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======= | ||
K-means | ||
======= | ||
:math:`K`-means clustering aims to partition :math:`n` observations into :math:`k\leq n` clusters (sets :math:`\mathbf{S}`), | ||
in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. | ||
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In other words, its objective is to minimize: | ||
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.. math:: | ||
\argmin_\mathbf{S} \sum_{i=1}^{k}\sum_{\mathbf{x}\in S_k}\left \|\boldsymbol{x} - \boldsymbol{\mu}_i \right \|^{2} | ||
where :math:`\mathbf{μ}_i` is the mean of points in :math:`S_i`. | ||
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See Chapter 20 in :cite:`barber2012bayesian` for a detailed introduction. | ||
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------- | ||
Example | ||
------- | ||
Imagine we have files with training and test data. We create CDenseFeatures (here 64 bit floats aka RealFeatures) as | ||
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.. sgexample:: kmeans.sg:create_features | ||
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In order to run :sgclass:`CKMeans`, we need to choose a distance, for example :sgclass:`CEuclideanDistance`, or other sub-classes of :sgclass:`CDistance`. The distance is initialized with the data we want to classify. | ||
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.. sgexample:: kmeans.sg:choose_distance | ||
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Once we have chosen a distance, we create an instance of the :sgclass:`CKMeans` classifier. | ||
We explicitly set :math:`k`, the number of clusters we are expecting to have as 3 and pass it to :sgclass:`CKMeans`. In this example, we apply Lloyd's method for `k`-means clustering. | ||
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.. sgexample:: kmeans.sg:create_instance_lloyd | ||
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Then we train the model: | ||
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.. sgexample:: kmeans.sg:train_dataset | ||
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We can extract centers and radius of each cluster: | ||
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.. sgexample:: kmeans.sg:extract_centers_and_radius | ||
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:sgclass:`CKMeans` also supports mini batch :math:`k`-means clustering. | ||
We can create an instance of :sgclass:`CKMeans` classifier with mini batch :math:`k`-means method by providing the batch size and iteration number. | ||
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.. sgexample:: kmeans.sg:create_instance_mb | ||
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Then train the model and extract the centers and radius information as mentioned above. | ||
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---------- | ||
References | ||
---------- | ||
:wiki:`K-means_clustering` | ||
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:wiki:`Lloyd's_algorithm` | ||
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.. bibliography:: ../../references.bib | ||
:filter: docname in docnames |
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CSVFile f_feats_train("../../data/classifier_binary_2d_linear_features_train.dat") | ||
Math:init_random(1) | ||
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#![create_features] | ||
RealFeatures features_train(f_feats_train) | ||
#![create_features] | ||
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#![choose_distance] | ||
EuclideanDistance distance(features_train, features_train) | ||
#![choose_distance] | ||
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#![create_instance_lloyd] | ||
KMeans kmeans(2, distance, enum EKMeansMethod.KMM_LLOYD) | ||
#![create_instance_lloyd] | ||
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#![train_dataset] | ||
kmeans.train() | ||
#![train_dataset] | ||
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#![extract_centers_and_radius] | ||
RealMatrix c = kmeans.get_cluster_centers() | ||
RealVector r = kmeans.get_radiuses() | ||
#![extract_centers_and_radius] | ||
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#![create_instance_mb] | ||
KMeans kmeans_mb(2, distance, enum EKMeansMethod.KMM_MINI_BATCH) | ||
kmeans_mb.set_mini_batch_parameters(4, 1000) | ||
#![create_instance_mb] |
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examples/undocumented/csharp_modular/clustering_kmeans_modular.cs
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examples/undocumented/java_modular/clustering_kmeans_modular.java
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examples/undocumented/octave_modular/clustering_kmeans_modular.m
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examples/undocumented/python_modular/clustering_kmeans_modular.py
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