MAQUINA-DE-VECTORES-SOPORTE
CIENCIA DE DATOS
Docente: Dr. Edgar Eloy Carpio Vargas
Estudiante: Britman Salcedo Pumaccola
UNIVERSIDAD NACIONAL DEL ALTIPLANO - INGENIERIA ESTADISTICA E INFORMATICA
2022-07-22
# UNIVERSIDAD NACIONAL DEL ALTIPLANO
# FACULTAD DE INGENIERIA ESTADISTICA E INFORMATICA
# TECNICAS DE ESTADISTICAS MULTIVARIADAS
# MAQUINA DE VECTORES SOPORTEFunciones para análisis de clases latentes, transformada de Fourier de tiempo corto, agrupamiento difuso, máquinas de vectores de soporte, cálculo de la ruta más corta, agrupamiento en bolsas, clasificador de Bayes ingenuo, vecino más cercano k-generalizado
library(e1071)## Warning: package 'e1071' was built under R version 4.1.3Es un paquete diseñado para hacer una sola tarea: importar hojas de Excel a R. Esto hace que sea un paquete ligero y eficiente, a cambio de no contar con funciones avanzadas.
library(readxl)## Warning: package 'readxl' was built under R version 4.1.3La librería ggplot2 de R es un sistema organizado de visualización de datos. Forma parte del conjunto de librerías llamado tidyverse.
library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.1.3Herramientas para visualizar, suavizar y comparar las características operativas del receptor (curvas ROC).El área (parcial) bajo la curva (AUC) se puede comparar con pruebas estadísticas basadas en estadísticas U oreja. Los intervalos de confianza se pueden calcular para las curvas (p)AUC o ROC. Tamaño de muestra/potencia están disponibles los cálculos para una o dos curvas ROC.
library(pROC)## Warning: package 'pROC' was built under R version 4.1.3## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, varLos datos proceden de un estudio sobre diagnóstico del venta de vehiculos de la ciudad de Juliaca. Mediante una recoleccion se extrae una muestra de la venta por genero. La muestra se tiñe para resaltar si compran o no compran los vehiculos de acuerdo al salario estimado. Las variables consideradas corresponden al salario estimado. La data cuenta con 5 variables ID, Genero, Edad, Salario estimado,Compras posteriormente como Compra o no compra y el factor y que toma los valores 0 o 1 en función de si la correspondiente fila corresponde a un tumor benigno o maligno respectivamente. Más información sobre los datos se puede encontrar en esta dirección. En el fichero original se considera un total de 5 variables explicativas hay 400 observaciones.
# Datos de Venta de Carros
dato <- read.csv("https://media.geeksforgeeks.org/wp-content/uploads/social.csv
")
dato## User.ID Gender Age EstimatedSalary Purchased
## 1 15624510 Male 19 19000 0
## 2 15810944 Male 35 20000 0
## 3 15668575 Female 26 43000 0
## 4 15603246 Female 27 57000 0
## 5 15804002 Male 19 76000 0
## 6 15728773 Male 27 58000 0
## 7 15598044 Female 27 84000 0
## 8 15694829 Female 32 150000 1
## 9 15600575 Male 25 33000 0
## 10 15727311 Female 35 65000 0
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## 12 15606274 Female 26 52000 0
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## 400 15594041 Female 49 36000 1Elegimos las variables de interes de la data, de esta manera nosotros podemos eliminar los datos que no son de nuetsro interes para realizar el modelo Maquina de Soporte Vectores. Seguidamente, convirtiendo en factor la variable venta si compra o no compra la unidad vehicular y con head() podremos visualizar los datos de la nueva data.
# Variable de la Data
dato <- dato[3:5]
# Convirtiendo en factor
dato$Purchased <- as.factor(dato$Purchased)
# Vista de los datos
head(dato)## Age EstimatedSalary Purchased
## 1 19 19000 0
## 2 35 20000 0
## 3 26 43000 0
## 4 27 57000 0
## 5 19 76000 0
## 6 27 58000 0Vemos la estructura de los datos de la data en los años podemos ver que es la variable años con int(), luego, podemos ver el salario estimado con int() y finalmente vemos la variable venta como factor.
