hierarchical-spectral-clustering (empty) → 0.2.1.0
raw patch · 14 files changed
+2048/−0 lines, 14 filesdep +aesondep +aeson-prettydep +basesetup-changed
Dependencies added: aeson, aeson-pretty, base, bytestring, cassava, clustering, containers, eigen, fgl, filepath, hierarchical-clustering, hierarchical-spectral-clustering, hmatrix, lens, managed, modularity, mtl, optparse-generic, safe, sparse-linear-algebra, spectral-clustering, streaming, streaming-bytestring, streaming-cassava, streaming-with, text, text-show, tree-fun, vector
Files
- LICENSE +674/−0
- Setup.hs +2/−0
- app/Main.hs +231/−0
- hierarchical-spectral-clustering.cabal +76/−0
- src/Math/Clustering/Hierarchical/Spectral/Dense.hs +94/−0
- src/Math/Clustering/Hierarchical/Spectral/Eigen/AdjacencyMatrix.hs +100/−0
- src/Math/Clustering/Hierarchical/Spectral/Eigen/FeatureMatrix.hs +113/−0
- src/Math/Clustering/Hierarchical/Spectral/Load.hs +167/−0
- src/Math/Clustering/Hierarchical/Spectral/Sparse.hs +177/−0
- src/Math/Clustering/Hierarchical/Spectral/Test.hs +188/−0
- src/Math/Clustering/Hierarchical/Spectral/Types.hs +90/−0
- src/Math/Clustering/Hierarchical/Spectral/Utility.hs +28/−0
- src/Math/Graph/Components.hs +37/−0
- src/Math/Graph/Types.hs +71/−0
+ LICENSE view
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+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ app/Main.hs view
@@ -0,0 +1,231 @@+{- cluster-tree+Gregory W. Schwartz++Hierarchical spectral clustering of data.+-}++{-# LANGUAGE BangPatterns #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveGeneric #-}+{-# LANGUAGE OverloadedStrings #-}+{-# LANGUAGE TypeOperators #-}+{-# LANGUAGE StandaloneDeriving #-}++module Main where++-- Standard+import Data.Maybe (fromMaybe, catMaybes)+import GHC.Generics++-- Cabal+import Data.Char (ord)+import Data.List (intercalate)+import Data.Monoid ((<>))+import Options.Generic+import Safe (atMay)+import System.IO (stdin)+import Text.Read (readMaybe)+import TextShow (showt)+import qualified Control.Lens as L+import qualified Data.Aeson as A+import qualified Data.Aeson.Encode.Pretty as A+import qualified Data.ByteString.Lazy.Char8 as B+import qualified Data.Csv as CSV+import qualified Data.Map.Strict as Map+import qualified Data.Set as Set+import qualified Data.Text as T+import qualified Data.Vector as V+import qualified Numeric.LinearAlgebra as H+import qualified System.FilePath as File+import Math.Graph.Types++-- Local+import Math.Clustering.Hierarchical.Spectral.Load+import Math.Clustering.Hierarchical.Spectral.Types+import Math.Graph.Components+import qualified Math.Clustering.Hierarchical.Spectral.Dense as HD+import qualified Math.Clustering.Hierarchical.Spectral.Eigen.AdjacencyMatrix as HS++newtype Delimiter = Delimiter { unDelimiter :: Char } deriving (Read, Show)+newtype Row = Row { unRow :: Int } deriving (Eq, Ord, Read, Show)+newtype Column = Column { unColumn :: Int } deriving (Eq, Ord, Read, Show)+newtype OutputTree = OutputTree { unOutputTree :: String } deriving (Read, Show)+newtype MinSize = MinSize { unMinSize :: Int } deriving (Read, Show)+newtype NumEigen = NumEigen { unNumEigen :: Int } deriving (Read, Show)++data ClusteringType = Sparse | Dense deriving (Read, Show)+data Components a = Single (ClusteringTree a) | Multiple [ClusteringTree a]++instance A.ToJSON Q where+ toEncoding = A.genericToEncoding A.defaultOptions+instance A.FromJSON Q++instance (A.ToJSON a) => A.ToJSON (ClusteringVertex a) where+ toEncoding = A.genericToEncoding A.defaultOptions+instance (A.FromJSON a) => A.FromJSON (ClusteringVertex a)++-- | Command line arguments+data Options = Options { clusteringType :: Maybe String+ <?> "([Sparse] | Dense) Method for clustering data."+ , delimiter :: Maybe Char+ <?