temporales: En esta etapa se extrajeron los segmentos de tiemp= o en que destelló la imagen en la que se concentró cada paciente y= los segmentos de tiempo en los que destellaron el resto de imágenes, conformando matrices para cada caso.

 

      Windsorización: Los valores de amplitud de cad= a una de las muestras por encima del 90° percentil y por debajo del 10° percentil fueron ajustados a los percentiles 90 y 10 respectivamente, esto = se efectuó como una medida para atenuar las señales biológicas que se presentan fuera de estos rangos.=

 

      Escalamient= o: Las muestras de cada electrodo fueron escaladas al rango entre -1 y 1.

      =

3.      RESULTADOS

 

      Se trabaj&o= acute; con una configuración de 4 electrodos.
En la parte superior de la Figura 3 se observa la ubicación de estos electrodos, en la parte inferior se observan las señales medidas por estos electrodos.

Figura 3. Ubicación y medición de los electrodos.=

 

      Se observa = en la Figura 3 que al final de cada señal hay una caída abrupta de voltaje, para obviar esta caída que podría alterar los resultados, se obviaron las muestras finales. En la Figura 4 se observan las señales cerebrales sin caídas de voltaje.

 

Figura 4. Señales de los electrodos sin caídas de voltaje.

 

      A estas señales se les sustrajo el promedio de las señales de referencia. En la Figura 5 se observan las señales resultantes.=

Figura 5. Señales de los electrodos menos la referencia.

 

      Previamente a la aplicación del Filtro Digital Butterworth<= /span>, se estudió el desempeño de otros filtros digitales para la identificación de las ondas P300, en la Tabla 1 se compara el rendimiento de cada uno de los filtros estudiados.

 

TABLA 1. Valores por cada electrodo y filtro analizado.

 

      Posteriormente fue aplicado el filtro pasa banda, en la Figura 6 se observan las señales resultantes.

 

Figura 6. Señales de los electrodos filtrad= as en banda entre 1 y 12Hz.

 

   = Luego las señales fueron sub muestreadas a 32 Hz, las señales se observan en la Figura 7.

Figura 7. Señales de los electrodos sub muestreadas a 32Hz.

 

      Las señales cerebrales posteriormente son segmentadas en intervalos en l= os que destelló la imagen elegida por el paciente e intervalos en los q= ue destellaron el resto de imágenes, construyendo así dos matric= es. Al promediar los intervalos de tiempo en los que destelló la imagen = en la que se concentró el paciente, se consiguió aumentar el niv= el de señal a ruido y quedó en evidencia la presencia de la onda P300, tal como se observa en la Figura 8.

 

Figura 8. Onda P300 detectada.

 

      Dado que el ruido biológico presente = en las señales EEG registradas produce valores atípicos de ampli= tud, se aplicó la técnica estadística de windsorización, el resultado se observa en la Figura 9.

 

Figura 9. Resultado de aplicar Windsorizing.

 

Para la obtención de un buen desempeñ= ;o del clasificador a emplearse, se escaló la señal de entrada, = con valores en el rango de [-1,1].  Esto permitió evitar que los datos fueran altamente variab= les haciendo así más rápida la clasificación y evit= ando caer en óptimos locales, el resultado se observa en la Figura 10.

&nb= sp;

Figura 10. Resultado de aplicar Escalamiento.=

 

    Seguidamente se aplicó el Diagrama de C= ajas (Boxplot) a las señales obtenidas, los resultados se observan en la Figura 11.

 =

Figura 11. Boxplot de las señales cerebrales.

      =

En la Figura 11= se observa que hay baja variabilidad en las señales de los electrodos 3= 1 (Fz) y 32 (Cz), mientras q= ue en los electrodos 13 (Pz) y 16 (Oz), la variabilid= ad es mayor. Las muestras que conforman las dos primeras componentes principales pueden ser graficadas de forma escalada, en la Figura 12 se observa el gráfico respectivo.

 

Figura 12.= Muestras escaladas en las primeras compo= nentes principales.

 

      En la Figur= a 12 se observa que se han indicado las muestras 332, 838 y 1454, estos son algu= nas de las muestras que se encuentran más distancias del cúmulo de muestras de la gráfica.

 

      A continuación, en la Figura 13 se observa la variabilidad porcentual = para cada componente principal. Así, la primera componente principal cont= iene el 77.85% de toda la información medida por los 4 electrodos, mientr= as que la segunda componente principal alberga el 19%, la tercera y cuarta componente principal contienen el 2.6% y 0.6% respectivamente.

 

Figura 13. Diagrama de Componentes Principales

 

    En la Figu= ra 14 se observa a cada uno de los cuatro electrodos representados por un vector,= la dirección y la longitud del vector indican cómo cada electrodo contribuye a los dos componentes principales de la Figura 13.

Figura 14. Representación vectorial de electrodos.

 

    El primer componente principal en el eje horizontal tiene coeficientes positivos y negativos para los cuatro electrodos, así los 4 vectores se dirigen = al lado derecho e izquierdo del plano.

