09-dimensionality-reduction.Rmd

# Dimensionality Reduction

## Principal Component Analysis (PCA)

### Importing the libraries

**Python**

```{python}
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
```

### Importing the dataset

**Python**

```{python}
dataset = pd.read_csv('Wine.csv')
X = dataset.iloc[:, :-1].values
y = dataset.iloc[:, -1].values
```

**R**

```{r}
dataset = read.csv('Wine.csv')
```

### Splitting the dataset into the Training set and Test set

**Python**

```{python}
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)
```

**R**

```{r}
# install.packages('caTools')
library(caTools)
set.seed(123)
split = sample.split(dataset$Customer_Segment, SplitRatio = 0.8)
training_set = subset(dataset, split == TRUE)
test_set = subset(dataset, split == FALSE)
```

### Feature Scaling

**Python**

```{python}
from sklearn.preprocessing import StandardScaler
sc = StandardScaler()
X_train = sc.fit_transform(X_train)
X_test = sc.transform(X_test)
```

**R**

```{r}
training_set[-14] = scale(training_set[-14])
test_set[-14] = scale(test_set[-14])
```

### Applying PCA

**Python**

```{python}
from sklearn.decomposition import PCA
pca = PCA(n_components = 2)
X_train = pca.fit_transform(X_train)
X_test = pca.transform(X_test)
```

**R**

```{r}
# install.packages('caret')
library(caret)
# install.packages('e1071')
library(e1071)
pca = preProcess(x = training_set[-14], method = 'pca', pcaComp = 2)
training_set = predict(pca, training_set)
training_set = training_set[c(2, 3, 1)]
test_set = predict(pca, test_set)
test_set = test_set[c(2, 3, 1)]
```

### Training the Logistic Regression model on the Training set

**Python**

```{python}
from sklearn.linear_model import LogisticRegression
classifier = LogisticRegression(random_state = 0)
classifier.fit(X_train, y_train)
```

### Fitting SVM to the Training set

**R**

```{r}
# install.packages('e1071')
library(e1071)
classifier = svm(formula = Customer_Segment ~ .,
                 data = training_set,
                 type = 'C-classification',
                 kernel = 'linear')
```

### Predicting the Test set results

**R**

```{r}
y_pred = predict(classifier, newdata = test_set[-3])
```

### Making the Confusion Matrix

**Python**

```{python}
from sklearn.metrics import confusion_matrix, accuracy_score
y_pred = classifier.predict(X_test)
cm = confusion_matrix(y_test, y_pred)
print(cm)
accuracy_score(y_test, y_pred)
```

**R**

```{r}
cm = table(test_set[, 3], y_pred)
```

### Visualising the Training set results

**Python**

```{python}
from matplotlib.colors import ListedColormap
X_set, y_set = X_train, y_train
X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1, stop = X_set[:, 0].max() + 1, step = 0.01),
                     np.arange(start = X_set[:, 1].min() - 1, stop = X_set[:, 1].max() + 1, step = 0.01))
plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
             alpha = 0.75, cmap = ListedColormap(('red', 'green', 'blue')))
plt.xlim(X1.min(), X1.max())
plt.ylim(X2.min(), X2.max())
for i, j in enumerate(np.unique(y_set)):
    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
                c = ListedColormap(('red', 'green', 'blue'))(i), label = j)
plt.title('Logistic Regression (Training set)')
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.legend()
plt.show()
```

**R**

```{r}
library(ElemStatLearn)
set = training_set
X1 = seq(min(set[, 1]) - 1, max(set[, 1]) + 1, by = 0.01)
X2 = seq(min(set[, 2]) - 1, max(set[, 2]) + 1, by = 0.01)
grid_set = expand.grid(X1, X2)
colnames(grid_set) = c('PC1', 'PC2')
y_grid = predict(classifier, newdata = grid_set)
plot(set[, -3],
     main = 'SVM (Training set)',
     xlab = 'PC1', ylab = 'PC2',
     xlim = range(X1), ylim = range(X2))
contour(X1, X2, matrix(as.numeric(y_grid), length(X1), length(X2)), add = TRUE)
points(grid_set, pch = '.', col = ifelse(y_grid == 2, 'deepskyblue', ifelse(y_grid == 1, 'springgreen3', 'tomato')))
points(set, pch = 21, bg = ifelse(set[, 3] == 2, 'blue3', ifelse(set[, 3] == 1, 'green4', 'red3')))
```

