de.citec.ml.rng

Interface RNGModel

All Known Subinterfaces:

RNGErrorModel

All Known Implementing Classes:

RNGModelImpl

public interface RNGModel

This is an interface for the result of a Relational Neural Gas algorithm. It encapsulates two fundamental properties of a RNG algorithm: 1.) It assigns data points to clusters. 2.) Each cluster has a prototype, which is represented as a convex combination. We represent data points here only in terms of indices, numbered from 0 to m-1, where m is the number of data points. Similarly, we represent clusters as indices, from 0 to K-1, where K is the number of clusters/prototypes.

As representation of prototypes, we choose the alpha-vector of convex coefficients. Each prototype in the RNG framework is given as a convex combination of the data points, where the coefficients are positive real numbers that sum up to 1. Note, that there are techniques which make the coefficient vectors sparse (e.g. median approaches, which select only one alpha_i = 1).

Author:

Benjamin Paassen - bpaassen(at)techfak.uni-bielefeld.de

Method Summary

Modifier and Type	Method and Description
double[][]	getConvexCoefficients() Returns the convex coefficients representing all prototypes.
double[][]	getDistancesToPrototypes() Returns the matrix of distances from all training data points to all prototypes.
double[]	getNormalizationTerms() Returns a K x 1 vector containing the normalization terms for for relational distances to each prototype.
int	getNumberOfDatapoints() Returns the number of datapoints N.
int	getNumberOfPrototypes() Returns the number of clusters/prototypes K.

Method Detail

getNumberOfDatapoints

int getNumberOfDatapoints()

Returns the number of datapoints N.

Returns:

the number of datapoints N.

getNumberOfPrototypes

int getNumberOfPrototypes()

Returns the number of clusters/prototypes K.

Returns:

the number of clusters/prototypes K.

getConvexCoefficients

double[][] getConvexCoefficients()

Returns the convex coefficients representing all prototypes. If m is the number of data points and K is the number of clusters/prototypes, this is a K x m matrix, where Alpha[k][i] represents the contribution of data point i to prototype k with Alpha[k][i] being always non-negative and the entries in Alpha[k] adding up to 1 for all k.

Returns:

the convex coefficients representing all prototypes.

getDistancesToPrototypes

double[][] getDistancesToPrototypes()

Returns the matrix of distances from all training data points to all prototypes. For K prototypes and m datapoints, this is a K x m matrix Dp where entry Dp[i][k] contains the distance of data point i to prototype K.

Returns:

the matrix of distances from all prototypes to the data.

getNormalizationTerms

double[] getNormalizationTerms()

Returns a K x 1 vector containing the normalization terms for for relational distances to each prototype. In particular, the distance of a data point x to prototype w_k is given as

d(w_k, x)² = Σ_i=1,...,m α_{k, i} · d(x, x_i)² - 0.5 · α_k · D² · α_k^T

where x₁, ..., x_m are the training data points and D is the matrix of pairwise distances between all training data points. The k-th entry of the returned vector contains exactly the term

- 0.5 · α_k · D² · α_k^T

Returns:

a K x 1 vector containing the normalization terms for for relational distances to each prototype.