> "([,] | CHAR) The delimiter of the CSV file. Format is row,column,value with no header."+ , minSize :: Maybe Int+ <?> "([Nothing] | INT) Minimum size of a cluster."+ , numEigen :: Maybe Int+ <?> "([1] | INT) Number of eigenvectors to use while clustering with kmeans. Takes from the first eigenvector. Recommended to start at 2 and work up from there if needed."+ , minModularity :: Maybe Double+ <?> "([0] | DOUBLE) Minimum modularity to be over to continue recursion."+ , eigenGroup :: Maybe String+ <?> "([SignGroup] | KMeansGroup) Whether to group the eigenvector using the sign or kmeans while clustering. While the default is sign, kmeans may be more accurate (but starting points are arbitrary)."+ , separateComponents :: Bool+ <?> "Whether to first separate connected components of the graph first. Will output a dendrogram for each component with the name of the tree and the number of nodes within the tree, along with the base set by --output-tree."+ , outputTree :: Maybe String+ <?> "([Nothing] | FILE) The name of the file to output the tree in JSON format."+ }+ deriving (Generic)++modifiers :: Modifiers+modifiers = lispCaseModifiers { shortNameModifier = short }+ where+ short "minSize" = Just 'S'+ short x = firstLetter x++instance ParseRecord Options where+ parseRecord = parseRecordWithModifiers modifiers++main :: IO ()+main = do+ opts <- getRecord "cluster-tree, Gregory W. Schwartz.\+ \ Hierarchical spectral clustering of data Computes real\+ \ symmetric part of matrix, so ensure the input is real\+ \ and symmetric. Diagonal should be 0s for\+ \ adjacency matrix.\+ \ Format is row,column,value with no header.\+ \ Must end with a newline."++ let readOrErr err = fromMaybe (error err) . readMaybe+ clusteringType' =+ maybe Sparse (readOrErr "Cannot read --clustering-type")+ . unHelpful+ . clusteringType+ $ opts+ delim' =+ Delimiter . fromMaybe ',' . unHelpful . delimiter $ opts+ minSize' = fmap MinSize . unHelpful . minSize $ opts+ numEigen' = fmap NumEigen . unHelpful . numEigen $ opts+ minModularity' = fmap Q . unHelpful . minModularity $ opts+ eigenGroup' =+ maybe SignGroup (readOrErr "Cannot read --eigen-group")+ . unHelpful+ . eigenGroup+ $ opts+ separateComponents' = unHelpful . separateComponents $ opts+ outputTree' = fmap OutputTree . unHelpful . outputTree $ opts+ decodeOpt = CSV.defaultDecodeOptions+ { CSV.decDelimiter =+ fromIntegral (ord . unDelimiter $ delim')+ }+ encodeOpt = CSV.defaultEncodeOptions+ { CSV.encDelimiter =+ fromIntegral (ord . unDelimiter $ delim')+ }++ clusteringTree <-+ case clusteringType' of+ Dense -> do+ (items, mat) <- readDenseAdjMatrix decodeOpt stdin++ let cluster items = HD.hierarchicalSpectralCluster+ eigenGroup'+ (fmap unNumEigen numEigen')+ (fmap unMinSize minSize')+ minModularity'+ items++ return $+ if separateComponents'+ then Multiple+ . fmap (uncurry cluster)+ . getComponentMatsItems items+ $ mat+ else Single $ cluster items mat+ Sparse -> do+ (items, mat) <- readEigenSparseAdjMatrix decodeOpt stdin++ let cluster items = HS.hierarchicalSpectralCluster+ eigenGroup'+ (fmap unNumEigen numEigen')+ (fmap unMinSize minSize')+ minModularity'+ items++ return $+ if separateComponents'+ then Multiple+ . fmap (uncurry cluster)+ . getComponentMatsItems items+ $ mat+ else Single $ cluster items mat++ body <- case clusteringTree of+ (Single ct) -> do+ let clustering = zip ([1..] :: [Int]) . getClusterItemsTree $ ct+ body :: [(T.Text, T.Text)]+ body = concatMap+ (\(!c, xs) -> fmap (\ !x -> (x, showt c)) . V.toList $ xs)+ clustering++ case outputTree' of+ Nothing -> return ()+ Just (OutputTree file) -> B.writeFile file+ . A.encodePretty+ . clusteringTreeToDendrogram+ $ ct++ return body+ (Multiple cts) -> do+ let clustering =+ fmap (L.over L._2 (zip ([1..] :: [Int]) . getClusterItemsTree))+ . zip ([1..] :: [Int])+ $ cts+ body :: [(T.Text, T.Text)]+ body = concatMap+ (\ (!t, xs)+ -> concatMap (\ (!c, ys)+ -> fmap (\ x -> (x, showt t <> "/" <> showt c))+ . V.toList+ $ ys+ )+ xs+ )+ clustering++ case outputTree' of+ Nothing -> return ()+ Just (OutputTree file) -> do+ let getSize :: ClusteringTree a -> Int+ getSize = sum . fmap V.length . getClusterItemsTree+ getFileName :: Int -> Int -> String+ getFileName t n =+ uncurry (File.