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UNIVERSIDAD CATOLICA DE LA SANTÍSIMA CONCEPCIÓN
Facultad de Ingeniería
ANÁLISIS DE COMPONENTES
PRINCIPALES
(ACP)
I. Objetivos del Análisis de Componentes Principales
I.1. La Tabla de Datos
El ACP permite analizar la información de una tabla de tipo «individuos x variables cuantitativas».
Tabla de Datos
![Análisis de componentes principales](https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/6/1/9/000336190.png)
2. Objetivos del ACP
¿Existen grupos de individuos semejantes...?
¿Se observa una tipología de individuos...?
¿Existen grupos de variables correlacionadas entre ellas...?
¿Se observa una tipología de variables...?
Comparación de los individuos y relación entre las variables de la tabla en el ACP
II.1. Semejanza entre los individuos de la Tabla de Datos
![Análisis de componentes principales](https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/6/1/9/000336191.png)
-
Como las variables son consideradas con la misma importancia en la comparación, se les atribuye el mismo peso, mk = 1,
![Análisis de componentes principales](https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/6/1/9/000336192.png)
II. 2. Relación entre las variables de la Tabla de Datos
![Análisis de componentes principales](https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/6/1/9/000336193.png)
-
Como a los individuos se les atribuye, normalmente, la misma importancia (el mismo peso, mi = 1/n)...
![Análisis de componentes principales](https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/6/1/9/000336194.png)
III. Transformación de la Matriz de Datos
Matriz de Datos : X
![Análisis de componentes principales](https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/6/1/9/000336195.png)
Matriz de Datos Centrada-Reducida : Z
![Análisis de componentes principales](https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/6/1/9/000336196.png)
IV . La nube de puntos-individuos en R3 y en Rk
![Análisis de componentes principales](https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/6/1/9/000336197.png)
![Análisis de componentes principales](https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/6/1/9/000336198.png)
![Análisis de componentes principales](https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/6/1/9/000336199.png)
![Análisis de componentes principales](0https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/1/9/1/003361910.png)
![Análisis de componentes principales](0https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/1/9/1/003361911.png)
1. Origen del espacio
2. Inercia total de la nube de puntos-individuos
Dispersión de Inercia total de
![Análisis de componentes principales](0https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/1/9/1/003361912.png)
![Análisis de componentes principales](0https://rdv-files.nyc3.cdn.digitaloceanspaces.com/pub/html/files_html/1/9/1/003361913.png)
¿Como se define la matriz V...?
3. La matriz de inercia de la nube de puntos-individuos
4. Contribución a la inercia del individuo i
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Enviado por: | Marcelo |
Idioma: | castellano |
País: | Chile |