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 x 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.

Constructors

DSOM

Fields

• gridMap :: gm p

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

• learningRate :: x -> x -> x -> x

  A function which determines the how quickly the SOM learns.

• 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.

Instances

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

Defined in Data.Datamining.Clustering.DSOMInternal

Methods

toList :: DSOM gm x k p -> [(k, p)]

numModels :: DSOM gm x k p -> Int

models :: DSOM gm x k p -> [p]

differences :: DSOM gm x k p -> p -> [(k, x)]

classify :: DSOM gm x k p -> p -> k

train :: DSOM gm x k p -> p -> DSOM gm x k p

trainBatch :: DSOM gm x k p -> [p] -> DSOM gm x k p

classifyAndTrain :: DSOM gm x k p -> p -> (k, DSOM gm x k p)

diffAndTrain :: DSOM gm x k p -> p -> ([(k, x)], DSOM gm x k p)

reportAndTrain :: DSOM gm x k p -> p -> (k, [(k, x)], DSOM gm x k p)

Foldable gm => Foldable (DSOM gm x k)

Defined in Data.Datamining.Clustering.DSOMInternal

Methods

fold :: Monoid m => DSOM gm x k m -> m

foldMap :: Monoid m => (a -> m) -> DSOM gm x k a -> m

foldr :: (a -> b -> b) -> b -> DSOM gm x k a -> b

foldr' :: (a -> b -> b) -> b -> DSOM gm x k a -> b

foldl :: (b -> a -> b) -> b -> DSOM gm x k a -> b

foldl' :: (b -> a -> b) -> b -> DSOM gm x k a -> b

foldr1 :: (a -> a -> a) -> DSOM gm x k a -> a

foldl1 :: (a -> a -> a) -> DSOM gm x k a -> a

toList :: DSOM gm x k a -> [a]

null :: DSOM gm x k a -> Bool

length :: DSOM gm x k a -> Int

elem :: Eq a => a -> DSOM gm x k a -> Bool

maximum :: Ord a => DSOM gm x k a -> a

minimum :: Ord a => DSOM gm x k a -> a

sum :: Num a => DSOM gm x k a -> a

product :: Num a => DSOM gm x k a -> a

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

Defined in Data.Datamining.Clustering.DSOMInternal

Associated Types

type BaseGrid (DSOM gm x k) p :: Type

Methods

(!) :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => DSOM gm x k p -> k0 -> p

toMap :: k0 ~ Index (BaseGrid (DSOM gm x k) p) => DSOM gm x k p -> Map k0 p

toGrid :: DSOM gm x k p -> BaseGrid (DSOM gm x k) p

toList :: k0 ~ Index (BaseGrid (DSOM gm x k) p) => DSOM gm x k p -> [(k0, p)]

lookup :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => k0 -> DSOM gm x k p -> Maybe p

insert :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => k0 -> p -> DSOM gm x k p -> DSOM gm x k p

insertWith :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => (p -> p -> p) -> k0 -> p -> DSOM gm x k p -> DSOM gm x k p

insertWithKey :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => (k0 -> p -> p -> p) -> k0 -> p -> DSOM gm x k p -> DSOM gm x k p

insertLookupWithKey :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => (k0 -> p -> p -> p) -> k0 -> p -> DSOM gm x k p -> (Maybe p, DSOM gm x k p)

delete :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => k0 -> DSOM gm x k p -> DSOM gm x k p

adjust :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => (p -> p) -> k0 -> DSOM gm x k p -> DSOM gm x k p

adjustWithKey :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => (k0 -> p -> p) -> k0 -> DSOM gm x k p -> DSOM gm x k p

alter :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => (Maybe p -> Maybe p) -> k0 -> DSOM gm x k p -> DSOM gm x k p

findWithDefault :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => p -> k0 -> DSOM gm x k p -> p

keys :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), Ord k0) => DSOM gm x k p -> [k0]

elems :: DSOM gm x k p -> [p]

map :: (GridMap (DSOM gm x k) v2, Index (BaseGrid (DSOM gm x k) p) ~ Index (BaseGrid (DSOM gm x k) v2)) => (p -> v2) -> DSOM gm x k p -> DSOM gm x k v2

mapWithKey :: (k0 ~ Index (BaseGrid (DSOM gm x k) p), k0 ~ Index (BaseGrid (DSOM gm x k) v2), GridMap (DSOM gm x k) v2) => (k0 -> p -> v2) -> DSOM gm x k p -> DSOM gm x k v2

filter :: (p -> Bool) -> DSOM gm x k p -> DSOM gm x k p

filterWithKey :: k0 ~ Index (BaseGrid (DSOM gm x k) p) => (k0 -> p -> Bool) -> DSOM gm x k p -> DSOM gm x k p

Generic (DSOM gm x k p)

