17 O-Cluster

This chapter describes Orthogonal Partitioning Clustering (O-Cluster), an Oracle-proprietary clustering algorithm.

About O-Cluster

The O-Cluster algorithm creates a hierarchical grid-based clustering model, that is, it creates axis-parallel (orthogonal) partitions in the input attribute space. The algorithm operates recursively. The resulting hierarchical structure represents an irregular grid that tessellates the attribute space into clusters. The resulting clusters define dense areas in the attribute space.

The clusters are described by intervals along the attribute axes and the corresponding centroids and histograms. A parameter called sensitivity defines a baseline density level. Only areas with peak density above this baseline level can be identified as clusters.

The k-means algorithm tessellates the space even when natural clusters may not exist. For example, if there is a region of uniform density, k-Means tessellates it into n clusters (where n is specified by the user). O-Cluster separates areas of high density by placing cutting planes through areas of low density. O-Cluster needs multi-modal histograms (peaks and valleys). If an area has projections with uniform or monotonically changing density, O-Cluster does not partition it.

The clusters discovered by O-Cluster are used to generate a Bayesian probability model that is then used during scoring (model apply) for assigning data points to clusters. The generated probability model is a mixture model where the mixture components are represented by a product of independent normal distributions for numerical attributes and multinomial distributions for categorical attributes.

Data Preparation for O-Cluster

Automatic Data Preparation bins numerical attributes for O-Cluster. It uses a specialized form of equi-width binning that computes the number of bins per attribute automatically. Numerical columns with all nulls or a single value are removed.

O-Cluster handles missing values naturally as missing at random. The algorithm does not support nested tables and thus does not support sparse data.

User-Specified Data Preparation for O-Cluster

Keep the following in mind if you choose to prepare the data for O-Cluster"

O-Cluster does not necessarily use all the input data when it builds a model. It reads the data in batches (the default batch size is 50000). It will only read another batch if it believes, based on statistical tests, that there may still exist clusters that it has not yet uncovered.

Because O-Cluster may stop the model build before it reads all of the data, it is highly recommended that the data be randomized.
Binary attributes should be declared as categorical. O-Cluster maps categorical data to numerical values.
The use of Oracle Data Mining's equi-width binning transformation with automated estimation of the required number of bins is highly recommended.
The presence of outliers can significantly impact clustering algorithms. Use a clipping transformation before binning or normalizing. Outliers with equi-width binning can prevent O-Cluster from detecting clusters. As a result, the whole population appears to falls within a single cluster.