# Item Distribution Performance (AI Studio Core)

## Synopsis

This operator is used for performance evaluation of flat clustering methods. It evaluates a cluster model based on the distribution of examples.## Description

The clustering operators like the K-Means and K-Medoids produce a flat cluster model and a clustered set. The cluster model has information regarding the clustering performed. It tells which examples are parts of which cluster. The Item Distribution Performance operator takes this cluster model as input and evaluates the performance of the model based on the distribution of examples i.e. how well the examples are distributed over the clusters. Two distribution measures are supported: Sum of Squares and Gini Coefficient. These distribution measures are explained in the parameters. Flat clustering creates a flat set of clusters without any explicit structure that would relate clusters to each other. Hierarchical clustering, on the other hand, creates a hierarchy of clusters. This operator can only be applied on models produced by operators that produce flat cluster models e.g. K-Means or K-Medoids operators. It cannot be applied on models created by the operators that produce a hierarchy of clusters e.g. the Agglomerative Clustering operator.

Clustering is concerned with grouping together objects that are similar to each other and dissimilar to the objects belonging to other clusters. It is a technique for extracting information from unlabeled data and can be very useful in many different scenarios e.g. in a marketing application we may be interested in finding clusters of customers with similar buying behavior.

## Input

- cluster model (Cluster Model)
This input port expects a flat cluster model. It is output of the K-Medoids operator in the attached Example Process. The cluster model has information regarding the clustering performed. It tells which examples are part of which cluster.

- performance vector (Performance Vector)
This input port expects a Performance Vector.

## Output

- cluster model (Cluster Model)
The cluster model that was given as input is passed without changing to the output through this port. This is usually used to reuse the same cluster model in further operators or to view it in the Results Workspace.

- performance vector (Performance Vector)
The performance of the cluster model is evaluated and the resultant Performance Vector is delivered through this port. It is a list of performance criteria values.

## Parameters

- measureThis parameter specifies the item distribution measure to apply. It has two options:
- sum of squares: If this option is selected, the sum of squares is used as the item distribution measure.
- gini coefficient: The Gini coefficient (also known as the Gini index or Gini ratio) is a measure of statistical dispersion. It measures the inequality among values of a frequency distribution. A low Gini coefficient indicates a more equal distribution, with 0 corresponding to complete equality, while higher Gini coefficients indicate a more unequal distribution, with 1 corresponding to complete inequality.

## Tutorial Processes

### Evaluating the performance of the K-Medoids clustering model

The 'Ripley-Set' data set is loaded using the Retrieve operator. Note that the *label* is loaded too, but it is only used for visualization and comparison and not for building the clusters themselves. A *breakpoint* is inserted at this step so that you can have a look at the ExampleSet before the application of the K-Medoids operator. The 'Ripley-Set' has two real attributes; 'att1' and 'att2'. The K-Medoids operator is applied on this data set with default values for all parameters. A *breakpoint* is inserted at this step so that you can have a look at the results of the K-Medoids operator. You can see that two new attributes are created by the K-Medoids operator. The *id* attribute is created to distinguish examples clearly. The *cluster* attribute is created to show which cluster the examples belong to. As parameter *k* was set to 2, only two clusters are possible. That is why each example is assigned to either 'cluster_0' or 'cluster_1'. A cluster model is also delivered through the *cluster model* output port. It has information regarding the clustering performed. Under the *Folder View* you can see members of each cluster in folder format and under the *Centroid Table* and *Centroid Plot View* tabs information regarding centroids.

The Item Distribution Performance operator is applied to measure the performance of this clustering model on the basis of how well the examples are distributed over the clusters. The *cluster model* produced by the K-Medoids operator is provided as input to the Item Distribution Performance operator which evaluates the performance of this model and delivers a performance vector that has performance measured on the basis of example distribution. The resultant performance vector can be seen in the results workspace.