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467 KiB
467 KiB
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Hierarchal Clustering¶
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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
The Data¶
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df = pd.read_csv('../DATA/cluster_mpg.csv')
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df = df.dropna()
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df.head()
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df.describe()
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df['origin'].value_counts()
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df_w_dummies = pd.get_dummies(df.drop('name',axis=1))
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df_w_dummies
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from sklearn.preprocessing import MinMaxScaler
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scaler = MinMaxScaler()
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scaled_data = scaler.fit_transform(df_w_dummies)
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scaled_data
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scaled_df = pd.DataFrame(scaled_data,columns=df_w_dummies.columns)
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plt.figure(figsize=(15,8))
sns.heatmap(scaled_df,cmap='magma');
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sns.clustermap(scaled_df,row_cluster=False)
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sns.clustermap(scaled_df,col_cluster=False)
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Using Scikit-Learn¶
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from sklearn.cluster import AgglomerativeClustering
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model = AgglomerativeClustering(n_clusters=4)
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cluster_labels = model.fit_predict(scaled_df)
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cluster_labels
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plt.figure(figsize=(12,4),dpi=200)
sns.scatterplot(data=df,x='mpg',y='weight',hue=cluster_labels)
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Exploring Number of Clusters with Dendrograms¶
Make sure to read the documentation online! https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.dendrogram.html
Assuming every point starts as its own cluster¶
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model = AgglomerativeClustering(n_clusters=None,distance_threshold=0)
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cluster_labels = model.fit_predict(scaled_df)
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cluster_labels
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from scipy.cluster.hierarchy import dendrogram
from scipy.cluster import hierarchy
Linkage Model¶
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linkage_matrix = hierarchy.linkage(model.children_)
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linkage_matrix
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plt.figure(figsize=(20,10))
# Warning! This plot will take awhile!!
dn = hierarchy.dendrogram(linkage_matrix)
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plt.figure(figsize=(20,10))
dn = hierarchy.dendrogram(linkage_matrix,truncate_mode='lastp',p=48)
Choosing a Threshold Distance¶
What is the distance between two points?
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scaled_df.describe()
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scaled_df['mpg'].idxmax()
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scaled_df['mpg'].idxmin()
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# https://stackoverflow.com/questions/1401712/how-can-the-euclidean-distance-be-calculated-with-numpy
a = scaled_df.iloc[320]
b = scaled_df.iloc[28]
dist = np.linalg.norm(a-b)
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dist
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Max possible distance?¶
Recall Euclidean distance: https://en.wikipedia.org/wiki/Euclidean_distance
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np.sqrt(len(scaled_df.columns))
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Creating a Model Based on Distance Threshold¶
- distance_threshold
- The linkage distance threshold above which, clusters will not be merged.
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model = AgglomerativeClustering(n_clusters=None,distance_threshold=2)
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cluster_labels = model.fit_predict(scaled_data)
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cluster_labels
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np.unique(cluster_labels)
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Linkage Matrix¶
A (n-1) by 4 matrix Z is returned. At the i-th iteration, clusters with indices Z[i, 0] and Z[i, 1] are combined to form cluster n + i. A cluster with an index less than n corresponds to one of the original observations. The distance between clusters Z[i, 0] and Z[i, 1] is given by Z[i, 2]. The fourth value Z[i, 3] represents the number of original observations in the newly formed cluster.
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linkage_matrix = hierarchy.linkage(model.children_)
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linkage_matrix
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plt.figure(figsize=(20,10))
dn = hierarchy.dendrogram(linkage_matrix,truncate_mode='lastp',p=11)
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