Copyright	(c) 2012-2021 Amy de Buitléir
License	BSD-style
Maintainer	amy@nualeargais.ie
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Datamining.Clustering.SOMInternal

Description

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

Synopsis

decayingGaussian :: Floating x => x -> x -> x -> x -> x -> x -> x -> x
stepFunction :: (Num d, Fractional x, Eq d) => x -> t -> d -> x
constantFunction :: x -> t -> d -> x
data SOM t d gm x k p = SOM {
- gridMap :: gm p
- learningRate :: t -> d -> x
- difference :: p -> p -> x
- makeSimilar :: p -> x -> p -> p
- counter :: t
}
withGridMap :: (gm p -> gm p) -> SOM t d gm x k p -> SOM t d gm x k p
currentLearningFunction :: Num t => SOM t d gm x k p -> d -> x
toGridMap :: GridMap gm p => SOM t d gm x k p -> gm p
adjustNode :: (Grid g, k ~ Index g, Num t) => g -> (t -> x) -> (p -> x -> p -> p) -> p -> k -> k -> p -> p
trainNeighbourhood :: (Grid (gm p), GridMap gm p, Index (BaseGrid gm p) ~ Index (gm p), Num t, Num x, Num d) => SOM t d gm x k p -> Index (gm p) -> p -> SOM t d gm x k p
incrementCounter :: Num t => SOM t d gm x k p -> SOM t d gm x k p
justTrain :: (Ord x, Grid (gm p), GridMap gm x, GridMap gm p, Index (BaseGrid gm x) ~ Index (gm p), Index (BaseGrid gm p) ~ Index (gm p), Num t, Num x, Num d) => SOM t d gm x k p -> p -> SOM t d gm x k p

Documentation

decayingGaussian :: Floating x => x -> x -> x -> x -> x -> x -> x -> x Source #

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!)

stepFunction :: (Num d, Fractional x, Eq d) => x -> t -> d -> x Source #

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

constantFunction :: x -> t -> d -> x Source #

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

data SOM t d gm x k p Source #

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:

The functions adjust, and adjustWithKey do not increment the counter. You can do so manually with incrementCounter.
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"
learningRate :: t -> d -> x
A function which determines the how quickly the SOM learns. For example, if the function is f, then f t d returns the learning rate for a node. 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.
difference :: p -> p -> x
A function which compares two patterns and returns a non-negative number representing how different the patterns are. A result of 0 indicates that the patterns are identical.
makeSimilar :: p -> x -> p -> p
A function which updates models. If this function is f, then f target amount pattern returns a modified copy of pattern that is more similar to target than pattern is. The magnitude of the adjustment is controlled by the amount parameter, which should be a number between 0 and 1. Larger values for amount permit greater adjustments. If amount=1, the result should be identical to the target. If amount=0, the result should be the unmodified pattern.
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

