Unsupervised_Learning.md

Unsupervised Learning

Eduardo Muñoz

1. Distance Matrix

Normalizar las variables antes de aplicar la matriz de distancias

# Import Libraries
from scipy.spatial import distance_matrix # To calculate the ditance_matrix
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline

from mpl_toolkits.mplot3d import Axes3D # To show a 3d plot

# Import Dataset
data = pd.read_csv('../datasets/movies/movies.csv',sep=';')
data

user_id	star_wars	lord_of_the_rings	harry_potter
1	1.2	4.9	2.1
2	2.1	8.1	7.9
3	7.4	3	9.9
4	5.6	0.5	1.8
5	1.5	8.3	2.6
6	2.5	3.7	6.5
7	2	8.2	8.5
8	1.8	9.3	4.5
9	2.6	1.7	3.1
10	1.5	4.7	2.3

movies = data.columns.values.tolist()[1:] # List of column names: star_wars,lord_of_the_rings,harry_potter

dm1 = distance_matrix(data[movies],data[movies],p=1) # Manhattan Distance
dm2 = distance_matrix(data[movies],data[movies],p=2) # Euclidean Distance
dm10 = distance_matrix(data[movies],data[movies],p=10) # p>>> distance<<<

# Function to convert distance_matrix to a Dataframe
def distance_matrix_to_df(dd,col_name):
    return pd.DataFrame(dd,index=col_name,columns=col_name)
    
distance_matrix_to_df(dm1,data['user_id'])
distance_matrix_to_df(dm2,data['user_id'])
distance_matrix_to_df(dm10,data['user_id'])

Example: Distance Matrix (Manhattan Distance)

1	2	3	4	5	6	7	8	9	10
0	9.9	15.9	9.1	4.2	6.9	10.5	7.4	5.6	0.7
9.9	0	12.4	17.2	6.1	6.2	0.8	4.9	11.7	9.6
15.9	12.4	0	12.4	18.5	9	12	17.3	12.9	15.2
9.1	17.2	12.4	0	12.7	11	18	15.3	5.5	8.8
4.2	6.1	18.5	12.7	0	9.5	6.5	3.2	8.2	3.9
6.9	6.2	9	11	9.5	0	7	8.3	5.5	6.2
10.5	0.8	12	18	6.5	7	0	5.3	12.5	10.2
7.4	4.9	17.3	15.3	3.2	8.3	5.3	0	9.8	7.1
5.6	11.7	12.9	5.5	8.2	5.5	12.5	9.8	0	4.9
0.7	9.6	15.2	8.8	3.9	6.2	10.2	7.1	4.9	0

fig = plt.figure()
ax = fig.add_subplot(111,projection='3d')
ax.scatter(xs=data['star_wars'],ys=data['lord_of_the_rings'],zs=data['harry_potter']);

2. Hierarchical Clustering

2.1 Linkage Criterions

2.1.1 Single (Enlace Simple)

• Uses the minimum of the distances between all observations of the two clusters
• La distancia entre dos clusters es el mínimo de las distancias entre cualquier dos puntos del cluster 1 y el cluster 2

2.1.2 Complete (Enlace Completo)

• Uses the maximum of the distances between all observations of the two clusters
• La distancia entre dos clusters es el máximo de las distancias entre cualquier dos puntos del cluster 1 y el cluster 2

2.1.3 Average (Enlace Promedio)

• Uses the average of the distances between all observations of the two clusters
• La distancia entre dos clusters es el promedio de las distancias entre cualquier dos puntos del cluster 1 y el cluster 2

2.1.4 Centroid (Enlace del Centroide)

• Distances between centroids of two clusters
• La distancia entre dos clusters es la distancia entre el centroide (punto medio) del cluster 1 y el del cluster 2

2.1.5 Ward (Enlace de Ward)

• Minimizes the variance of the clustes bieng merged
• Los clusters minimizan la varianza dentro de los puntos del mismo y en el dataset global

# Hierarchical Clustering
import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import dendrogram, linkage

# Linkage: WARD Distance: EUCLIDEAN 
Z = linkage(data[movies],method='ward',metric='euclidean') # data[movies] definido arriba

# Plot Dendrogram 
plt.figure(figsize=(25,10))
plt.title('Dendograma para el Clustering Jerarquico')
plt.xlabel('ID usuarios Netflix')
plt.ylabel('Distancia')
dendrogram(Z, leaf_rotation=0, leaf_font_size=10)
plt.show();

# Linkage: CENTROID Distance: EUCLIDEAN 
Z = linkage(data[movies],method='centroid',metric='euclidean') # data[movies] definido arriba

# Plot Dendrogram 
plt.figure(figsize=(25,10))
plt.title('Dendograma para el Clustering Jerarquico')
plt.xlabel('ID usuarios Netflix')
plt.ylabel('Distancia')
dendrogram(Z, leaf_rotation=0, leaf_font_size=10)
plt.show();

Example: Hierarchical Clustering

• X dataset (array n x m) de puntos a clusterizar
• n número de datos (Rows)
• m número de rasgos (Columns)
• Z array de enlace del cluster con la info de uniones
• k número de clusters

2.2 Pros and Cons

Pros

• We don't need to specify number of clusters
• It does not make any assumption in the data shape so it's suitebale for any shape

Cons

• We need to specify a threshold distance
• Very sensitive to distance and linkage criterion

3. KMeans