# K-Medoids (RapidMiner Studio Core)

## Synopsis

This operator performs clustering using the k-medoids algorithm. Clustering is concerned with grouping objects together that are similar to each other and dissimilar to the objects belonging to other clusters. Clustering is a technique for extracting information from unlabelled data. k-medoids clustering is an exclusive clustering algorithm i.e. each object is assigned to precisely one of a set of clusters.

## Description

This operator performs clustering using the k-medoids algorithm. K-medoids clustering is an exclusive clustering algorithm i.e. each object is assigned to precisely one of a set of clusters. Objects in one cluster are similar to each other. The similarity between objects is based on a measure of the distance between them.

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.

Here is a simple explanation of how the k-medoids algorithm works. First of all we need to introduce the notion of the center of a cluster, generally called its centroid. Assuming that we are using Euclidean distance or something similar as a measure we can define the centroid of a cluster to be the point for which each attribute value is the average of the values of the corresponding attribute for all the points in the cluster. The centroid of a cluster will always be one of the points in the cluster. This is the major difference between the k-means and k-medoids algorithm. In the k-means algorithm the centroid of a cluster will frequently be an imaginary point, not part of the cluster itself, which we can take to mark its center. For more information about the k-means algorithm please study the k-means operator.

## Differentiation

### k-Means

In case of the k-medoids algorithm the centroid of a cluster will always be one of the points in the cluster. This is the major difference between the k-means and k-medoids algorithm. In the k-means algorithm the centroid of a cluster will frequently be an imaginary point, not part of the cluster itself, which we can take to mark its center.

## Input

• example set input (Data Table)

The input port expects an ExampleSet. It is the output of the Retrieve operator in the attached Example Process. The output of other operators can also be used as input.

## Output

• cluster model (Centroid Cluster Model)

This port delivers the cluster model. It has information regarding the clustering performed. It tells which examples are part of which cluster. It also has information regarding centroids of each cluster.

• clustered set (Data Table)

The ExampleSet that was given as input is passed with minor changes to the output through this port. An attribute with id role is added to the input ExampleSet to distinguish examples. An attribute with cluster role may also be added depending on the state of the add cluster attribute parameter.

