13 k-Means

About k-Means

The k-Means algorithm is a distance-based clustering algorithm that partitions the data into a predetermined number of clusters (provided there are enough distinct cases).

Distance-based algorithms rely on a distance metric (function) to measure the similarity between data points. The distance metric is either Euclidean, Cosine, or Fast Cosine distance. Data points are assigned to the nearest cluster according to the distance metric used.

Oracle Data Mining implements an enhanced version of the k-means algorithm with the following features:

• The algorithm builds models in a hierarchical manner. The algorithm builds a model top down using binary splits and refinement of all nodes at the end. In this sense, the algorithm is similar to the bisecting k-means algorithm. The centroid of the inner nodes in the hierarchy are updated to reflect changes as the tree evolves. The whole tree is returned.

• The algorithm grows the tree one node at a time (unbalanced approach). Based on a user setting available in either of the programming interfaces, the node with the largest variance is split to increase the size of the tree until the desired number of clusters is reached. The maximum number of clusters is specified in the build setting for clustering models, CLUS_NUM_CLUSTERS. (See Chapter 7, "Clustering".)

• The algorithm provides probabilistic scoring and assignment of data to clusters.

• The algorithm returns, for each cluster, a centroid (cluster prototype), histograms (one for each attribute), and a rule describing the hyperbox that encloses the majority of the data assigned to the cluster. The centroid reports the mode for categorical attributes or the mean and variance for numerical attributes.

This approach to k-means avoids the need for building multiple k-means models and provides clustering results that are consistently superior to the traditional k-means.

The clusters discovered by enhanced k-Means are used to generate a Bayesian probability model that is then used during scoring (model apply) for assigning data points to clusters. The k-means algorithm can be interpreted as a mixture model where the mixture components are spherical multivariate normal distributions with the same variance for all components.

Data Preparation for k-Means

Automatic Data Preparation performs outlier-sensitive normalization for k-Means.

When there are missing values in columns with simple data types (not nested), k-Means interprets them as missing at random. The algorithm replaces missing categorical values with the mode and missing numerical values with the mean.

When there are missing values in nested columns, k-Means interprets them as sparse. The algorithm replaces sparse numerical data with zeros and sparse categorical data with zero vectors.

If you manage your own data preparation for k-Means, keep in mind that outliers with equi-width binning can prevent k-Means from creating clusters that are different in content. The clusters may have very similar centroids, histograms, and rules.