Data.Datamining.Clustering.SOMInternal

A module containing private SOM internals. Most developers should use SOM instead. This module is subject to change without notice.

Documentation

class LearningFunction f where

A function used to adjust the models in a classifier.

Associated Types

type LearningRate f

Methods

rate :: f -> LearningRate f -> LearningRate f -> LearningRate f

rate f t d returns the learning rate for a node. The parameter f is the learning function. The parameter t indicates how many patterns (or pattern batches) have previously been presented to the classifier. Typically this is used to make the learning rate decay over time. The parameter d is the grid distance from the node being updated to the BMU (Best Matching Unit). 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.

Instances

Fractional a => LearningFunction (ConstantFunction a)

(Fractional a, Eq a) => LearningFunction (StepFunction a)

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

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)

type Rep (DecayingGaussian a)

type LearningRate (DecayingGaussian a) = a

data StepFunction a

A learning function that only updates the BMU and has a constant learning rate.

Constructors

StepFunction a

Instances

Eq a => Eq (StepFunction a)

Show a => Show (StepFunction a)

Generic (StepFunction a)

(Fractional a, Eq a) => LearningFunction (StepFunction a)

type Rep (StepFunction a)

type LearningRate (StepFunction a) = a

data ConstantFunction a

A learning function that updates all nodes with the same, constant learning rate. This can be useful for testing.

Constructors

ConstantFunction a

Instances

Eq a => Eq (ConstantFunction a)

Show a => Show (ConstantFunction a)

Generic (ConstantFunction a)

Fractional a => LearningFunction (ConstantFunction a)

type Rep (ConstantFunction a)

type LearningRate (ConstantFunction a) = a

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)

type BaseGrid (SOM f t gm k) p = BaseGrid gm p

type Rep (SOM f t gm k p)

type Direction (SOM f t gm k p) = Direction (gm p)

type Index (SOM f t gm k p) = Index (gm p)

currentLearningFunction :: (LearningFunction f, Metric p ~ LearningRate f, Num (LearningRate f), Integral t) => SOM f t gm k p -> LearningRate f -> Metric p

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.

adjustNode :: (Pattern p, Grid g, k ~ Index g, Num t) => g -> (t -> Metric p) -> p -> k -> k -> p -> p

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.

incrementCounter :: Num t => SOM f t gm k p -> SOM f t gm k p

justTrain :: (Ord (Metric p), Pattern p, Grid (gm p), GridMap gm (Metric p), GridMap gm p, Index (BaseGrid gm (Metric p)) ~ Index (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 -> p -> SOM f t gm k p