</>)+ . L.over L._2 (\x -> intercalate "_" ["tree", show t, "size", show n, x])+ . File.splitFileName+ $ file+ write :: (A.ToJSON a) => Int -> ClusteringTree a -> IO ()+ write t tree = do+ B.writeFile (getFileName t (getSize tree))+ . A.encodePretty+ . clusteringTreeToDendrogram+ $ tree++ mapM_ (uncurry write) . zip [1..] $ cts++ return body++ -- | Print final result.+ B.putStr+ . (<>) "item,cluster\n"+ . CSV.encodeWith encodeOpt+ $ body++ return ()
+ hierarchical-spectral-clustering.cabal view
@@ -0,0 +1,76 @@+name: hierarchical-spectral-clustering+version: 0.2.1.0+synopsis: Hierarchical spectral clustering of a graph.+description: Generate a tree of hierarchical spectral clustering using Newman-Girvan modularity as a stopping criteria.+homepage: http://github.com/GregorySchwartz/hierarchical-spectral-clustering#readme+license: GPL-3+license-file: LICENSE+author: Gregory W. Schwartz+maintainer: gsch@pennmedicine.upenn.edu+copyright: 2018 Gregory W. Schwartz+category: Bioinformatics+build-type: Simple+-- extra-source-files:+cabal-version: >=1.10++library+ hs-source-dirs: src+ exposed-modules: Math.Clustering.Hierarchical.Spectral.Dense+ , Math.Clustering.Hierarchical.Spectral.Sparse+ , Math.Clustering.Hierarchical.Spectral.Load+ , Math.Clustering.Hierarchical.Spectral.Eigen.AdjacencyMatrix+ , Math.Clustering.Hierarchical.Spectral.Eigen.FeatureMatrix+ , Math.Clustering.Hierarchical.Spectral.Types+ , Math.Clustering.Hierarchical.Spectral.Utility+ , Math.Graph.Components+ , Math.Graph.Types+ other-modules: Math.Clustering.Hierarchical.Spectral.Test+ build-depends: base >= 4.7 && < 5+ , aeson+ , cassava+ , clustering+ , containers+ , eigen == 3.3.4.1+ , hierarchical-clustering+ , hmatrix+ , fgl+ , managed+ , modularity+ , mtl+ , safe+ , sparse-linear-algebra+ , spectral-clustering+ , streaming+ , streaming-bytestring+ , streaming-cassava+ , streaming-with+ , text+ , tree-fun+ , vector+ ghc-options: -O2+ default-language: Haskell2010++executable cluster-tree+ hs-source-dirs: app+ main-is: Main.hs+ ghc-options: -threaded -rtsopts -O2+ build-depends: base+ , hierarchical-spectral-clustering+ , aeson+ , aeson-pretty+ , bytestring+ , cassava+ , containers+ , filepath+ , hmatrix+ , lens+ , optparse-generic+ , safe+ , text+ , text-show+ , vector+ default-language: Haskell2010++source-repository head+ type: git+ location: https://github.com/GregorySchwartz/hierarchical-spectral-clustering
+ src/Math/Clustering/Hierarchical/Spectral/Dense.hs view
@@ -0,0 +1,94 @@+{- Math.Clustering.Hierarchical.Spectral+Gregory W. Schwartz++Collects the functions pertaining to hierarchical spectral clustering.+-}++{-# LANGUAGE BangPatterns #-}++module Math.Clustering.Hierarchical.Spectral.Dense+ ( hierarchicalSpectralCluster+ , AdjacencyMatrix (..)+ , Items (..)+ ) where++-- Remote+import Data.Bool (bool)+import Data.Clustering.Hierarchical (Dendrogram (..))+import Data.Maybe (fromMaybe)+import Data.Tree (Tree (..))+import Math.Clustering.Spectral.Dense (spectralClusterNorm, spectralClusterKNorm)+import Math.Modularity.Dense (getModularity)+import Math.Modularity.Types (Q (..))