9.38. Compute K Means

Group (Subgroup)

DREAM3D Review (Clustering)

Description

Warning: The randomnes in this filter is not currently consistent between operating systems even if the same seed is used. Specifically between Unix and Windows. This does not affect the results, but the IDs will not correspond. For example if the Cluster Identifier at index one on Linux is 1 it could be 2 on Windows, the overarching clusters will be the same, but their IDs will be different.

This Filter applies the k means algorithm to an Attribute Array. K means 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 means partitioning is a Voronoi tesselation; an optimal solution to the k means problem is such that each point in the data set is associated with the cluster that has the closest mean. This partitioning is the one that minimizes the within cluster variance (i.e., minimizes the within cluster sum of squares differences). Thus, the “metric” used for k means is the 2-norm (the Euclidean norm; the squared Euclidean norm may also be used since this maintains the triangle inequality).

Optimal solutions to the k means partitioning problem are computationally difficult; this Filter used Lloyd’s algorithm to approximate the solution. Lloyd’s algorithm is an iterative algorithm that proceeds as follows:

  1. Choose k points at random to serve as the initial cluster “means”

  2. Until convergence, repeat the following steps:

  • Associate each point with the closest mean, where “closest” is the smallest 2-norm distance

  • Recompute the means based on the new tesselation

Convergence is defined as when the computed means change very little (precisely, when the differences are within machine epsilon). Since Lloyd’s 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.

Note: In SIMPLNX there is no explicit positional subtyping for Attribute Matrix, so the next section should be treated as a high-level understanding of what is being created. Naming the Attribute Matrix to include the type listed on the respective line in the ‘Attribute Matrix Created’ column is encouraged to help with readability and comprehension.

A clustering algorithm can be considered a kind of segmentation; this implementation of k means 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 means for the final clusters within the created Attribute Matrix.

Random Number Seed Parameters

Parameter Name

Parameter Type

Parameter Notes

Description

Use Seed for Random Generation

Bool

When true the user will be able to put in a seed for random generation

Seed Value

Scalar Value

UInt64

The seed fed into the random generator

Stored Seed Value Array Name

DataObjectName

Name of array holding the seed value

Input Parameter(s)

Parameter Name

Parameter Type

Parameter Notes

Description

Number of Clusters

Scalar Value

UInt64

This will be the tuple size for Cluster Attribute Matrix and the values within

Distance Metric

Choices

Distance Metric type to be used for calculations

Optional Data Mask

Parameter Name

Parameter Type

Parameter Notes

Description

Use Mask Array

Bool

Specifies whether or not to use a mask array

Cell Mask Array

Array Selection

Allowed Types: uint8, boolean

DataPath to the boolean or uint8 mask array. Values that are true will mark that cell/point as usable.

Input Data Objects

Parameter Name

Parameter Type

Parameter Notes

Description

Attribute Array to Cluster

Array Selection

Allowed Types: int8, uint8, int16, uint16, int32, uint32, int64, uint64, float32, float64

The array to cluster from

Output Data Object(s)

Parameter Name

Parameter Type

Parameter Notes

Description

Cluster Ids Array Name

DataObjectName

name of the ids array to be created in Attribute Array to Cluster’s parent group

Cluster Attribute Matrix

DataGroupCreation

name and path of Attribute Matrix to hold Cluster Data

Cluster Means Array Name

DataObjectName

name of the Means array to be created in Cluster Attribute Matrix

References

[1] Least squares quantization in PCM, S.P. Lloyd, IEEE Transactions on Information Theory, vol. 28 (2), pp. 129-137, 1982.

Example Pipelines

DREAM3D-NX Help

If you need help, need to file a bug report or want to request a new feature, please head over to the DREAM3DNX-Issues GitHub site where the community of DREAM3D-NX users can help answer your questions.