### Visualising the Test set results

**Python**

```{python}
from matplotlib.colors import ListedColormap
X_set, y_set = X_test, y_test
X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1, stop = X_set[:, 0].max() + 1, step = 0.01),
                     np.arange(start = X_set[:, 1].min() - 1, stop = X_set[:, 1].max() + 1, step = 0.01))
plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
             alpha = 0.75, cmap = ListedColormap(('red', 'green', 'blue')))
plt.xlim(X1.min(), X1.max())
plt.ylim(X2.min(), X2.max())
for i, j in enumerate(np.unique(y_set)):
    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
                c = ListedColormap(('red', 'green', 'blue'))(i), label = j)
plt.title('Logistic Regression (Test set)')
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.legend()
plt.show()
```

**R**

```{r}
library(ElemStatLearn)
set = test_set
X1 = seq(min(set[, 1]) - 1, max(set[, 1]) + 1, by = 0.01)
X2 = seq(min(set[, 2]) - 1, max(set[, 2]) + 1, by = 0.01)
grid_set = expand.grid(X1, X2)
colnames(grid_set) = c('PC1', 'PC2')
y_grid = predict(classifier, newdata = grid_set)
plot(set[, -3], main = 'SVM (Test set)',
     xlab = 'PC1', ylab = 'PC2',
     xlim = range(X1), ylim = range(X2))
contour(X1, X2, matrix(as.numeric(y_grid), length(X1), length(X2)), add = TRUE)
points(grid_set, pch = '.', col = ifelse(y_grid == 2, 'deepskyblue', ifelse(y_grid == 1, 'springgreen3', 'tomato')))
points(set, pch = 21, bg = ifelse(set[, 3] == 2, 'blue3', ifelse(set[, 3] == 1, 'green4', 'red3')))
```

## Linear Discriminant Analysis (LDA)

### Importing the libraries

**Python**

```{python}
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
```

### Importing the dataset

**Python**

```{python}
dataset = pd.read_csv('Wine.csv')
X = dataset.iloc[:, :-1].values
y = dataset.iloc[:, -1].values
```

**R**

```{r}
dataset = read.csv('Wine.csv')
```

### Splitting the dataset into the Training set and Test set

**Python**

```{python}
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)
```

**R**

```{r}
# install.packages('caTools')
library(caTools)
set.seed(123)
split = sample.split(dataset$Customer_Segment, SplitRatio = 0.8)
training_set = subset(dataset, split == TRUE)
test_set = subset(dataset, split == FALSE)
```

### Feature Scaling

**Python**

```{python}
from sklearn.preprocessing import StandardScaler
sc = StandardScaler()
X_train = sc.fit_transform(X_train)
X_test = sc.transform(X_test)
```

**R**

```{r}
training_set[-14] = scale(training_set[-14])
test_set[-14] = scale(test_set[-14])
```

### Applying LDA

**Python**

```{python}
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA
lda = LDA(n_components = 2)
X_train = lda.fit_transform(X_train, y_train)
X_test = lda.transform(X_test)
```

**R**

```{r}
library(MASS)
lda = lda(formula = Customer_Segment ~ ., data = training_set)
training_set = as.data.frame(predict(lda, training_set))
training_set = training_set[c(5, 6, 1)]
test_set = as.data.frame(predict(lda, test_set))
test_set = test_set[c(5, 6, 1)]
```

### Training the Logistic Regression model on the Training set

**Python**

```{python}
from sklearn.linear_model import LogisticRegression
classifier = LogisticRegression(random_state = 0)
classifier.fit(X_train, y_train)
```

### Fitting SVM to the Training set

**R**

```{r}
# install.packages('e1071')
library(e1071)
classifier = svm(formula = class ~ .,
                 data = training_set,
                 type = 'C-classification',
                 kernel = 'linear')
```

### Predicting the Test set results

**R**

```{r}
y_pred = predict(classifier, newdata = test_set[-3])
```

### Making the Confusion Matrix

**Python**

```{python}
from sklearn.metrics import confusion_matrix, accuracy_score
y_pred = classifier.predict(X_test)
cm = confusion_matrix(y_test, y_pred)
print(cm)
accuracy_score(y_test, y_pred)
```

**R**

```{r}
cm = table(test_set[, 3], y_pred)
```

### Visualising the Training set results

**Python**

```{python}
from matplotlib.colors import ListedColormap
X_set, y_set = X_train, y_train
X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1, stop = X_set[:, 0].max() + 1, step = 0.01),
                     np.arange(start = X_set[:, 1].min() - 1, stop = X_set[:, 1].max() + 1, step = 0.01))
plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
             alpha = 0.75, cmap = ListedColormap(('red', 'green', 'blue')))
plt.xlim(X1.min(), X1.max())
plt.ylim(X2.min(), X2.max())
for i, j in enumerate(np.unique(y_set)):
    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
                c = ListedColormap(('red', 'green', 'blue'))(i), label = j)
plt.title('Logistic Regression (Training set)')
plt.xlabel('LD1')
plt.ylabel('LD2')
plt.legend()
plt.show()
```