Instances details

(GridMap gm p, k ~ Index (BaseGrid gm p), Grid (gm p), GridMap gm x, k ~ Index (gm p), k ~ Index (BaseGrid gm x), Num t, Ord x, Num x, Num d) => Classifier (SOM t d gm) x k p Source #
Instance details Defined in Data.Datamining.Clustering.SOMInternal Methods toList :: SOM t d gm x k p -> [(k, p)] Source # numModels :: SOM t d gm x k p -> Int Source # models :: SOM t d gm x k p -> [p] Source # differences :: SOM t d gm x k p -> p -> [(k, x)] Source # classify :: SOM t d gm x k p -> p -> k Source # train :: SOM t d gm x k p -> p -> SOM t d gm x k p Source # trainBatch :: SOM t d gm x k p -> [p] -> SOM t d gm x k p Source # classifyAndTrain :: SOM t d gm x k p -> p -> (k, SOM t d gm x k p) Source # diffAndTrain :: SOM t d gm x k p -> p -> ([(k, x)], SOM t d gm x k p) Source # reportAndTrain :: SOM t d gm x k p -> p -> (k, [(k, x)], SOM t d gm x k p) Source #
Foldable gm => Foldable (SOM t d gm x k) Source #
Instance details Defined in Data.Datamining.Clustering.SOMInternal Methods fold :: Monoid m => SOM t d gm x k m -> m # foldMap :: Monoid m => (a -> m) -> SOM t d gm x k a -> m # foldMap' :: Monoid m => (a -> m) -> SOM t d gm x k a -> m # foldr :: (a -> b -> b) -> b -> SOM t d gm x k a -> b # foldr' :: (a -> b -> b) -> b -> SOM t d gm x k a -> b # foldl :: (b -> a -> b) -> b -> SOM t d gm x k a -> b # foldl' :: (b -> a -> b) -> b -> SOM t d gm x k a -> b # foldr1 :: (a -> a -> a) -> SOM t d gm x k a -> a # foldl1 :: (a -> a -> a) -> SOM t d gm x k a -> a # toList :: SOM t d gm x k a -> [a] # null :: SOM t d gm x k a -> Bool # length :: SOM t d gm x k a -> Int # elem :: Eq a => a -> SOM t d gm x k a -> Bool # maximum :: Ord a => SOM t d gm x k a -> a # minimum :: Ord a => SOM t d gm x k a -> a # sum :: Num a => SOM t d gm x k a -> a # product :: Num a => SOM t d gm x k a -> a #
(Foldable gm, GridMap gm p, Grid (BaseGrid gm p)) => GridMap (SOM t d gm x k) p Source #
Instance details Defined in Data.Datamining.Clustering.SOMInternal Associated Types type BaseGrid (SOM t d gm x k) p # Methods (!) :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => SOM t d gm x k p -> k0 -> p # toMap :: k0 ~ Index (BaseGrid (SOM t d gm x k) p) => SOM t d gm x k p -> Map k0 p # toGrid :: SOM t d gm x k p -> BaseGrid (SOM t d gm x k) p # toList :: k0 ~ Index (BaseGrid (SOM t d gm x k) p) => SOM t d gm x k p -> [(k0, p)] # lookup :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => k0 -> SOM t d gm x k p -> Maybe p # insert :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => k0 -> p -> SOM t d gm x k p -> SOM t d gm x k p # insertWith :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => (p -> p -> p) -> k0 -> p -> SOM t d gm x k p -> SOM t d gm x k p # insertWithKey :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => (k0 -> p -> p -> p) -> k0 -> p -> SOM t d gm x k p -> SOM t d gm x k p # insertLookupWithKey :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => (k0 -> p -> p -> p) -> k0 -> p -> SOM t d gm x k p -> (Maybe p, SOM t d gm x k p) # delete :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => k0 -> SOM t d gm x k p -> SOM t d gm x k p # adjust :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => (p -> p) -> k0 -> SOM t d gm x k p -> SOM t d gm x k p # adjustWithKey :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => (k0 -> p -> p) -> k0 -> SOM t d gm x k p -> SOM t d gm x k p # alter :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => (Maybe p -> Maybe p) -> k0 -> SOM t d gm x k p -> SOM t d gm x k p # findWithDefault :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => p -> k0 -> SOM t d gm x k p -> p # keys :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), Ord k0) => SOM t d gm x k p -> [k0] # elems :: SOM t d gm x k p -> [p] # map :: (GridMap (SOM t d gm x k) v2, Index (BaseGrid (SOM t d gm x k) p) ~ Index (BaseGrid (SOM t d gm x k) v2)) => (p -> v2) -> SOM t d gm x k p -> SOM t d gm x k v2 # mapWithKey :: (k0 ~ Index (BaseGrid (SOM t d gm x k) p), k0 ~ Index (BaseGrid (SOM t d gm x k) v2), GridMap (SOM t d gm x k) v2) => (k0 -> p -> v2) -> SOM t d gm x k p -> SOM t d gm x k v2 # filter :: (p -> Bool) -> SOM t d gm x k p -> SOM t d gm x k p # filterWithKey :: k0 ~ Index (BaseGrid (SOM t d gm x k) p) => (k0 -> p -> Bool) -> SOM t d gm x k p -> SOM t d gm x k p #
Generic (SOM t d gm x k p) Source #
Instance details Defined in Data.Datamining.Clustering.SOMInternal Associated Types type Rep (SOM t d gm x k p) :: Type -> Type # Methods from :: SOM t d gm x k p -> Rep (SOM t d gm x k p) x0 # to :: Rep (SOM t d gm x k p) x0 -> SOM t d gm x k p #
(NFData t, NFData (gm p)) => NFData (SOM t d gm x k p) Source #
Instance details Defined in Data.Datamining.Clustering.SOMInternal Methods rnf :: SOM t d gm x k p -> () #
Grid (gm p) => Grid (SOM t d gm x k p) Source #