## Parameters

• add_cluster_attributeIf enabled, a new attribute with cluster role is generated directly in this operator, otherwise this operator does not add the cluster attribute. In the latter case you have to use the Apply Model operator to generate the cluster attribute. Range: boolean
• add_as_labelIf true, the cluster id is stored in an attribute with the label role instead of cluster role Range: boolean
• remove_unlabeledIf set to true, unlabeled examples are deleted. Range: boolean
• kThis parameter specifies the number of clusters to form. There is no hard and fast rule of number of clusters to form. But, generally it is preferred to have a small number of clusters with examples scattered (not too scattered) around them in a balanced way. Range: integer
• max_runsThis parameter specifies the maximal number of runs of k-medoids with random initialization that are performed. Range: integer
• max_optimization_stepsThis parameter specifies the maximal number of iterations performed for one run of k-medoids. Range: integer
• use_local_random_seedIndicates if a local random seed should be used for randomization. Randomization may be used for selecting k different points at the start of the algorithm as potential centroids. Range: boolean
• local_random_seedThis parameter specifies the local random seed. This parameter is only available if the use local random seed parameter is set to true. Range: integer
• measure_typesThis parameter is used for selecting the type of measure to be used for measuring the distance between points.The following options are available: mixed measures, nominal measures, numerical measures and Bregman divergences. Range: selection
• mixed_measureThis parameter is available when the measure type parameter is set to 'mixed measures'. The only available option is the 'Mixed Euclidean Distance' Range: selection
• nominal_measureThis parameter is available when the measure type parameter is set to 'nominal measures'. This option cannot be applied if the input ExampleSet has numerical attributes. In this case the 'numerical measure' option should be selected. Range: selection
• numerical_measureThis parameter is available when the measure type parameter is set to 'numerical measures'. This option cannot be applied if the input ExampleSet has nominal attributes. If the input ExampleSet has nominal attributes the 'nominal measure' option should be selected. Range: selection
• divergenceThis parameter is available when the measure type parameter is set to 'bregman divergences'. Range: selection
• kernel_typeThis parameter is only available when the numerical measure parameter is set to 'Kernel Euclidean Distance'. The type of the kernel function is selected through this parameter. Following kernel types are supported:
• dot: The dot kernel is defined by k(x,y)=x*y i.e.it is inner product of x and y.
• radial: The radial kernel is defined by exp(-g ||x-y||^2) where g is the gamma that is specified by the kernel gamma parameter. The adjustable parameter gamma plays a major role in the performance of the kernel, and should be carefully tuned to the problem at hand.
• polynomial: The polynomial kernel is defined by k(x,y)=(x*y+1)^d where d is the degree of the polynomial and it is specified by the kernel degree parameter. The Polynomial kernels are well suited for problems where all the training data is normalized.
• neural: The neural kernel is defined by a two layered neural net tanh(a x*y+b) where a is alpha and b is the intercept constant. These parameters can be adjusted using the kernel a and kernel b parameters. A common value for alpha is 1/N, where N is the data dimension. Note that not all choices of a and b lead to a valid kernel function.
• sigmoid: This is the sigmoid kernel. Please note that the sigmoid kernel is not valid under some parameters.
• anova: This is the anova kernel. It has adjustable parameters gamma and degree.
• epachnenikov: The Epanechnikov kernel is this function (3/4)(1-u2) for u between -1 and 1 and zero for u outside that range. It has two adjustable parameters kernel sigma1 and kernel degree.
• gaussian_combination: This is the gaussian combination kernel. It has adjustable parameters kernel sigma1, kernel sigma2 and kernel sigma3.
• multiquadric: The multiquadric kernel is defined by the square root of ||x-y||^2 + c^2. It has adjustable parameters kernel sigma1 and kernel sigma shift.
Range: selection
• kernel_gammaThis is the SVM kernel parameter gamma. This parameter is only available when the numerical measure parameter is set to 'Kernel Euclidean Distance' and the kernel type parameter is set to radial or anova. Range: real
• kernel_sigma1This is the SVM kernel parameter sigma1. This parameter is only available when the numerical measure parameter is set to 'Kernel Euclidean Distance' and the kernel type parameter is set to epachnenikov, gaussian combination or multiquadric. Range: real
• kernel_sigma2This is the SVM kernel parameter sigma2. This parameter is only available when the numerical measure parameter is set to 'Kernel Euclidean Distance' and the kernel type parameter is set to gaussian combination. Range: real
• kernel_sigma3This is the SVM kernel parameter sigma3. This parameter is only available when the numerical measure parameter is set to 'Kernel Euclidean Distance' and the kernel type parameter is set to gaussian combination. Range: real
• kernel_shiftThis is the SVM kernel parameter shift. This parameter is only available when the numerical measure parameter is set to 'Kernel Euclidean Distance' and the kernel type parameter is set to multiquadric. Range: real
• kernel_degreeThis is the SVM kernel parameter degree. This parameter is only available when the numerical measure parameter is set to 'Kernel Euclidean Distance' and the kernel type parameter is set to polynomial, anova or epachnenikov. Range: real
• kernel_aThis is the SVM kernel parameter a. This parameter is only available when the numerical measure parameter is set to 'Kernel Euclidean Distance' and the kernel type parameter is set to neural. Range: real
• kernel_bThis is the SVM kernel parameter b. This parameter is only available when the numerical measure parameter is set to 'Kernel Euclidean Distance' and the kernel type parameter is set to neural. Range: real

## Tutorial Processes

### Clustering of Ripley-Set data set by the K-Medoids operator

In many cases, no target attribute (i.e. label) can be defined and the data should be automatically grouped. This procedure is called Clustering. RapidMiner supports a wide range of clustering schemes which can be used in just the same way like any other learning scheme. This includes the combination with all preprocessing operators.

In this Example Process, 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 itself. A breakpoint is inserted at this step so that you can have a look at the ExampleSet before application of the K-Medoids operator. Other than the label attribute 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. Run the process and you will 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'. Also note the Plot View of this data. You can clearly see how the algorithm has created two separate groups in the Plot View. A cluster model is also delivered through the cluster model output port. It has information regarding the clustering performed. Under Folder View you can see members of each cluster in folder format. You can see information regarding centroids under the Centroid Table and Centroid Plot View tabs.