Data.Datamining.Clustering.SOM

A Kohonen Self-organising Map (SOM). A SOM maps input patterns onto a regular grid (usually two-dimensional) where each node in the grid is a model of the input data, and does so using a method which ensures that any topological relationships within the input data are also represented in the grid. This implementation supports the use of non-numeric patterns.

In layman's terms, a SOM can be useful when you you want to discover the underlying structure of some data. A tutorial is available at https://github.com/mhwombat/som/wiki.

NOTES:

• Version 5.0 fixed a bug in the decayingGaussian function. If you use defaultSOM (which uses this function), your SOM should now learn more quickly.
• The gaussian function has been removed because it is not as useful for SOMs as I originally thought. It was originally designed to be used as a factor in a learning function. However, in most cases the user will want to introduce a time decay into the exponent, rather than simply multiply by a factor.

References:

• Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43 (1), 59–69.

Construction

data SOM f t gm k p

A Self-Organising Map (SOM).

Although SOM implements GridMap, most users will only need the interface provided by Data.Datamining.Clustering.Classifier. If you chose to use the GridMap functions, please note:

1. The functions adjust, and adjustWithKey do not increment the counter. You can do so manually with incrementCounter.
2. The functions map and mapWithKey are not implemented (they just return an error). It would be problematic to implement them because the input SOM and the output SOM would have to have the same Metric type.

Constructors

SOM

Fields

gridMap :: gm p

Maps patterns to tiles in a regular grid. In the context of a SOM, the tiles are called nodes

learningFunction :: f

The function used to update the nodes.

counter :: t

A counter used as a time parameter. If you create the SOM with a counter value 0, and don't directly modify it, then the counter will represent the number of patterns that this SOM has classified.

Instances

(GridMap gm p, ~ * k (Index (BaseGrid gm p)), Pattern p, Grid (gm p), GridMap gm (Metric p), ~ * k (Index (gm p)), ~ * k (Index (BaseGrid gm (Metric p))), Ord (Metric p), LearningFunction f, ~ * (Metric p) (LearningRate f), Num (LearningRate f), Integral t) => Classifier (SOM f t gm) k p

Foldable gm => Foldable (SOM f t gm k)

(Foldable gm, GridMap gm p, Grid (BaseGrid gm p)) => GridMap (SOM f t gm k) p

(Eq f, Eq t, Eq (gm p)) => Eq (SOM f t gm k p)

(Show f, Show t, Show (gm p)) => Show (SOM f t gm k p)

Generic (SOM f t gm k p)

Grid (gm p) => Grid (SOM f t gm k p)

data DecayingGaussian a

A typical learning function for classifiers. DecayingGaussian r0 rf w0 wf tf returns a bell curve-shaped function. At time zero, the maximum learning rate (applied to the BMU) is r0, and the neighbourhood width is w0. Over time the bell curve shrinks and the learning rate tapers off, until at time tf, the maximum learning rate (applied to the BMU) is rf, and the neighbourhood width is wf. Normally the parameters should be chosen such that:

• 0 < rf << r0 < 1
• 0 < wf << w0
• 0 < tf

where << means is much smaller than (not the Haskell << operator!)

Constructors

DecayingGaussian a a a a a

Instances

Eq a => Eq (DecayingGaussian a)

Show a => Show (DecayingGaussian a)

Generic (DecayingGaussian a)

(Floating a, Fractional a, Num a) => LearningFunction (DecayingGaussian a)

Deconstruction

toGridMap :: GridMap gm p => SOM f t gm k p -> gm p

Extracts the grid and current models from the SOM. A synonym for gridMap.

Advanced control

trainNeighbourhood :: (Pattern p, Grid (gm p), GridMap gm p, Index (BaseGrid gm p) ~ Index (gm p), LearningFunction f, Metric p ~ LearningRate f, Num (LearningRate f), Integral t) => SOM f t gm k p -> Index (gm p) -> p -> SOM f t gm k p

Trains the specified node and the neighbourood around it to better match a target. Most users should use train, which automatically determines the BMU and trains it and its neighbourhood.