**R**

```{r}
library(ElemStatLearn)
set = training_set
X1 = seq(min(set[, 1]) - 1, max(set[, 1]) + 1, by = 0.01)
X2 = seq(min(set[, 2]) - 1, max(set[, 2]) + 1, by = 0.01)
grid_set = expand.grid(X1, X2)
colnames(grid_set) = c('x.LD1', 'x.LD2')
y_grid = predict(classifier, newdata = grid_set)
plot(set[, -3],
     main = 'SVM (Training set)',
     xlab = 'LD1', ylab = 'LD2',
     xlim = range(X1), ylim = range(X2))
contour(X1, X2, matrix(as.numeric(y_grid), length(X1), length(X2)), add = TRUE)
points(grid_set, pch = '.', col = ifelse(y_grid == 2, 'deepskyblue', ifelse(y_grid == 1, 'springgreen3', 'tomato')))
points(set, pch = 21, bg = ifelse(set[, 3] == 2, 'blue3', ifelse(set[, 3] == 1, 'green4', 'red3')))
```

### Visualising the Test set results

**Python**

```{python}
from matplotlib.colors import ListedColormap
X_set, y_set = X_test, y_test
X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1, stop = X_set[:, 0].max() + 1, step = 0.01),
                     np.arange(start = X_set[:, 1].min() - 1, stop = X_set[:, 1].max() + 1, step = 0.01))
plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
             alpha = 0.75, cmap = ListedColormap(('red', 'green', 'blue')))
plt.xlim(X1.min(), X1.max())
plt.ylim(X2.min(), X2.max())
for i, j in enumerate(np.unique(y_set)):
    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
                c = ListedColormap(('red', 'green', 'blue'))(i), label = j)
plt.title('Logistic Regression (Test set)')
plt.xlabel('LD1')
plt.ylabel('LD2')
plt.legend()
plt.show()
```

**R**

```{r}
library(ElemStatLearn)
set = test_set
X1 = seq(min(set[, 1]) - 1, max(set[, 1]) + 1, by = 0.01)
X2 = seq(min(set[, 2]) - 1, max(set[, 2]) + 1, by = 0.01)
grid_set = expand.grid(X1, X2)
colnames(grid_set) = c('x.LD1', 'x.LD2')
y_grid = predict(classifier, newdata = grid_set)
plot(set[, -3], main = 'SVM (Test set)',
     xlab = 'LD1', ylab = 'LD2',
     xlim = range(X1), ylim = range(X2))
contour(X1, X2, matrix(as.numeric(y_grid), length(X1), length(X2)), add = TRUE)
points(grid_set, pch = '.', col = ifelse(y_grid == 2, 'deepskyblue', ifelse(y_grid == 1, 'springgreen3', 'tomato')))
points(set, pch = 21, bg = ifelse(set[, 3] == 2, 'blue3', ifelse(set[, 3] == 1, 'green4', 'red3')))
```

## Kernel PCA

### Importing the libraries

**Python**

```{python}
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
```

### Importing the dataset

**Python**

```{python}
dataset = pd.read_csv('Wine.csv')
X = dataset.iloc[:, :-1].values
y = dataset.iloc[:, -1].values
```

**R**

```{r}
dataset = read.csv('Social_Network_Ads.csv')
# dataset = dataset[, 3:5]
```

### Splitting the dataset into the Training set and Test set

**Python**

```{python}
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)
```

**R**

```{r}
# install.packages('caTools')
library(caTools)
set.seed(123)
split = sample.split(dataset$Purchased, SplitRatio = 0.75)
training_set = subset(dataset, split == TRUE)
test_set = subset(dataset, split == FALSE)
```

### Feature Scaling

**Python**

```{python}
from sklearn.preprocessing import StandardScaler
sc = StandardScaler()
X_train = sc.fit_transform(X_train)
X_test = sc.transform(X_test)
```

**R**

```{r}
training_set[, 1:2] = scale(training_set[, 1:2])
test_set[, 1:2] = scale(test_set[, 1:2])
```

### Applying Kernel PCA

**Python**

```{python}
from sklearn.decomposition import KernelPCA
kpca = KernelPCA(n_components = 2, kernel = 'rbf')
X_train = kpca.fit_transform(X_train)
X_test = kpca.transform(X_test)
```

**R**

```{r}
# install.packages('kernlab')
library(kernlab)
kpca = kpca(~., data = training_set[-3], kernel = 'rbfdot', features = 2)
training_set_pca = as.data.frame(predict(kpca, training_set))
training_set_pca$Purchased = training_set$Purchased
test_set_pca = as.data.frame(predict(kpca, test_set))
test_set_pca$Purchased = test_set$Purchased
```

