HMath.MachineLearning.Neighbors¶

Description

Exact branch-and-bound KD/ball trees and budgeted approximate search. IDs always refer to original training rows. Neighbors sort by distance then ID. LSH is Euclidean p-stable Gaussian projection hashing (Datar et al. 2004). Isolation forest follows Liu et al. ICDM 2008, with seeded subsampling and the harmonic-number correction for unsplit leaves. Larger anomaly scores indicate more isolated observations. One-class SVM returns positive inlier decisions.

On this page¶

API	Purpose
IndexKind	Axis-aligned KD partitions or enclosing Euclidean ball partitions.
KDTree	Declaration and type contract below.
BallTree	Declaration and type contract below.
SpatialIndex	Immutable tree retaining original observation IDs and its validated feature dimension.
buildIndex	Build an exact search tree with at most leafSize observations per leaf.
NeighborResult	Neighbor indices/distances plus visited-leaf and exhaustive-search diagnostics.
NeighborResult	Declaration and type contract below.
neighbors	Training-row indices paired with returned Euclidean distances, ordered by distance and then index.
visitedLeaves	Number of leaves visited against the explicit query budget.
exhaustive	True if the neighbor search completed its exact stopping condition; False if unexplored nodes may improve candidates.
nearestNeighbors	maxLeaves is a query work budget.
knnRegress	Average the k exact nearest training responses for each query row.
knnClassify	Majority vote among k exact neighbors; targets follow original training row order.
LSH	Seeded p-stable Euclidean hash tables retaining Gaussian projections and offset buckets.
buildLSH	Build tables with projections scalar hashes each and positive bucket width.
queryLSH	Rank matching-bucket candidates by exact distance; may return fewer than k results, including none.
localOutlierFactor	Training-set LOF with ties included at the kth neighbor distance.
IsolationForest	Owned random isolation trees with fixed training dimension and subsample size.
fitIsolationForest	Seeded independent isolation trees using subsamples of 2..2048 observations.
scoreIsolationForest	Return 2^(-mean corrected path length / expected random-tree path length); larger means more anomalous.
OneClassSVM	Kernel novelty detector with normalized nonnegative dual weights and learned offset.
fitOneClassSVM	nu-SVM dual coordinate descent: sum alpha=1, 0<=alpha<=1/(nu*n).
decisionOneClassSVM	Return signed novelty margins: positive indicates an inlier under the fitted kernel boundary.

Documentation

IndexKind

data IndexKind Source #

Axis-aligned KD partitions or enclosing Euclidean ball partitions.

Constructors

KDTree
BallTree

Instances

Instances details

Show IndexKind Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods showsPrec :: Int -> IndexKind -> ShowS # show :: IndexKind -> String # showList :: [IndexKind] -> ShowS #
Eq IndexKind Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods (==) :: IndexKind -> IndexKind -> Bool # (/=) :: IndexKind -> IndexKind -> Bool #

SpatialIndex

data SpatialIndex Source #

Immutable tree retaining original observation IDs and its validated feature dimension.

Instances

Instances details

Show SpatialIndex Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods showsPrec :: Int -> SpatialIndex -> ShowS # show :: SpatialIndex -> String # showList :: [SpatialIndex] -> ShowS #
Eq SpatialIndex Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods (==) :: SpatialIndex -> SpatialIndex -> Bool # (/=) :: SpatialIndex -> SpatialIndex -> Bool #

buildIndex

buildIndex :: IndexKind -> Int -> Dataset -> Either MathError SpatialIndex Source #

Build an exact search tree with at most leafSize observations per leaf.

NeighborResult

data NeighborResult Source #

Neighbor indices/distances plus visited-leaf and exhaustive-search diagnostics. Budget-limited candidates are explicitly marked approximate.

Constructors

NeighborResult
Fields neighbors :: [(Int, Double)] Training-row indices paired with returned Euclidean distances, ordered by distance and then index. visitedLeaves :: Int Number of leaves visited against the explicit query budget. exhaustive :: Bool True if the neighbor search completed its exact stopping condition; False if unexplored nodes may improve candidates.

