K- MEANS

K-means clustering is a type of unsupervised learning, which is used when you have unlabeled data (i.e., data without defined categories or groups). The goal of this algorithm is to find groups in the data, with the number of groups represented by the variable K. The algorithm works iteratively to assign each data point to one of K groups based on the features that are provided. Data points are clustered based on feature similarity. The results of the K-means clustering algorithm are:

The centroids of the K clusters, which can be used to label new data

Labels for the training data (each data point is assigned to a single cluster)

Rather than defining groups before looking at the data, clustering allows you to find and analyze the groups that have formed organically. The "Choosing K" section below describes how the number of groups can be determined.

Each centroid of a cluster is a collection of feature values which define the resulting groups. Examining the centroid feature weights can be used to qualitatively interpret what kind of group each cluster represents.

The Κ-means clustering algorithm uses iterative refinement to produce a final result. The algorithm inputs are the number of clusters Κ and the data set. The data set is a collection of features for each data point. The algorithms starts with initial estimates for the Κ centroids, which can either be randomly generated or randomly selected from the data set. The algorithm then iterates between two steps:

Data assigment step:

Each centroid defines one of the clusters. In this step, each data point is assigned to its nearest centroid, based on the squared Euclidean distance. More formally, if ci is the collection of centroids in set C, then each data point x is assigned to a cluster based on

$$\underset{c_i \in C}{\arg\min} ; dist(c_i,x)^2$$

where dist( · ) is the standard (L2) Euclidean distance. Let the set of data point assignments for each ith cluster centroid be Si.

Centroid update step:

In this step, the centroids are recomputed. This is done by taking the mean of all data points assigned to that centroid's cluster. $$c_i=\frac{1}{|S_i|}\sum_{x_i \in S_i x_i}$$

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans

df = pd.read_csv('vinos.csv')

df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 178 entries, 0 to 177
Data columns (total 14 columns):
 #   Column           Non-Null Count  Dtype  
---  ------           --------------  -----  
 0   Vino             178 non-null    int64  
 1   Alcohol          178 non-null    float64
 2   Malic            178 non-null    float64
 3   Ash              178 non-null    float64
 4   Alcalinity       178 non-null    float64
 5   Magnesium        178 non-null    int64  
 6   Phenols          178 non-null    float64
 7   Flavanoids       178 non-null    float64
 8   Nonflavanoids    178 non-null    float64
 9   Proanthocyanins  178 non-null    float64
 10  Color            178 non-null    float64
 11  Hue              178 non-null    float64
 12  Dilution         178 non-null    float64
 13  Proline          178 non-null    int64  
dtypes: float64(11), int64(3)
memory usage: 19.6 KB

df.head()
df.drop(['Vino'], axis=1, inplace=True)

df.describe()

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	Alcohol	Malic	Ash	Alcalinity	Magnesium	Phenols	Flavanoids	Nonflavanoids	Proanthocyanins	Color	Hue	Dilution	Proline
count	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000
mean	13.000618	2.336348	2.366517	19.494944	99.741573	2.295112	2.029270	0.361854	1.590899	5.058090	0.957449	2.611685	746.893258
std	0.811827	1.117146	0.274344	3.339564	14.282484	0.625851	0.998859	0.124453	0.572359	2.318286	0.228572	0.709990	314.907474
min	11.030000	0.740000	1.360000	10.600000	70.000000	0.980000	0.340000	0.130000	0.410000	1.280000	0.480000	1.270000	278.000000
25%	12.362500	1.602500	2.210000	17.200000	88.000000	1.742500	1.205000	0.270000	1.250000	3.220000	0.782500	1.937500	500.500000
50%	13.050000	1.865000	2.360000	19.500000	98.000000	2.355000	2.135000	0.340000	1.555000	4.690000	0.965000	2.780000	673.500000
75%	13.677500	3.082500	2.557500	21.500000	107.000000	2.800000	2.875000	0.437500	1.950000	6.200000	1.120000	3.170000	985.000000
max	14.830000	5.800000	3.230000	30.000000	162.000000	3.880000	5.080000	0.660000	3.580000	13.000000	1.710000	4.000000	1680.000000