Defined in Data.Datamining.Clustering.DSOMInternal

Associated Types

type Rep (DSOM gm x k p) :: Type -> Type

Methods

from :: DSOM gm x k p -> Rep (DSOM gm x k p) x0

to :: Rep (DSOM gm x k p) x0 -> DSOM gm x k p

NFData (gm p) => NFData (DSOM gm x k p)

Defined in Data.Datamining.Clustering.DSOMInternal

Methods

rnf :: DSOM gm x k p -> ()

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

Defined in Data.Datamining.Clustering.DSOMInternal

Associated Types

type Index (DSOM gm x k p) :: Type

type Direction (DSOM gm x k p) :: Type

Methods

indices :: DSOM gm x k p -> [Index (DSOM gm x k p)]

distance :: DSOM gm x k p -> Index (DSOM gm x k p) -> Index (DSOM gm x k p) -> Int

minDistance :: DSOM gm x k p -> [Index (DSOM gm x k p)] -> Index (DSOM gm x k p) -> Int

neighbours :: DSOM gm x k p -> Index (DSOM gm x k p) -> [Index (DSOM gm x k p)]

neighboursOfSet :: DSOM gm x k p -> [Index (DSOM gm x k p)] -> [Index (DSOM gm x k p)]

neighbour :: DSOM gm x k p -> Index (DSOM gm x k p) -> Direction (DSOM gm x k p) -> Maybe (Index (DSOM gm x k p))

numNeighbours :: DSOM gm x k p -> Index (DSOM gm x k p) -> Int

contains :: DSOM gm x k p -> Index (DSOM gm x k p) -> Bool

tileCount :: DSOM gm x k p -> Int

null :: DSOM gm x k p -> Bool

nonNull :: DSOM gm x k p -> Bool

edges :: DSOM gm x k p -> [(Index (DSOM gm x k p), Index (DSOM gm x k p))]

viewpoint :: DSOM gm x k p -> Index (DSOM gm x k p) -> [(Index (DSOM gm x k p), Int)]

isAdjacent :: DSOM gm x k p -> Index (DSOM gm x k p) -> Index (DSOM gm x k p) -> Bool

adjacentTilesToward :: DSOM gm x k p -> Index (DSOM gm x k p) -> Index (DSOM gm x k p) -> [Index (DSOM gm x k p)]

minimalPaths :: DSOM gm x k p -> Index (DSOM gm x k p) -> Index (DSOM gm x k p) -> [[Index (DSOM gm x k p)]]

directionTo :: DSOM gm x k p -> Index (DSOM gm x k p) -> Index (DSOM gm x k p) -> [Direction (DSOM gm x k p)]

defaultMinDistance :: DSOM gm x k p -> [Index (DSOM gm x k p)] -> Index (DSOM gm x k p) -> Int

defaultNeighbours :: DSOM gm x k p -> Index (DSOM gm x k p) -> [Index (DSOM gm x k p)]

defaultNeighboursOfSet :: DSOM gm x k p -> [Index (DSOM gm x k p)] -> [Index (DSOM gm x k p)]

defaultNeighbour :: DSOM gm x k p -> Index (DSOM gm x k p) -> Direction (DSOM gm x k p) -> Maybe (Index (DSOM gm x k p))

defaultTileCount :: DSOM gm x k p -> Int

defaultEdges :: DSOM gm x k p -> [(Index (DSOM gm x k p), Index (DSOM gm x k p))]

defaultIsAdjacent :: DSOM gm x k p -> Index (DSOM gm x k p) -> Index (DSOM gm x k p) -> Bool

defaultAdjacentTilesToward :: DSOM gm x k p -> Index (DSOM gm x k p) -> Index (DSOM gm x k p) -> [Index (DSOM gm x k p)]

defaultMinimalPaths :: DSOM gm x k p -> Index (DSOM gm x k p) -> Index (DSOM gm x k p) -> [[Index (DSOM gm x k p)]]

type BaseGrid (DSOM gm x k) p

Defined in Data.Datamining.Clustering.DSOMInternal

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

type Rep (DSOM gm x k p)

Defined in Data.Datamining.Clustering.DSOMInternal

type Rep (DSOM gm x k p) = D1 (MetaData "DSOM" "Data.Datamining.Clustering.DSOMInternal" "som-10.1.8-4U7idyllz4eEJA79g8KqEw" False) (C1 (MetaCons "DSOM" PrefixI True) ((S1 (MetaSel (Just "gridMap") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (gm p)) :*: S1 (MetaSel (Just "learningRate") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (x -> x -> x -> x))) :*: (S1 (MetaSel (Just "difference") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (p -> p -> x)) :*: S1 (MetaSel (Just "makeSimilar") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (p -> x -> p -> p)))))

type Direction (DSOM gm x k p)

Defined in Data.Datamining.Clustering.DSOMInternal

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

type Index (DSOM gm x k p)

Defined in Data.Datamining.Clustering.DSOMInternal

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

Deconstruction

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

Extracts the grid and current models from the DSOM.

Learning functions

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.

Advanced control

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