Instance details Defined in Data.Datamining.Clustering.SOMInternal Associated Types type Index (SOM t d gm x k p) # type Direction (SOM t d gm x k p) # Methods indices :: SOM t d gm x k p -> [Index (SOM t d gm x k p)] # distance :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Index (SOM t d gm x k p) -> Int # minDistance :: SOM t d gm x k p -> [Index (SOM t d gm x k p)] -> Index (SOM t d gm x k p) -> Int # neighbours :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> [Index (SOM t d gm x k p)] # neighboursOfSet :: SOM t d gm x k p -> [Index (SOM t d gm x k p)] -> [Index (SOM t d gm x k p)] # neighbour :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Direction (SOM t d gm x k p) -> Maybe (Index (SOM t d gm x k p)) # numNeighbours :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Int # contains :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Bool # tileCount :: SOM t d gm x k p -> Int # null :: SOM t d gm x k p -> Bool # nonNull :: SOM t d gm x k p -> Bool # edges :: SOM t d gm x k p -> [(Index (SOM t d gm x k p), Index (SOM t d gm x k p))] # viewpoint :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> [(Index (SOM t d gm x k p), Int)] # isAdjacent :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Index (SOM t d gm x k p) -> Bool # adjacentTilesToward :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Index (SOM t d gm x k p) -> [Index (SOM t d gm x k p)] # minimalPaths :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Index (SOM t d gm x k p) -> [[Index (SOM t d gm x k p)]] # directionTo :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Index (SOM t d gm x k p) -> [Direction (SOM t d gm x k p)] # defaultMinDistance :: SOM t d gm x k p -> [Index (SOM t d gm x k p)] -> Index (SOM t d gm x k p) -> Int # defaultNeighbours :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> [Index (SOM t d gm x k p)] # defaultNeighboursOfSet :: SOM t d gm x k p -> [Index (SOM t d gm x k p)] -> [Index (SOM t d gm x k p)] # defaultNeighbour :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Direction (SOM t d gm x k p) -> Maybe (Index (SOM t d gm x k p)) # defaultTileCount :: SOM t d gm x k p -> Int # defaultEdges :: SOM t d gm x k p -> [(Index (SOM t d gm x k p), Index (SOM t d gm x k p))] # defaultIsAdjacent :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Index (SOM t d gm x k p) -> Bool # defaultAdjacentTilesToward :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Index (SOM t d gm x k p) -> [Index (SOM t d gm x k p)] # defaultMinimalPaths :: SOM t d gm x k p -> Index (SOM t d gm x k p) -> Index (SOM t d gm x k p) -> [[Index (SOM t d gm x k p)]] #
type BaseGrid (SOM t d gm x k) p Source #
Instance details Defined in Data.Datamining.Clustering.SOMInternal type BaseGrid (SOM t d gm x k) p = BaseGrid gm p
type Rep (SOM t d gm x k p) Source #
Instance details Defined in Data.Datamining.Clustering.SOMInternal type Rep (SOM t d gm x k p) = D1 ('MetaData "SOM" "Data.Datamining.Clustering.SOMInternal" "som-10.1.11-inplace" 'False) (C1 ('MetaCons "SOM" 'PrefixI 'True) ((S1 ('MetaSel ('Just "gridMap") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (gm p)) :: S1 ('MetaSel ('Just "learningRate") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (t -> d -> x))) :: (S1 ('MetaSel ('Just "difference") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (p -> p -> x)) :: (S1 ('MetaSel ('Just "makeSimilar") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (p -> x -> p -> p)) :: S1 ('MetaSel ('Just "counter") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 t)))))
type Direction (SOM t d gm x k p) Source #
Instance details Defined in Data.Datamining.Clustering.SOMInternal type Direction (SOM t d gm x k p) = Direction (gm p)
type Index (SOM t d gm x k p) Source #
Instance details Defined in Data.Datamining.Clustering.SOMInternal type Index (SOM t d gm x k p) = Index (gm p)

withGridMap :: (gm p -> gm p) -> SOM t d gm x k p -> SOM t d gm x k p Source #

Internal method.

currentLearningFunction :: Num t => SOM t d gm x k p -> d -> x Source #

Returns the learning function currently being used by the SOM.

toGridMap :: GridMap gm p => SOM t d gm x k p -> gm p Source #

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

adjustNode :: (Grid g, k ~ Index g, Num t) => g -> (t -> x) -> (p -> x -> p -> p) -> p -> k -> k -> p -> p Source #

Internal method.

trainNeighbourhood :: (Grid (gm p), GridMap gm p, Index (BaseGrid gm p) ~ Index (gm p), Num t, Num x, Num d) => SOM t d gm x k p -> Index (gm p) -> p -> SOM t d gm x k p Source #

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 t d gm x k p -> SOM t d gm x k p Source #

Increment the match counter.

justTrain :: (Ord x, Grid (gm p), GridMap gm x, GridMap gm p, Index (BaseGrid gm x) ~ Index (gm p), Index (BaseGrid gm p) ~ Index (gm p), Num t, Num x, Num d) => SOM t d gm x k p -> p -> SOM t d gm x k p Source #

Internal method.