Add kmeans page to cookbook

doc/cookbook/source/examples/clustering/kmeans.rst

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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.
+
+In other words, its objective is to minimize:
+
+.. 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`.
+
+See Chapter 20 in :cite:`barber2012bayesian` for a detailed introduction.
+
+-------
+Example
+-------
+Imagine we have files with training and test data. We create CDenseFeatures (here 64 bit floats aka RealFeatures) as
+
+.. sgexample:: kmeans.sg:create_features
+
+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.
+
+.. sgexample:: kmeans.sg:choose_distance
+
+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.
+
+.. sgexample:: kmeans.sg:create_instance_lloyd
+
+Then we train the model:
+
+.. sgexample:: kmeans.sg:train_dataset
+
+We can extract centers and radius of each cluster:
+
+.. sgexample:: kmeans.sg:extract_centers_and_radius
+
+
+: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.
+
+.. sgexample:: kmeans.sg:create_instance_mb
+
+Then train the model and extract the centers and radius information as mentioned above.
+
+----------
+References
+----------
+:wiki:`K-means_clustering`
+
+:wiki:`Lloyd's_algorithm`
+
+.. bibliography:: ../../references.bib
+    :filter: docname in docnames

examples/meta/src/clustering/kmeans.sg

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+CSVFile f_feats_train("../../data/classifier_binary_2d_linear_features_train.dat")
+Math:init_random(1)
+
+#![create_features]
+RealFeatures features_train(f_feats_train)
+#![create_features]
+
+#![choose_distance]
+EuclideanDistance distance(features_train, features_train)
+#![choose_distance]
+
+#![create_instance_lloyd]
+KMeans kmeans(2, distance)
+#![create_instance_lloyd]
+
+#![train_dataset]
+kmeans.train()
+#![train_dataset]
+
+#![extract_centers_and_radius]
+RealMatrix c = kmeans.get_cluster_centers()
+RealVector r = kmeans.get_radiuses()
+#![extract_centers_and_radius]
+
+#![create_instance_mb]
+KMeansMiniBatch kmeans_mb(2, distance)
+kmeans_mb.set_mb_params(4, 1000)
+#![create_instance_mb]