# Distributed Processing¶

This mode assumes that the data set is split into nblocks blocks across computation nodes.

## Algorithm Parameters¶

The K-Means clustering algorithm in the distributed processing mode has the following parameters:

Algorithm Parameters for K-Means Computaion (Distributed Processing)

Parameter

Default Value

Description

computeStep

Not applicable

The parameter required to initialize the algorithm. Can be:

• step1Local - the first step, performed on local nodes

• step2Master - the second step, performed on a master node

algorithmFPType

float

The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

method

defaultDense

Available computation methods for K-Means clustering:

• defaultDense - implementation of Lloyd’s algorithm

• lloydCSR - implementation of Lloyd’s algorithm for CSR numeric tables

nClusters

Not applicable

The number of clusters. Required to initialize the algorithm.

gamma

$$1.0$$

The weight to be used in distance calculation for binary categorical features.

distanceType

euclidean

The measure of closeness between points (observations) being clustered. The only distance type supported so far is the Euclidian distance.

assignFlag

false

A flag that enables computation of assignments, that is, assigning cluster indices to respective observations.

To compute K-Means clustering in the distributed processing mode, use the general schema described in Algorithms as follows:

## Step 1 - on Local Nodes¶

In this step, the K-Means clustering algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Input for K-Means Computaion (Distributed Processing, Step 1)

Input ID

Input

data

Pointer to the $$n_i \times p$$ numeric table that represents the $$i$$-th data block on the local node. The input can be an object of any class derived from NumericTable.

inputCentroids

Pointer to the $$\mathrm{nClusters} \times p$$ numeric table with the initial cluster centroids. This input can be an object of any class derived from NumericTable.

In this step, the K-Means clustering algorithm calculates the partial results and results described below. Pass the Partial Result ID or Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Partial Results for K-Means Computaion (Distributed Processing, Step 1)

Partial Result ID

Result

nObservations

Pointer to the $$\mathrm{nClusters} \times 1$$ numeric table that contains the number of observations assigned to the clusters on local node.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define this result as an object of any class derived from NumericTable except CSRNumericTable.

partialSums

Pointer to the $$\mathrm{nClusters} \times p$$ numeric table with partial sums of observations assigned to the clusters on the local node.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedTriangularMatrix, PackedSymmetricMatrix, and CSRNumericTable.

partialObjectiveFunction

Pointer to the $$1 \times 1$$ numeric table that contains the value of the partial objective function for observations processed on the local node.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define this result as an object of any class derived from NumericTable except CSRNumericTable.

partialCandidatesDistances

Pointer to the $$\mathrm{nClusters} \times 1$$ numeric table that contains the value of the nClusters largest objective function for the observations processed on the local node and stored in descending order.

Note

By default, this result if an object of the HomogenNumericTable class, but you can define this result as an object of any class derived from NumericTable except PackedTriangularMatrix, PackedSymmetricMatrix, CSRNumericTable.

partialCandidatesCentroids

Pointer to the $$\mathrm{nClusters} \times 1$$ numeric table that contains the observations of the nClusters largest objective function value processed on the local node and stored in descending order of the objective function.

Note

By default, this result if an object of the HomogenNumericTable class, but you can define this result as an object of any class derived from NumericTable except PackedTriangularMatrix, PackedSymmetricMatrix, CSRNumericTable.

Output for K-Means Computaion (Distributed Processing, Step 1)

Result ID

Result

assignments

Use when assignFlag = true. Pointer to the $$n_i \times 1$$ numeric table with 32-bit integer assignments of cluster indices to feature vectors in the input data on the local node.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define this result as an object of any class derived from NumericTable except PackedTriangularMatrix, PackedSymmetricMatrix, and CSRNumericTable.

## Step 2 - on Master Node¶

In this step, the K-Means clustering algorithm accepts the input from each local node described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Input for K-Means Computaion (Distributed Processing, Step 2)

Input ID

Input

partialResuts

A collection that contains results computed in Step 1 on local nodes.

In this step, the K-Means clustering algorithm calculates the results described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Output for K-Means Computaion (Distributed Processing, Step 2)

Result ID

Result

centroids

Pointer to the $$\mathrm{nClusters} \times p$$ numeric table with centroids.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedTriangularMatrix, PackedSymmetricMatrix, and CSRNumericTable.

objectiveFunction

Pointer to the $$1 \times 1$$ numeric table that contains the value of the objective function.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define this result as an object of any class derived from NumericTable except CSRNumericTable.

Important

The algorithm computes assignments using input centroids. Therefore, to compute assignments using final computed centroids, after the last call to Step2compute() method on the master node, on each local node set assignFlag to true and do one additional call to Step1compute() and finalizeCompute() methods. Always set assignFlag to true and call finalizeCompute() to obtain assignments in each step.

Note

To compute assignments using original inputCentroids on the given node, you can use K-Means clustering algorithm in the batch processing mode with the subset of the data available on this node. See Batch Processing for more details.