Data.Datamining.Clustering.SGM3

A Self-generating Model (SGM). An SGM maps input patterns onto a set, where each element in the set is a model of the input data. An SGM is like a Kohonen Self-organising Map (SOM), except:

• Instead of a grid, it uses a simple set of unconnected models. Since the models are unconnected, only the model that best matches the input is ever updated. This makes it faster, however, topological relationships within the input data are not preserved.
• New models are created on-the-fly when no existing model is similar enough to an input pattern. If the SGM is at capacity, the least useful model will be deleted.

This implementation supports the use of non-numeric patterns.

In layman's terms, a SGM can be useful when you you want to build a set of models on some data. A tutorial is available at https://github.com/mhwombat/som/wiki.

References:

• Amy de Buitléir, Mark Daly, and Michael Russell. The Self-generating Model: an Adaptation of the Self-organizing Map for Intelligent Agents and Data Mining. In: Artificial Life and Intelligent Agents: Second International Symposium, ALIA 2016, Birmingham, UK, June 14-15, 2016, Revised Selected Papers. Ed. by Peter R. Lewis et al. Springer International Publishing, 2018, pp. 59–72. Available at http://amydebuitleir.eu/publications/.
• Amy de Buitléir, Michael Russell, and Mark Daly. Wains: A pattern-seeking artificial life species. Artificial Life, (18)4:399–423, 2012. Available at http://amydebuitleir.eu/publications/.
• Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43 (1), 59–69.

Construction

data SGM t x k p

A Simplified Self-Organising Map (SGM). t is the type of the counter. x is the type of the learning rate and the difference metric. k is the type of the model indices. p is the type of the input patterns and models.

Constructors

SGM

Fields

• toMap :: Map k (p, t)

  Maps patterns and match counts to nodes.

• learningRate :: t -> x

  A function which determines the learning rate for a node. The input parameter 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 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.

• capacity :: Int

  The maximum number of models this SGM can hold.

• 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. For example, 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.

• nextIndex :: k

  Index for the next node to add to the SGM.

Instances

Generic (SGM t x k p)

Defined in Data.Datamining.Clustering.SGM3Internal

Associated Types

type Rep (SGM t x k p) :: Type -> Type

Methods

from :: SGM t x k p -> Rep (SGM t x k p) x0

to :: Rep (SGM t x k p) x0 -> SGM t x k p

(NFData k, NFData p, NFData t) => NFData (SGM t x k p)

Defined in Data.Datamining.Clustering.SGM3Internal

Methods

rnf :: SGM t x k p -> ()

type Rep (SGM t x k p)

Defined in Data.Datamining.Clustering.SGM3Internal

type Rep (SGM t x k p) = D1 (MetaData "SGM" "Data.Datamining.Clustering.SGM3Internal" "som-10.1.4-9TgYmlNCjOGdUT1YiQt03" False) (C1 (MetaCons "SGM" PrefixI True) ((S1 (MetaSel (Just "toMap") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Map k (p, t))) :*: (S1 (MetaSel (Just "learningRate") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (t -> x)) :*: S1 (MetaSel (Just "capacity") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Int))) :*: (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 "nextIndex") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 k)))))

makeSGM :: Bounded k => (t -> x) -> Int -> (p -> p -> x) -> (p -> x -> p -> p) -> SGM t x k p

makeSGM lr n diff ms creates a new SGM that does not (yet) contain any models. It will learn at the rate determined by the learning function lr, and will be able to hold up to n models. It will create a new model based on a pattern presented to it when the SGM is not at capacity, or a less useful model can be replaced. It will use the function diff to measure the similarity between an input pattern and a model. It will use the function ms to adjust models as needed to make them more similar to input patterns.

Deconstruction

time :: Num t => SGM t x k p -> t

The current "time" (number of times the SGM has been trained).

isEmpty :: SGM t x k p -> Bool

Returns true if the SGM has no models, false otherwise.

size :: SGM t x k p -> Int

Returns the number of models the SGM currently contains.

modelMap :: SGM t x k p -> Map k p

Returns a map from node ID to model.

counterMap :: SGM t x k p -> Map k t

Returns a map from node ID to counter (number of times the node's model has been the closest match to an input pattern).

modelAt :: Ord k => SGM t x k p -> k -> p

Returns the model at a specified node.

Learning and classification

exponential :: (Floating a, Integral t) => a -> a -> t -> a

A typical learning function for classifiers. exponential r0 d t returns the learning rate at time t. When t = 0, the learning rate is r0. Over time the learning rate decays exponentially; the decay rate is d. Normally the parameters are chosen such that:

• 0 < r0 < 1
• 0 < d

classify :: (Num t, Ord t, Num x, Ord x, Enum k, Ord k) => SGM t x k p -> p -> (k, x, Map k (p, x))

classify s p identifies the model s that most closely matches the pattern p. It will not make any changes to the classifier. (I.e., it will not change the models or match counts.) Returns the ID of the node with the best matching model, the difference between the best matching model and the pattern, and the SGM labels paired with the model and the difference between the input and the corresponding model. The final paired list is sorted in decreasing order of similarity.

trainAndClassify :: (Num t, Ord t, Fractional x, Real x, Num x, Ord x, Enum k, Ord k) => SGM t x k p -> p -> (k, x, Map k (p, x), SGM t x k p)

trainAndClassify s p identifies the model in s that most closely matches p, and updates it to be a somewhat better match. If necessary, it will create a new node and model. Returns the ID of the node with the best matching model, the difference between the pattern and the best matching model in the original SGM (before training or adding a new model), the differences between the pattern and each model in the updated SGM, and the updated SGM.

train :: (Num t, Ord t, Fractional x, Real x, Num x, Ord x, Enum k, Ord k) => SGM t x k p -> p -> SGM t x k p

train s p identifies the model in s that most closely matches p, and updates it to be a somewhat better match. If necessary, it will create a new node and model.

trainBatch :: (Num t, Ord t, Fractional x, Real x, Num x, Ord x, Enum k, Ord k) => SGM t x k p -> [p] -> SGM t x k p

For each pattern p in ps, trainBatch s ps identifies the model in s that most closely matches p, and updates it to be a somewhat better match.