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from scipy import stats
import numpy as np
import pandas as pd
from pingouin import multivariate_normality
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.stats import multivariate_normal

rng = np.random.default_rng()

pts = 1000

a = rng.normal(0, 1, size=pts)

b = rng.normal(2, 1, size=pts)

df = pd.read_csv("Football teams.csv")


data = df.drop(['Team','Tournament'], axis=1) 


multivariate_normality(data, alpha=.5)

df.head()



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sns.pairplot(data, hue="Rating")


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data['Rating'] = np.where(df["Rating"] <= 6.6, 0, 1)
sum(data['Rating'] == 0)


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sns.pairplot(data, hue="Rating")


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K = 2 # number of clusters

means = np.zeros((K,8))
covs = np.zeros((K,8,8))
for k in range(K):
    means[k] = np.random.normal(size=(8,))
    covs[k] = np.eye(8)

weights = np.ones((K,1))/K
print("Initial mean vectors (one per row):\n" + str(means))
print(data.shape)


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r = np.zeros((K,98)) # will store the responsibilities
X, Y = np.meshgrid(np.linspace(-10,10,100), np.linspace(-10,10,100))
N=98
for em_iter in range(100):    
    means_old = means.copy()
    
    # E-step: update responsibilities
    for k in range(K):
        r[k] = weights[k]*multivariate_normal.pdf(mean=means[k,:], cov=covs[k,:,:], x=data)  
       
        
    r = r/np.sum(r, axis=0) 
        
    # M-step
    N_k = np.sum(r, axis=1)

    for k in range(K): 
        # update means
        means[k] = np.sum(r[k]*data.T, axis=1)/N_k[k]
        
        # update covariances
        diff = data.T - means[k:k+1].T
        _tmp = np.sqrt(r[k:k+1])*diff
        covs[k] = np.inner(_tmp, _tmp)/N_k[k]
        
    # weights
    weights = N_k/N 
    
    # log-likelihood
    gmm_nll = 0
    for k in range(K):
        gmm_nll += weights[k]*multivariate_normal.pdf(mean=means[k,:].ravel(), cov=covs[k,:,:], x=data)
    NLL += [-np.sum(np.log(gmm_nll))]
    
    plt.figure() 
    plt.plot(x, y, 'ko', alpha=0.3)
    plt.plot(means[:,0], means[:,1], 'oy', markersize=25)
    for k in range(K):
        rv = multivariate_normal(means[k,:], covs[k])
        plt.contour(X, Y, rv.pdf(pos), alpha = 1.0, zorder=10)
        
    plt.xlabel("$x_1$")
    plt.ylabel("$x_2$")
    plt.text(x=3.5, y=8, s="EM iteration "+str(em_iter+1))
    
    if la.norm(NLL[em_iter+1]-NLL[em_iter]) < 1e-6:
        print("Converged after iteration ", em_iter+1)
        break
   
# plot final the mixture model
plt.figure() 
gmm = 0
for k in range(3):
    mix_comp = multivariate_normal(means[k,:].ravel(), covs[k,:,:])
    gmm += weights[k]*mix_comp.pdf(pos)

plt.plot(data['Goals'], data['yellow_cards'], 'ko', alpha=0.3)
plt.contour(X, Y, gmm,  alpha = 1.0, zorder=10)    
plt.xlim([-8,8]);
plt.ylim([-6,6]);


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