### Training the Logistic Regression model on the Training set

**Python**

```{python}
from sklearn.linear_model import LogisticRegression
classifier = LogisticRegression(random_state = 0)
classifier.fit(X_train, y_train)
```

**R**

```{r}
classifier = glm(formula = Purchased ~ .,
                 family = binomial,
                 data = training_set_pca)
```

### Predicting the Test set results

**R**

```{r}
prob_pred = predict(classifier, type = 'response', newdata = test_set_pca[-3])
y_pred = ifelse(prob_pred > 0.5, 1, 0)
```

### Making the Confusion Matrix

**Python**

```{python}
from sklearn.metrics import confusion_matrix, accuracy_score
y_pred = classifier.predict(X_test)
cm = confusion_matrix(y_test, y_pred)
print(cm)
accuracy_score(y_test, y_pred)
```

**R**

```{r}
cm = table(test_set_pca[, 3], y_pred)
```

### Visualising the Training set results

**Python**

```{python}
from matplotlib.colors import ListedColormap
X_set, y_set = X_train, y_train
X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1, stop = X_set[:, 0].max() + 1, step = 0.01),
                     np.arange(start = X_set[:, 1].min() - 1, stop = X_set[:, 1].max() + 1, step = 0.01))
plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
             alpha = 0.75, cmap = ListedColormap(('red', 'green', 'blue')))
plt.xlim(X1.min(), X1.max())
plt.ylim(X2.min(), X2.max())
for i, j in enumerate(np.unique(y_set)):
    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
                c = ListedColormap(('red', 'green', 'blue'))(i), label = j)
plt.title('Logistic Regression (Training set)')
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.legend()
plt.show()
```

**R**

```{r, cache = TRUE}
# install.packages('ElemStatLearn')
library(ElemStatLearn)
set = training_set_pca
X1 = seq(min(set[, 1]) - 1, max(set[, 1]) + 1, by = 0.01)
X2 = seq(min(set[, 2]) - 1, max(set[, 2]) + 1, by = 0.01)
grid_set = expand.grid(X1, X2)
colnames(grid_set) = c('V1', 'V2')
prob_set = predict(classifier, type = 'response', newdata = grid_set)
y_grid = ifelse(prob_set > 0.5, 1, 0)
plot(set[, -3],
     main = 'Logistic Regression (Training set)',
     xlab = 'PC1', ylab = 'PC2',
     xlim = range(X1), ylim = range(X2))
contour(X1, X2, matrix(as.numeric(y_grid), length(X1), length(X2)), add = TRUE)
points(grid_set, pch = '.', col = ifelse(y_grid == 1, 'springgreen3', 'tomato'))
points(set, pch = 21, bg = ifelse(set[, 3] == 1, 'green4', 'red3'))
```

### Visualising the Test set results

**Python**

```{python}
from matplotlib.colors import ListedColormap
X_set, y_set = X_test, y_test
X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1, stop = X_set[:, 0].max() + 1, step = 0.01),
                     np.arange(start = X_set[:, 1].min() - 1, stop = X_set[:, 1].max() + 1, step = 0.01))
plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
             alpha = 0.75, cmap = ListedColormap(('red', 'green', 'blue')))
plt.xlim(X1.min(), X1.max())
plt.ylim(X2.min(), X2.max())
for i, j in enumerate(np.unique(y_set)):
    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
                c = ListedColormap(('red', 'green', 'blue'))(i), label = j)
plt.title('Logistic Regression (Test set)')
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.legend()
plt.show()
```

**R**

```{r, cache = TRUE}
# install.packages('ElemStatLearn')
library(ElemStatLearn)
set = test_set_pca
X1 = seq(min(set[, 1]) - 1, max(set[, 1]) + 1, by = 0.01)
X2 = seq(min(set[, 2]) - 1, max(set[, 2]) + 1, by = 0.01)
grid_set = expand.grid(X1, X2)
colnames(grid_set) = c('V1', 'V2')
prob_set = predict(classifier, type = 'response', newdata = grid_set)
y_grid = ifelse(prob_set > 0.5, 1, 0)
plot(set[, -3],
     main = 'Logistic Regression (Test set)',
     xlab = 'Age', ylab = 'Estimated Salary',
     xlim = range(X1), ylim = range(X2))
contour(X1, X2, matrix(as.numeric(y_grid), length(X1), length(X2)), add = TRUE)
points(grid_set, pch = '.', col = ifelse(y_grid == 1, 'springgreen3', 'tomato'))
points(set, pch = 21, bg = ifelse(set[, 3] == 1, 'green4', 'red3'))
```