Expectation Maximization is an iterative method. It starts with an initial parameter guess. The parameter values are used to compute the likelihood of the current model. This is the Expectation step. The parameter values are then recomputed to maximize the likelihood. This is the Maximization step. The new parameter estimates are used to compute a new expectation and then they are optimized again to maximize the likelihood. This iterative process continues until model convergence.

In density estimation, the goal is to construct a density function that captures how a given population is distributed. In probability density estimation, the density estimate is based on observed data that represents a sample of the population. Areas of high data density in the model correspond to the peaks of the underlying distribution.

Density-based clustering is conceptually different from distance-based clustering (for example k-Means) where emphasis is placed on minimizing inter-cluster and maximizing the intra-cluster distances. Due to its probabilistic nature, density-based clustering can compute reliable probabilities in cluster assignment. It can also handle missing values automatically.

Expectation Maximization (EM) in Oracle Data Mining, uses database parallel processing to achieve excellent scalability.

The Oracle Data Mining implementation of Expectation Maximization (EM) uses database parallel processing to achieve excellent scalability. EM computations naturally lend themselves to row parallel processing, and the partial results are easily aggregated. The parallel implementation efficiently distributes the computationally intensive work across slave processes and then combines the partial results to produce the final solution.

The Oracle Data Mining implementation of Expectation Maximization (EM) can efficiently process high-dimensional data with thousands of attributes. This is achieved through a two-fold process:

• The data space of single-column (not nested) attributes is analyzed for pair-wise correlations. Only attributes that are significantly correlated with other attributes are included in the EM mixture model. The algorithm can also be configured to restrict the dimensionality to the M most correlated attributes.

• High-dimensional (nested) numerical data that measures events of similar type is projected into a set of low-dimensional features that are modeled by EM. Some examples of high-dimensional, numerical data are: text, recommendations, gene expressions, and market basket data.

Choosing appropriate initial parameter values can have a significant effect on the quality of the solution. Expectation Maximization (EM) is not guaranteed to converge to the global maximum of the likelihood function but may instead converge to a local maximum. Therefore different initial parameter values can lead to different model parameters and different model quality.

In the process of model search, the EM model is grown independently. As new components are added, their parameters are initialized to areas with poor distribution fit.

Expectation Maximization (EM) model components are often treated as clusters. However, this approach can be misleading. Cohesive clusters are often modeled by multiple components. The shape of the probability density function used in EM effectively predetermines the shape of the identified clusters. For example, Gaussian density functions can identify single peak symmetric clusters. Clusters of more complex shape need to be modeled by multiple components.

Ideally, high density areas of arbitrary shape must be interpreted as single clusters. To accomplish this, the Oracle Data Mining implementation of EM builds a component hierarchy that is based on the overlap of the individual components' distributions. Oracle Data Mining EM uses agglomerative hierarchical clustering. Component distribution overlap is measured using the Bhattacharyya distance function. Choosing an appropriate cutoff level in the hierarchy automatically determines the number of high-level clusters.

The Oracle Data Mining implementation of EM produces an assignment of the model components to high-level clusters. Statistics like means, variances, modes, histograms, and rules additionally describe the high-level clusters. The algorithm can be configured to either produce clustering assignments at the component level or at the cluster level.