Data.Datamining.Clustering.DSOM

A modified Kohonen Self-organising Map (SOM) which supports a time-independent learning function. (See SOM for a description of a SOM.)

References:

• Rougier, N. & Boniface, Y. (2011). Dynamic self-organising map. Neurocomputing, 74 (11), 1840-1847.
• Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43 (1), 59–69.

Construction

data DSOM gm k p

A Self-Organising Map (DSOM).

Although DSOM 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 DSOM and the output DSOM would have to have the same Metric type.

Instances

(GridMap gm p, (~) * k (Index (BaseGrid gm p)), Pattern p, FiniteGrid (gm p), GridMap gm (Metric p), (~) * k (Index (gm p)), (~) * k (Index (BaseGrid gm (Metric p))), Ord k, Ord (Metric p), Num (Metric p), Fractional (Metric p)) => Classifier (DSOM gm) k p

Foldable gm => Foldable (DSOM gm k)

(Foldable gm, GridMap gm p, FiniteGrid (BaseGrid gm p)) => GridMap (DSOM gm k) p

Grid (gm p) => Grid (DSOM gm k p)

type BaseGrid (DSOM gm k) p = BaseGrid gm p

type Index (DSOM gm k p) = Index (gm p)

type Direction (DSOM gm k p) = Direction (gm p)

defaultDSOM :: (Eq (Metric p), Ord (Metric p), Floating (Metric p)) => gm p -> Metric p -> Metric p -> DSOM gm k p

Creates a classifier with a default (bell-shaped) learning function. Usage is defaultDSOM gm r w t, where:

gm

The geometry and initial models for this classifier. A reasonable choice here is lazyGridMap g ps, where g is a HexHexGrid, and ps is a set of random patterns.

r

and [p] are the first two parameters to the rougierLearningFunction.

customDSOM :: gm p -> (Metric p -> Metric p -> Metric p -> Metric p) -> DSOM gm k p

Creates a classifier with a custom learning function. Usage is customDSOM gm g, where:

gm

The geometry and initial models for this classifier. A reasonable choice here is lazyGridMap g ps, where g is a HexHexGrid, and ps is a set of random patterns.

f

A function used to determine the learning rate (for adjusting the models in the classifier). This function will be invoked with three parameters. The first parameter will indicate how different the BMU is from the input pattern. The second parameter indicates how different the pattern of the node currently being trained is from the input pattern. The third parameter is the grid distance from the BMU to the node currently being trained, as a fraction of the maximum grid distance. The output is the learning rate for that node (the amount by which the node's model should be updated to match the target). The learning rate should be between zero and one.

rougierLearningFunction :: (Eq a, Ord a, Floating a) => a -> a -> a -> a -> a -> a

Configures a learning function that depends not on the time, but on how good a model we already have for the target. If the BMU is an exact match for the target, no learning occurs. Usage is rougierLearningFunction r p, where r is the maximal learning rate (0 <= r <= 1), and p is the elasticity.

NOTE: When using this learning function, ensure that abs . difference is always between 0 and 1, inclusive. Otherwise you may get invalid learning rates.

Deconstruction

toGridMap :: GridMap gm p => DSOM gm k p -> gm p

Extracts the grid and current models from the DSOM.

Advanced control

trainNeighbourhood :: (Pattern p, FiniteGrid (gm p), GridMap gm p, Num (Metric p), Ord k, k ~ Index (gm p), k ~ Index (BaseGrid gm p), Fractional (Metric p)) => DSOM gm t p -> k -> p -> DSOM 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.