- Scikit Learn - Discussion
- Scikit Learn - Useful Resources
- Scikit Learn - Quick Guide
- Dimensionality Reduction using PCA
- Clustering Performance Evaluation
- Scikit Learn - Clustering Methods
- Scikit Learn - Boosting Methods
- Randomized Decision Trees
- Scikit Learn - Decision Trees
- Classification with Naïve Bayes
- Scikit Learn - KNN Learning
- Scikit Learn - K-Nearest Neighbors
- Scikit Learn - Anomaly Detection
- Scikit Learn - Support Vector Machines
- Stochastic Gradient Descent
- Scikit Learn - Extended Linear Modeling
- Scikit Learn - Linear Modeling
- Scikit Learn - Conventions
- Scikit Learn - Estimator API
- Scikit Learn - Data Representation
- Scikit Learn - Modelling Process
- Scikit Learn - Introduction
- Scikit Learn - Home
Selected Reading
- Computer Glossary
- HR Interview Questions
- Effective Resume Writing
- Questions and Answers
- UPSC IAS Exams Notes
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Scikit Learn - Clustering Performance Evaluation
There are various functions with the help of which we can evaluate the performance of clustering algorithms.
Following are some important and mostly used functions given by the Scikit-learn for evaluating clustering performance −
Adjusted Rand Index
Rand Index is a function that computes a similarity measure between two clustering. For this computation rand index considers all pairs of samples and counting pairs that are assigned in the similar or different clusters in the predicted and true clustering. Afterwards, the raw Rand Index score is ‘adjusted for chance’ into the Adjusted Rand Index score by using the following formula −
$$Adjusted:RI=left(RI-Expected_{-}RI ight)/left(maxleft(RI ight)-Expected_{-}RI ight)$$It has two parameters namely labels_true, which is ground truth class labels, and labels_pred, which are clusters label to evaluate.
Example
from sklearn.metrics.cluster import adjusted_rand_score labels_true = [0, 0, 1, 1, 1, 1] labels_pred = [0, 0, 2, 2, 3, 3] adjusted_rand_score(labels_true, labels_pred)
Output
0.4444444444444445
Perfect labepng would be scored 1 and bad labelpng or independent labelpng is scored 0 or negative.
Mutual Information Based Score
Mutual Information is a function that computes the agreement of the two assignments. It ignores the permutations. There are following versions available −
Normapzed Mutual Information (NMI)
Scikit learn have sklearn.metrics.normapzed_mutual_info_score module.
Example
from sklearn.metrics.cluster import normapzed_mutual_info_score labels_true = [0, 0, 1, 1, 1, 1] labels_pred = [0, 0, 2, 2, 3, 3] normapzed_mutual_info_score (labels_true, labels_pred)
Output
0.7611702597222881
Adjusted Mutual Information (AMI)
Scikit learn have sklearn.metrics.adjusted_mutual_info_score module.
Example
from sklearn.metrics.cluster import adjusted_mutual_info_score labels_true = [0, 0, 1, 1, 1, 1] labels_pred = [0, 0, 2, 2, 3, 3] adjusted_mutual_info_score (labels_true, labels_pred)
Output
0.4444444444444448
Fowlkes-Mallows Score
The Fowlkes-Mallows function measures the similarity of two clustering of a set of points. It may be defined as the geometric mean of the pairwise precision and recall.
Mathematically,
$$FMS=frac{TP}{sqrt{left(TP+FP ight)left(TP+FN ight)}}$$Here, TP = True Positive − number of pair of points belonging to the same clusters in true as well as predicted labels both.
FP = False Positive − number of pair of points belonging to the same clusters in true labels but not in the predicted labels.
FN = False Negative − number of pair of points belonging to the same clusters in the predicted labels but not in the true labels.
The Scikit learn has sklearn.metrics.fowlkes_mallows_score module −
Example
from sklearn.metrics.cluster import fowlkes_mallows_score labels_true = [0, 0, 1, 1, 1, 1] labels_pred = [0, 0, 2, 2, 3, 3] fowlkes_mallows__score (labels_true, labels_pred)
Output
0.6546536707079771
Silhouette Coefficient
The Silhouette function will compute the mean Silhouette Coefficient of all samples using the mean intra-cluster distance and the mean nearest-cluster distance for each sample.
Mathematically,
$$S=left(b-a ight)/maxleft(a,b ight)$$Here, a is intra-cluster distance.
and, b is mean nearest-cluster distance.
The Scikit learn have sklearn.metrics.silhouette_score module −
Example
from sklearn import metrics.silhouette_score from sklearn.metrics import pairwise_distances from sklearn import datasets import numpy as np from sklearn.cluster import KMeans dataset = datasets.load_iris() X = dataset.data y = dataset.target kmeans_model = KMeans(n_clusters = 3, random_state = 1).fit(X) labels = kmeans_model.labels_ silhouette_score(X, labels, metric = eucpdean )
Output
0.5528190123564091
Contingency Matrix
This matrix will report the intersection cardinapty for every trusted pair of (true, predicted). Confusion matrix for classification problems is a square contingency matrix.
The Scikit learn have sklearn.metrics.contingency_matrix module.
Example
from sklearn.metrics.cluster import contingency_matrix x = ["a", "a", "a", "b", "b", "b"] y = [1, 1, 2, 0, 1, 2] contingency_matrix(x, y)
Output
array([ [0, 2, 1], [1, 1, 1] ])
The first row of above output shows that among three samples whose true cluster is “a”, none of them is in 0, two of the are in 1 and 1 is in 2. On the other hand, second row shows that among three samples whose true cluster is “b”, 1 is in 0, 1 is in 1 and 1 is in 2.
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