smile.vq

Class NeuralGas

java.lang.Object

smile.vq.NeuralGas

All Implemented Interfaces:

java.io.Serializable, VectorQuantizer

public class NeuralGas
extends java.lang.Object
implements VectorQuantizer

Neural Gas soft competitive learning algorithm. Neural Gas is inspired by the Self-Organizing Map (SOM) for finding optimal data representations based on feature vectors. The algorithm was coined "Neural Gas" because of the dynamics of the feature vectors during the adaptation process, which distribute themselves like a gas within the data space. Although it is mainly applied where data compression or vector quantization is an issue, it is also used for cluster analysis as a robustly converging alternative to k-means. A prominent extension is the Growing Neural Gas.

Compared to SOM, Neural Gas has no topology of a fixed dimensionality (in fact, no topology at all). For each input signal during learning, Neural Gas sorts the neurons of the network according to the distance of their reference vectors to the input signal. Based on this "rank order", neurons are adapted based on the adaptation strength that are decreased according to a fixed schedule.

The adaptation step of the Neural Gas can be interpreted as gradient descent on a cost function. By adapting not only the closest feature vector but all of them with a step size decreasing with increasing distance order, compared to k-means, a much more robust convergence of the algorithm can be achieved.

References

1. Thomas Martinetz and Klaus Schulten. A "neural gas" network learns topologies. Artificial Neural Networks, 397-402, 1991.
2. T. Martinetz, S. Berkovich, and K. Schulten. "Neural-gas" Network for Vector Quantization and its Application to Time-Series Prediction. IEEE Trans. on Neural Networks, 4(4):558-569, 1993.
3. T. Martinetz and K. Schulten. Topology representing networks. Neural Networks, 7(3):507-522, 1994.

See Also:

KMeans, GrowingNeuralGas, SOM, Serialized Form

Field Summary

Fields inherited from interface smile.vq.VectorQuantizer

OUTLIER

Constructor Summary

Constructors

Constructor and Description
NeuralGas(double[][] neurons, smile.math.TimeFunction alpha, smile.math.TimeFunction theta, int lifetime) Constructor.

Method Summary

Modifier and Type	Method and Description
smile.graph.Graph	network() Returns the network of neurons.
double[][]	neurons() Returns the neurons.
double[]	quantize(double[] x) Quantize a new observation.
static double[][]	seed(int k, double[][] samples) Selects random samples as initial neurons of Neural Gas.
void	update(double[] x) Update the codebook with a new observation.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

NeuralGas

public NeuralGas(double[][] neurons,
                 smile.math.TimeFunction alpha,
                 smile.math.TimeFunction theta,
                 int lifetime)

Constructor.

Parameters:

neurons - the initial neurons.

alpha - the learning rate function.

theta - the neighborhood function.

lifetime - the neuron connection lifetime, usually the number of iterations for one or two epochs.

Method Detail

seed

public static double[][] seed(int k,
                              double[][] samples)

Selects random samples as initial neurons of Neural Gas.

Parameters:

k - the number of neurons.

samples - some samples to select initial weight vectors.

neurons

public double[][] neurons()

Returns the neurons.

network

public smile.graph.Graph network()

Returns the network of neurons.

update

public void update(double[] x)

Description copied from interface: VectorQuantizer

Update the codebook with a new observation.

Specified by:

update in interface VectorQuantizer

quantize

public double[] quantize(double[] x)

Description copied from interface: VectorQuantizer

Quantize a new observation. Returns Optional.empty if the observation is noise.

Specified by:

quantize in interface VectorQuantizer

Parameters:

x - a new observation.