# Estructura de los datos
str(dato)## 'data.frame': 400 obs. of 3 variables:
## $ Age : int 19 35 26 27 19 27 27 32 25 35 ...
## $ EstimatedSalary: int 19000 20000 43000 57000 76000 58000 84000 150000 33000 65000 ...
## $ Purchased : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 2 1 1 ...# # Prepara los Datos
# x <- cbind(dato$Age, dato$EstimatedSalary)
# y <- dato$Purchased
# n0 <- sum(y==0)
# n1 <- sum(y==1)
# # Para que los graficos queden mas bonitos (rojo = maligno, verde = benigno)
# colores <- c(rep('green',n0),rep('red',n1))
# pchn <- 21
# # Diagrama de dispersion
# plot(x, pch = pchn, bg = colores, xlab='smoothness', ylab='concavepoints')
# Exploracion de los Datos
# Diagrama de Dispersion con la edad, Salario Estimado y la Compra
ggplot(data = dato, aes(x = Age, y = EstimatedSalary, color= Purchased )) + geom_point()Diagrama de Dispersion con la edad, Salrio estimado y la compra, podemos ver que el modelo SVM Lineal es el mas convniente para aplicar puesto que los datos negativos son pocos
# Eligiendo el mejor modelo
# SVM Lineal
# ==========
svm.lineal <- svm(Purchased ~ .,data = dato, kernel ='linear', cost = 10, scale = T)
summary(svm.lineal)##
## Call:
## svm(formula = Purchased ~ ., data = dato, kernel = "linear", cost = 10,
## scale = T)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: linear
## cost: 10
##
## Number of Support Vectors: 155
##
## ( 77 78 )
##
##
## Number of Classes: 2
##
## Levels:
## 0 1# Con el primer modelo SVM Lineal se obtuvo una precision del 84.25%
caret::confusionMatrix(predict(svm.lineal), dato$Purchased)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 240 46
## 1 17 97
##
## Accuracy : 0.8425
## 95% CI : (0.803, 0.8768)
## No Information Rate : 0.6425
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.641
##
## Mcnemar's Test P-Value : 0.0004192
##
## Sensitivity : 0.9339
## Specificity : 0.6783
## Pos Pred Value : 0.8392
## Neg Pred Value : 0.8509
## Prevalence : 0.6425
## Detection Rate : 0.6000
## Detection Prevalence : 0.7150
## Balanced Accuracy : 0.8061
##
## 'Positive' Class : 0
## svm.lineal2 <- svm(Purchased ~., data = dato, kernel = 'linear', cost = 10**2, scale = T)
summary(svm.lineal)##
## Call:
## svm(formula = Purchased ~ ., data = dato, kernel = "linear", cost = 10,
## scale = T)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: linear
## cost: 10
##
## Number of Support Vectors: 155
##
## ( 77 78 )
##
##
## Number of Classes: 2
##
## Levels:
## 0 1# Con el primer modelo SVM Lineal se obtuvo una precision del 84.50%
a <- caret::confusionMatrix(predict(svm.lineal2), dato$Purchased);
a$table; a$overall[1]## Reference
## Prediction 0 1
## 0 239 44
## 1 18 99## Accuracy
## 0.845# SVM Cuadratico
# ==============
svm.cuadratico <- svm(Purchased ~., data = dato, kernel='polynomial', degree = 2, gamma = 1, coef0 = 1, cost=10)
summary(svm.cuadratico)##
## Call:
## svm(formula = Purchased ~ ., data = dato, kernel = "polynomial",
## degree = 2, gamma = 1, coef0 = 1, cost = 10)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: polynomial
## cost: 10
## degree: 2
## coef.0: 1
##
## Number of Support Vectors: 100
##
## ( 49 51 )
##
##
## Number of Classes: 2
##
## Levels:
## 0 1# Con el segundo modelo SVM Cuadratico se obtuvo una precision del 89.75% mejorando notablemente el modelo
caret::confusionMatrix(predict(svm.cuadratico), dato$Purchased) ## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 233 17
