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def multivariateGaussian(X, mu, sigma):
    k = len(mu)
    sigma=np.diag(sigma)
    X = X - mu.T
    p = 1/((2*np.pi)**(k/2)*(np.linalg.det(sigma)**0.5))* np.exp(-0.5* np.sum(X @ np.linalg.pinv(sigma) * X,axis=1))
    return p
p = multivariateGaussian(X, mu, sigma)

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def estimateGaussian(X):
    m = X.shape[0]
    #compute mean of X
    sum_ = np.sum(X,axis=0)
    mu = (sum_/m)
    # compute variance of X
    var = np.var(X,axis=0)
    print(mu, var)
    return mu,var

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import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets.samples_generator import make_blobs
X, y_true = make_blobs(n_samples=500, centers=1, cluster_std=0.60, random_state=5)
X_append, y_true_append = make_blobs(n_samples=20,centers=1, cluster_std=5,random_state=5)
X = np.vstack([X,X_append])
y_true = np.hstack([y_true, [1 for _ in y_true_append]])
X = X[:, ::-1] 
plt.scatter(X[:,0],X[:,1],marker="x");

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plt.figure(figsize=(8,6))
plt.scatter(X[:,0],X[:,1],marker="x",c=p,cmap='viridis');
plt.colorbar();

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plt.figure(figsize=(8,6))
plt.scatter(X[:,0],X[:,1],marker="x",c=p,cmap='viridis');
# Circling of anomalies
outliers = np.nonzero(p<epsilon)[0]
plt.scatter(X[outliers,0],X[outliers,1],marker="o",facecolor="none",edgecolor="r",s=70);

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from sklearn.datasets.samples_generator import make_blobs
from sklearn.model_selection import train_test_split
X, y_true = make_blobs(n_samples=400, centers=5, cluster_std=0.60, random_state=1)
X_append, y_true_append = make_blobs(n_samples=50,centers=5, cluster_std=5,random_state=1)
X = np.vstack([X,X_append])
y_true = np.hstack([[0 for _ in y_true], [1 for _ in y_true_append]])
X = X[:, ::-1] # flip axes for better plotting
X_train, X_test, y_train, y_test = train_test_split(X, y_true, test_size=0.33, random_state=1, shuffle=True)
plt.scatter(X_train[:,0],X_train[:,1],marker="x");

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mu, sigma = estimateGaussian(X_train)
p = multivariateGaussian(X_test, mu, sigma)
plt.figure(figsize=(8,6))
plt.scatter(X_test[:,0],X_test[:,1],marker="x",c=p,cmap='viridis');
outliers = np.nonzero(p<0.001)[0]
plt.scatter(X_test[outliers,0],X_test[outliers,1],marker="o",facecolor="none",edgecolor="r",s=70);

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from sklearn.mixture import GaussianMixture
gm = GaussianMixture(n_components = 5, covariance_type = 'full', random_state=0, )
gm.fit(X_train)

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plt.figure(figsize=(10,10))
for i in range(5):
    plt.subplot(3,2,i+1)
    plt.scatter(X_train[:,0],X_train[:,1],c=gm.predict_proba(X_train)[:,i],cmap='viridis',marker='x')

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import re 
import nltk
nltk.download('stopwords')
from nltk.corpus import stopwords
stop_words = set(stopwords.words('english'))