Instances

Instances details

Show NeighborResult Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods showsPrec :: Int -> NeighborResult -> ShowS # show :: NeighborResult -> String # showList :: [NeighborResult] -> ShowS #
Eq NeighborResult Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods (==) :: NeighborResult -> NeighborResult -> Bool # (/=) :: NeighborResult -> NeighborResult -> Bool #

nearestNeighbors

nearestNeighbors :: Int -> Int -> SpatialIndex -> [Double] -> Either MathError NeighborResult Source #

maxLeaves is a query work budget. A False exhaustive flag means unexplored nodes might improve the result. Even approximate results have exact distances.

knnRegress

knnRegress :: Int -> SpatialIndex -> [Double] -> Dataset -> Either MathError [Double] Source #

Average the k exact nearest training responses for each query row.

knnClassify

knnClassify :: Int -> SpatialIndex -> [Int] -> Dataset -> Either MathError [Int] Source #

Majority vote among k exact neighbors; targets follow original training row order.

LSH

data LSH Source #

Seeded p-stable Euclidean hash tables retaining Gaussian projections and offset buckets.

Instances

Instances details

Show LSH Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods showsPrec :: Int -> LSH -> ShowS # show :: LSH -> String # showList :: [LSH] -> ShowS #
Eq LSH Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods (==) :: LSH -> LSH -> Bool # (/=) :: LSH -> LSH -> Bool #

buildLSH

buildLSH :: Word64 -> Int -> Int -> Double -> Dataset -> Either MathError LSH Source #

Build tables with projections scalar hashes each and positive bucket width. Storage budget is explicit.

queryLSH

queryLSH :: Int -> LSH -> [Double] -> Either MathError [(Int, Double)] Source #

Rank matching-bucket candidates by exact distance; may return fewer than k results, including none.

localOutlierFactor

localOutlierFactor :: Int -> Dataset -> Either MathError [Double] Source #

Training-set LOF with ties included at the kth neighbor distance. Identical neighborhoods have LOF 1, including the infinite-density 0/0 limiting case.

IsolationForest

data IsolationForest Source #

Owned random isolation trees with fixed training dimension and subsample size.

Instances

Instances details

Show IsolationForest Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods showsPrec :: Int -> IsolationForest -> ShowS # show :: IsolationForest -> String # showList :: [IsolationForest] -> ShowS #
Eq IsolationForest Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods (==) :: IsolationForest -> IsolationForest -> Bool # (/=) :: IsolationForest -> IsolationForest -> Bool #

fitIsolationForest

fitIsolationForest :: Word64 -> Int -> Int -> Dataset -> Either MathError IsolationForest Source #

Seeded independent isolation trees using subsamples of 2..2048 observations.

scoreIsolationForest

scoreIsolationForest :: IsolationForest -> Dataset -> Either MathError [Double] Source #

Return 2^(-mean corrected path length / expected random-tree path length); larger means more anomalous.

OneClassSVM

data OneClassSVM Source #

Kernel novelty detector with normalized nonnegative dual weights and learned offset.

Instances

Instances details

Show OneClassSVM Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods showsPrec :: Int -> OneClassSVM -> ShowS # show :: OneClassSVM -> String # showList :: [OneClassSVM] -> ShowS #
Eq OneClassSVM Source #
Instance details Defined in HMath.MachineLearning.Neighbors Methods (==) :: OneClassSVM -> OneClassSVM -> Bool # (/=) :: OneClassSVM -> OneClassSVM -> Bool #

fitOneClassSVM

fitOneClassSVM :: MLConfig -> Kernel -> Double -> Dataset -> Either MathError (Fit OneClassSVM) Source #

nu-SVM dual coordinate descent: sum alpha=1, 0<=alpha<=1/(nu*n). The reported gap is the pairwise box-constrained KKT violation.

decisionOneClassSVM

decisionOneClassSVM :: OneClassSVM -> Dataset -> Either MathError [Double] Source #

Return signed novelty margins: positive indicates an inlier under the fitted kernel boundary.