K Medoids

Group (Subgroup)

DREAM3D Review (Clustering)

Description

This Filter applies the k medoids algorithm to an Attribute Array. K medoids is a clustering algorithm that assigns to each point of the Attribute Array a cluster Id. The user must specify the number of clusters in which to partition the array. Specifically, a k medoids partitioning is such that each point in the data set is associated with the cluster that minimizes the sum of the pair-wise distances between the data points and their associated cluster centers (medoids). This approach is analogous to k means, but uses actual data points (the medoids) as the cluster exemplars instead of the means. Medoids in this context refer to the data point in each cluster that is most like all other data points, i.e., that data point whose average distance to all other data points in the cluster is smallest. Unlike k means, since pair-wise distances are minimized instead of variance, any arbirtary concept of "distance" may be used; this Filter allows for the selection of a variety of distance metrics.

This Filter uses the Voronoi iteration algorithm to produce the clustering. The algorithm is iterative and proceeds as follows:

  1. Choose k points at random to serve as the initial cluster medoids
  2. Associate each point to the closest medoid
  3. Until convergence, repeat the following steps:
  4. For each cluster, change the medoid to the point in that cluster that minimizes the sum of distances between that point and all other points in the cluster
  5. Reassign each point to the closest medoid

Convergence is defined as when the medoids no longer change position. Since the algorithm is iterative, it only serves as an approximation, and may result in different classifications on each execution with the same input data. The user may opt to use a mask to ignore certain points; where the mask is false, the points will be placed in cluster 0.

A clustering algorithm can be considered a kind of segmentation; this implementation of k medoids does not rely on the Geometry on which the data lie, only the topology of the space that the array itself forms. Therefore, this Filter has the effect of creating either Features or Ensembles depending on the kind of array passed to it for clustering. If an Element array (e.g., voxel-level Cell data) is passed to the Filter, then Features are created (in the previous example, a Cell Feature Attribute Matrix will be created). If a Feature array is passed to the Filter, then an Ensemble Attribute Matrix is created. The following table shows what type of Attribute Matrix is created based on what sort of array is used for clustering:

Attribute Matrix Source Attribute Matrix Created
Generic Generic
Vertex Vertex Feature
Edge Edge Feature
Face Face Feature
Cell Cell Feature
Vertex Feature Vertex Ensemble
Edge Feature Edge Ensemble
Face Feature Face Ensemble
Cell Feature Cell Ensemble
Vertex Ensemble Vertex Ensemble
Edge Ensemble Edge Ensemble
Face Ensemble Face Ensemble
Cell Ensemble Cell Ensemble

This Filter will store the medoids for the final clusters within the created Attribute Matrix.

Parameters

Name Type Description
Number of Clusters int32_t The number of clusters in which to partition the array
Distance Metric Enumeration The metric used to determine the distances between points
Use Mask bool Whether to use a boolean mask array to ignore certain points flagged as false from the algorithm

Required Geometry

None

Required Objects

Kind Default Name Type Component Dimensions Description
Any Attribute Array None Any Any The Attribute Array to cluster
Attrubute Array Mask bool (1) Specifies if the point is to be counted in the algorithm, if Use Mask is checked

Created Objects

Kind Default Name Type Component Dimensions Description
Attribute Matrix ClusterData Feature/Ensemble N/A The Attribute Matrix in which to store information associated with the created clusters
Attribute Array ClusterIds int32_t (1) Specifies to which cluster each point belongs
Attribute Array ClusterMeans double (1) The means of the final clusters

References ##

[1] A simple and fast algorithm for K-medoids clustering, H.S. Park and C.H. Jun, Expert Systems with Applications, vol. 28 (2), pp. 3336-3341, 2009.

Example Pipelines

Please see the description file distributed with this plugin.

DREAM3D Mailing Lists

If you need more help with a filter, please consider asking your question on the DREAM3D Users mailing list: https://groups.google.com/forum/?hl=en#!forum/dream3d-users