Normalizar valores

df_norm = (df - df.min())/(df.max()-df.min())
df_norm.head()

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	Alcohol	Malic	Ash	Alcalinity	Magnesium	Phenols	Flavanoids	Nonflavanoids	Proanthocyanins	Color	Hue	Dilution	Proline
0	0.842105	0.191700	0.572193	0.257732	0.619565	0.627586	0.573840	0.283019	0.593060	0.372014	0.455285	0.970696	0.561341
1	0.571053	0.205534	0.417112	0.030928	0.326087	0.575862	0.510549	0.245283	0.274448	0.264505	0.463415	0.780220	0.550642
2	0.560526	0.320158	0.700535	0.412371	0.336957	0.627586	0.611814	0.320755	0.757098	0.375427	0.447154	0.695971	0.646933
3	0.878947	0.239130	0.609626	0.319588	0.467391	0.989655	0.664557	0.207547	0.558360	0.556314	0.308943	0.798535	0.857347
4	0.581579	0.365613	0.807487	0.536082	0.521739	0.627586	0.495781	0.490566	0.444795	0.259386	0.455285	0.608059	0.325963

Cantidad de K

Codo de Jambu: Usar diferentes cluster e ir viendo que tan similares son los individuos dentro de los clusters

similaridad = []

for i in range(1,11):
    kmeans = KMeans(n_clusters = i, max_iter = 300)
    kmeans.fit(df_norm)
    similaridad.append(kmeans.inertia_)

plt.plot(range(1,11), k)
plt.title('Codo de Jambu')
plt.xlabel('Numero de CLusters')
plt.ylabel('Similaridad')

Text(0, 0.5, 'Similaridad')

Aplicando K-Means

clustering = KMeans(n_clusters=3, max_iter=300)
clustering.fit(df_norm)

KMeans(n_clusters=3)

Agregando al archivo original

df['Cluster'] = clustering.labels_
df.head()

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	Alcohol	Malic	Ash	Alcalinity	Magnesium	Phenols	Flavanoids	Nonflavanoids	Proanthocyanins	Color	Hue	Dilution	Proline
0	14.23	1.71	2.43	15.6	127	2.80	3.06	0.28	2.29	5.64	1.04	3.92	1065
1	13.20	1.78	2.14	11.2	100	2.65	2.76	0.26	1.28	4.38	1.05	3.40	1050
2	13.16	2.36	2.67	18.6	101	2.80	3.24	0.30	2.81	5.68	1.03	3.17	1185
3	14.37	1.95	2.50	16.8	113	3.85	3.49	0.24	2.18	7.80	0.86	3.45	1480
4	13.24	2.59	2.87	21.0	118	2.80	2.69	0.39	1.82	4.32	1.04	2.93	735

Visualizando

from sklearn.decomposition import PCA

pca = PCA(n_components=2)
pca_vinos = pca.fit_transform(df_norm)
pca_vinos_df = pd.DataFrame(data=pca_vinos, columns=['Componente_1', 'Componente_2'])
pca_nombres_vinos = pd.concat([pca_vinos_df, df[['Cluster']]], axis=1)

fig = plt.figure(figsize=(6,6))
ax = fig.add_subplot(1,1,1)
ax.set_xlabel('Componente_1', fontsize=14)
ax.set_ylabel('Componente_2', fontsize=14)
ax.set_title('Componentes principales', fontsize=20)

colores = np.array(['blue','red','orange'])
ax.scatter(x = pca_nombres_vinos.Componente_1, y=pca_nombres_vinos.Componente_2, c=colores[pca_nombres_vinos.Cluster], s=50)

<matplotlib.collections.PathCollection at 0x7f81cf4831d0>

df.to_csv('vinos_kmeans.csv')

JorgePablol/K-Means

K- MEANS

Normalizar valores

Cantidad de K

Aplicando K-Means

Agregando al archivo original

Visualizando