Marketing Analytics HW2.py

#!/usr/bin/env python
# coding: utf-8

# In[3]:


import pandas as pd
import numpy as np
from sklearn.preprocessing import StandardScaler
from sklearn.cluster import KMeans
import matplotlib.pyplot as plt
import seaborn as sns


# In[6]:


df = pd.read_csv('transactions_n100000.csv')
df.head()


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#drop longtitude, latitude, ticket_id, order_timestamp
df = df.iloc[:, 2:5]


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df


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categorical_features = df['item_name']
categorical_features.unique()


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dummies = pd.get_dummies(categorical_features)
print(dummies)


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df1 = pd.concat([df, dummies], axis=1)
del df1["item_name"]
df1


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df1[["location", "item_count"]] = StandardScaler().fit_transform(df1[["location", "item_count"]])
df1


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from sklearn.mixture import GaussianMixture
from sklearn.decomposition import PCA
from scipy.stats import multivariate_normal as mvn
sklearn_pca = PCA(n_components = 2)
Y_sklearn = sklearn_pca.fit_transform(df1)
clusters = 3
gmm = GaussianMixture(n_components=clusters, covariance_type='full').fit(Y_sklearn)
prediction_gmm = gmm.predict(Y_sklearn)
probs = gmm.predict_proba(Y_sklearn)

centers = np.zeros((clusters,2))
for i in range(clusters):
    density = mvn(cov=gmm.covariances_[i], mean=gmm.means_[i]).logpdf(Y_sklearn)
    centers[i, :] = Y_sklearn[np.argmax(density)]

plt.figure(figsize = (10,8))
plt.scatter(Y_sklearn[:, 0], Y_sklearn[:, 1],c=prediction_gmm ,s=50, cmap='viridis')
plt.scatter(centers[:, 0], centers[:, 1],c='black', s=300, alpha=0.6);


# In[64]:


import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse
from sklearn.mixture import GaussianMixture as GMM
from sklearn import metrics
from sklearn.model_selection import train_test_split
from matplotlib import rcParams
rcParams['figure.figsize'] = 16, 8

def draw_ellipse(position, covariance, ax=None, **kwargs):
    """Draw an ellipse with a given position and covariance"""
    ax = ax or plt.gca()
    # Convert covariance to principal axes
    if covariance.shape == (2, 2):
        U, s, Vt = np.linalg.svd(covariance)
        angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))
        width, height = 2 * np.sqrt(s)
    else:
        angle = 0
        width, height = 2 * np.sqrt(covariance)
    
    # Draw the Ellipse
    for nsig in range(1, 4):
        ax.add_patch(Ellipse(position, nsig * width, nsig * height,
                             angle, **kwargs))
        
def plot_gmm(gmm, X, label=True, ax=None):
    ax = ax or plt.gca()
    labels = gmm.fit(X).predict(X)
    if label:
        ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)
    else:
        ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2)
    
    w_factor = 0.2 / gmm.weights_.max()
    for pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):
        draw_ellipse(pos, covar, alpha=w * w_factor)
    plt.title("GMM with %d components"%len(gmm.means_), fontsize=(20))
    plt.xlabel("U.A.")
    plt.ylabel("U.A.")
def SelBest(arr:list, X:int)->list:
    '''
    returns the set of X configurations with shorter distance
    '''
    dx=np.argsort(arr)[:X]
    return arr[dx]


# In[65]:


plot_gmm(gmm, Y_sklearn)


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#But do we really want to use 3 clusters?
n_clusters=np.arange(2, 6)
bics=[]
bics_err=[]
iterations=6
for n in n_clusters:
    tmp_bic=[]
    for _ in range(iterations):
        gmm=GMM(n, n_init=2).fit(Y_sklearn) 
        
        tmp_bic.append(gmm.bic(Y_sklearn))
    val=np.mean(SelBest(np.array(tmp_bic), int(iterations/5)))
    err=np.std(tmp_bic)
    bics.append(val)
    bics_err.append(err)


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plt.errorbar(n_clusters,bics, yerr=bics_err, label='BIC')
plt.title("BIC Scores", fontsize=20)
plt.xticks(n_clusters)
plt.xlabel("N. of clusters")
plt.ylabel("Score")
plt.legend()


# In[70]:


plt.errorbar(n_clusters, np.gradient(bics), yerr=bics_err, label='BIC')
plt.title("Gradient of BIC Scores", fontsize=20)
plt.xticks(n_clusters)
plt.xlabel("N. of clusters")
plt.ylabel("grad(BIC)")
plt.legend()


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#Since we want to maximize the gradient as reasonably as possibly without using too many clusters (to make things simpler),
#then 2 clusters is the best.


# In[71]:


clusters = 2
gmm = GaussianMixture(n_components=clusters, covariance_type='full').fit(Y_sklearn)
prediction_gmm = gmm.predict(Y_sklearn)
probs = gmm.predict_proba(Y_sklearn)

centers = np.zeros((clusters,2))
for i in range(clusters):
    density = mvn(cov=gmm.covariances_[i], mean=gmm.means_[i]).logpdf(Y_sklearn)
    centers[i, :] = Y_sklearn[np.argmax(density)]

plt.figure(figsize = (10,8))
plt.scatter(Y_sklearn[:, 0], Y_sklearn[:, 1], c=prediction_gmm, s=50, cmap='viridis')
plt.scatter(centers[:, 0], centers[:, 1], c='black', s=300, alpha=0.6);


# In[72]:


plot_gmm(gmm, Y_sklearn)


# In[33]:


sklearn_pca.components_


# In[61]:


def visualize_components(components, feature_x, n_components, ):
    fig = plt.figure(figsize=(15, 15))
    ax = plt.subplot()
    ax.imshow(components.T)
    ax.set_yticks(np.arange(0, len(feature_x)))
    ax.set_yticklabels(feature_x, fontsize=15)
    ax.set_xticks(np.arange(0, n_components))
    ax.set_xticklabels([i + 1 for i in range(n_components)], fontsize=15)
    ax.set_xlabel('Components', fontsize=15)
    ax.set_ylabel('Features', fontsize=15)
    pos = ax.imshow(components.T, interpolation='none')
    fig.colorbar(pos, ax=ax)
    plt.show()


# In[62]:


visualize_components(sklearn_pca.components_, df1.columns, 2)


# In[73]:


df1['pred'] = pd.Series(prediction_gmm, index=df1.index)
df1


# In[96]:


df = pd.read_csv('transactions_n100000.csv')
df_final = df.copy()
df_final['pred'] = df1['pred']
df_final


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two_cluster_pred = df_final.to_csv('two_cluster_pred.csv', index = True)


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