## 1 24 126
##
## Accuracy : 0.8975
## 95% CI : (0.8635, 0.9254)
## No Information Rate : 0.6425
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.7793
##
## Mcnemar's Test P-Value : 0.3487
##
## Sensitivity : 0.9066
## Specificity : 0.8811
## Pos Pred Value : 0.9320
## Neg Pred Value : 0.8400
## Prevalence : 0.6425
## Detection Rate : 0.5825
## Detection Prevalence : 0.6250
## Balanced Accuracy : 0.8939
##
## 'Positive' Class : 0
## # SVM Radial
# ==========
# Con el tercer modelo SVM Radial se obtuvo una precision del 89.75% Teniendo un mejor modelo
svm.radial <- svm(Purchased ~., data = dato, kernel='radial', degree = 2, gamma = 1, coef0 = 1, cost=10)
summary(svm.radial)##
## Call:
## svm(formula = Purchased ~ ., data = dato, kernel = "radial", degree = 2,
## gamma = 1, coef0 = 1, cost = 10)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: radial
## cost: 10
##
## Number of Support Vectors: 94
##
## ( 42 52 )
##
##
## Number of Classes: 2
##
## Levels:
## 0 1caret::confusionMatrix(predict(svm.radial), dato$Purchased)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 238 10
## 1 19 133
##
## Accuracy : 0.9275
## 95% CI : (0.8975, 0.9509)
## No Information Rate : 0.6425
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.8444
##
## Mcnemar's Test P-Value : 0.1374
##
## Sensitivity : 0.9261
## Specificity : 0.9301
## Pos Pred Value : 0.9597
## Neg Pred Value : 0.8750
## Prevalence : 0.6425
## Detection Rate : 0.5950
## Detection Prevalence : 0.6200
## Balanced Accuracy : 0.9281
##
## 'Positive' Class : 0
## # Curva de ROC
objroc <- roc(dato$Purchased, dato$Age,auc=T,ci=T)## Setting levels: control = 0, case = 1## Setting direction: controls < casesobjroc##
## Call:
## roc.default(response = dato$Purchased, predictor = dato$Age, auc = T, ci = T)
##
## Data: dato$Age in 257 controls (dato$Purchased 0) < 143 cases (dato$Purchased 1).
## Area under the curve: 0.8686
## 95% CI: 0.8319-0.9052 (DeLong)Como podemos ver en el gráfico de las curvas de densidad generadas a partir de los datos, la distribución de la personas que compran o no compran segun el salario. Es precisamente debido a ese solapamiento por lo que se hace necesario recurrir a algún tipo de herramienta predictiva que ayude a decidir sobre los casos dudosos.
plot.roc(objroc,print.auc=T,print.thres = "best",
col="blue",xlab="1-No Compra",ylab="Compra")
# # Indices de los vectores soporte
# svm.lineal$index
#
# # Coeficientes por los que se multiplican las observaciones para obtener
# # el vector perpendicular al hiperplano que resuelve el problema
# svm.lineal$coefs
#
# # Termino independiente
# svm.lineal$rho
#
# # Termino independiente
# svm.lineal$rho
#
# # Termino independiente
# svm.lineal$rho
#
# x.svm <- x[svm.lineal$index,]
# w <- crossprod(x.svm, svm.lineal$coefs)
# w0 <- svm.lineal$rho
# plot(x, pch = pchn, bg = colores, xlab='smoothness', ylab='concavepoints')
# abline(w0/w[2], -w[1]/w[2], lwd=2, col='blue')