Los mayores coeficientes en el primer componente principal son los correspondientes a los electrodos Pz y Fz, de los cuales el electrodo P= z es el de mayor longitud, lo cual permite verificar lo aseverado por [3 - 6]= , en el que se indica que la amplitud de la onda P300 es máxima.

 

    Como prime= ra técnica de clasificación, se empleó el Coeficiente de Correlación de Pearson, el cual permitió medir el grado de asociación entre las variables X, Y. Siendo X el vector conformado p= or las muestras que constituyen el promedio de segmentos de tiempo en los que destellaron cada una de las imágenes y siendo Y el vector conformado= por las muestras de los destellos de cada imagen.

 

Figura 15. Diagrama de dispersión entre las variables y recta de regresión.

   

Los resultados de clasificación se observan en la Figura 16, = en la cual se deduce que para un ensayo específico la figura en la que = se concentró el paciente fue el televisor.

 

Figura 16. Coeficientes de correlación prom= edio de cada una de las seis imágenes.

 

Debido al impacto repetitivo de alguno de los estímulos en la señal cerebral aparecen eventos target. De esta forma la señal cerebral está compuesta de eventos target y eventos non - target [7 – 10].

 

Figura 17. Eventos target y= non – target.

 

      Cada uno de= estos eventos se representa por un vector espacial de 32 muestras o propiedades .

La representació= n de estos vectores será un conjunto de círculos en un espacio matemático de 32 dimensiones. El gráfico de estos vectores (c= írculos) en un plano (asumiendo que solo tienen dos componentes) se presenta en la F= igura 18 donde los círculos blancos representan los eventos target y los círculos negro= s, son los eventos non – target = [11 -13].

Figura 18. Hiperplano de separación de clases LDA.

 

Si se aplica la probabilidad de ocurrencia de las dos clases (asumiendo que ambas tienen distribución gaussiana), se obtiene la Figura 19.<= /p>

 

Figura 19. Separació= n de clases target y non target [4].

 

Si las Figuras 18 y 19 = se representan en un plano para visualización, se obtiene la Figura 20.=

 

 

Figura 20. Separación en clases 1 y 2 [5].

 =

El objetivo de LDA es h= allar los coeficientes W de la ecuación de un plano que permita separar en= la mejor forma (clasificación óptima) las dos clases de eventos: target y non – target en el espacio de eventos.

 

La ecuación del plano es:

 

Dónde: xi son las propiedades de los eventos.

       ωi pesos que definen la ubicación del plano.

 

Como se ve en la Figura= 20, al separar los eventos, por lo general se producirá un error debido a que las funciones probabilísticas de las dos clases se traslapan.

Evidentemente el error será mínimo cuando la distancia entre las medias de las dos clases sea la máxima posible y sus varianzas sean las mínimas posibles. Esto resulta en un problema de maximización con funci&oacu= te;n objetivo [14 – 16].


Donde:

m1 y m2= son medias vectoriales de las clases 1 y 2.

c1 y c2= son índices de las clases 1 y 2.

N1 y N2= son los números de muestras en las clases 1 y 2.

 

SB es la distancia matricial entre las medias de las clases.

SW es la sum= a de las varianzas matriciales de las dos clases.

 

El máximo valor = de J(ω) se encuentra calculando su derivada y haciéndola igual a cero, con esto se consigue el vector  ω.

 

Figura 21. Clasificación LDA y QDA en una dimensión.

 

En la = Tabla 2 se muestran los resultados de clasificación de los cuatro paciente= s.

 

TABLA 2. Resultados de clasificación (%).

 

4.      CONCLUSIONES<= /o:p>

 

Se concluye que las técnicas de clasificación empleadas permitieron identificar exitosamente las voluntades de los pacientes, esta tasa de clasificación se vio repotenciada con la aplicación de las técnicas de pre – procesamiento y PCA.

 

 

 

 

 

REFERENCIAS

 

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[2]     Hoffmann U. et a= l. 2007. An Efficient P300 – based brain – computer interface for disabled subjects.
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[3]     Franz E. 2014. D= evelopment of a Fast and Efficient Algorithm for P300 Event Related Potential Detectio= n.

Master’s Thesis. Temple Univers= ity. United States.

[4]   Polich<= /span> J. 1986.  Normal variation of = P300 from auditory stimuli.<= /b>

[5]     R. Sepúlv= eda et al. Clasificación de señales EEG mediante redes neuronales artificiales. Computación y sistemas, Vol. 19, N° 1, 2015, pp. 69 – 88.<= /p>

[6]     Artusi X. 2013. Interface Cereveau Machine avec adaptation automatique à l’uti= lisateur. PhD Dissertation. Éco= le Centrale de Nantes. France.

[7]        Fa= zel R et al. 2012. P300 brain computer interface: current challenges and emergi= ng trends. Frontiers in Neuroengineering, 1(1), 5:= 14.

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F. Cab= ezas, et al.

doi: https://doi.org/10.21754/tecnia.v28i2.573        =             &nb= sp;               =       Revista TECNIA Vol. 28 Nº 1 Agosto – Diciembre 2018

 

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