+import qualified Data.Foldable as F+import qualified Data.Set as Set+import qualified Data.Vector as V+import qualified Data.Vector.Storable as VS+import qualified Numeric.LinearAlgebra as H++-- Local+import Math.Clustering.Hierarchical.Spectral.Types+import Math.Clustering.Hierarchical.Spectral.Utility++type AdjacencyMatrix = H.Matrix Double+type Items a = V.Vector a++-- | Check if there is more than one cluster.+hasMultipleClusters :: H.Vector Double -> Bool+hasMultipleClusters = (> 1) . Set.size . Set.fromList . H.toList++-- | Generates a tree through divisive hierarchical clustering using+-- Newman-Girvan modularity as a stopping criteria. Can also use minimum number+-- of observations in a cluster as the stopping criteria.+hierarchicalSpectralCluster :: (Show a) => EigenGroup+ -> Maybe NumEigen+ -> Maybe Int+ -> Maybe Q+ -> Items a+ -> AdjacencyMatrix+ -> ClusteringTree a+hierarchicalSpectralCluster !eigenGroup !numEigenMay !minSizeMay !minModMay !items !adjMat =+ if H.rows adjMat > 1+ && hasMultipleClusters clusters+ && ngMod > minMod+ && H.rows left >= minSize+ && H.rows right >= minSize+ then+ Node { rootLabel = vertex+ , subForest =+ [ hierarchicalSpectralCluster+ eigenGroup+ numEigenMay+ minSizeMay+ minModMay+ (subsetVector items leftIdxs)+ left+ , hierarchicalSpectralCluster+ eigenGroup+ numEigenMay+ minSizeMay+ minModMay+ (subsetVector items rightIdxs)+ right+ ]+ }+ else+ Node {rootLabel = vertex, subForest = []}+ where+ minMod = fromMaybe (Q 0) minModMay+ minSize = fromMaybe 1 minSizeMay+ numEigen = fromMaybe 1 numEigenMay+ vertex = ClusteringVertex { _clusteringItems = items+ , _ngMod = ngMod+ }+ clusters = spectralClustering eigenGroup adjMat+ spectralClustering :: EigenGroup -> AdjacencyMatrix -> H.Vector Double+ spectralClustering SignGroup = spectralClusterNorm+ spectralClustering KMeansGroup = spectralClusterKNorm numEigen 2+ ngMod = getModularity clusters $ adjMat+ getIdxs val = VS.ifoldr' (\ !i !v !acc -> bool acc (i:acc) $ v == val) []+ leftIdxs = getIdxs 0 $ clusters+ rightIdxs = getIdxs 1 $ clusters+ left = adjMat H.?? (H.Pos (H.idxs leftIdxs), H.Pos (H.idxs leftIdxs))+ right =+ adjMat H.?? (H.Pos (H.idxs rightIdxs), H.Pos (H.idxs rightIdxs))
+ src/Math/Clustering/Hierarchical/Spectral/Eigen/AdjacencyMatrix.hs view
@@ -0,0 +1,100 @@+{- Math.Clustering.Hierarchical.Spectral.Eigen.AdjacencyMatrix+Gregory W. Schwartz++Collects the functions pertaining to hierarchical spectral clustering.+-}++{-# LANGUAGE BangPatterns #-}++module Math.Clustering.Hierarchical.Spectral.Eigen.AdjacencyMatrix+ ( hierarchicalSpectralCluster+ , AdjacencyMatrix (..)+ , Items (..)+ ) where++-- Remote+import Data.Bool (bool)+import Data.Clustering.Hierarchical (Dendrogram (..))+import Data.Maybe (fromMaybe)+import Data.Tree (Tree (..))+import Math.Clustering.Spectral.Eigen.AdjacencyMatrix (spectralClusterNorm, spectralClusterKNorm)+import Math.Modularity.Eigen.Sparse (getModularity)+import Math.Modularity.Types (Q (..))+import Safe (headMay)+import qualified Data.Foldable as F+import qualified Data.Set as Set+import qualified Data.Eigen.SparseMatrix as S+import qualified Data.Vector as V+import qualified Data.Vector.Storable as VS++-- Local+import Math.Clustering.Hierarchical.Spectral.Types+import Math.Clustering.Hierarchical.Spectral.Utility++type AdjacencyMatrix = S.SparseMatrixXd+type Items a = V.Vector a++-- | Check if there is more than one cluster.+hasMultipleClusters :: S.SparseMatrixXd -> Bool+hasMultipleClusters = (> 1)+ . Set.size+ . Set.fromList+ . concat+ . S.toDenseList++-- | Generates a tree through divisive hierarchical clustering using+-- Newman-Girvan modularity as a stopping criteria. Can also use minimum number+-- of observations in a cluster as the stopping criteria.+hierarchicalSpectralCluster :: EigenGroup+ -> Maybe NumEigen+ -> Maybe Int+ -> Maybe Q+ -> Items a+ -> AdjacencyMatrix+ -> ClusteringTree a+hierarchicalSpectralCluster !eigenGroup !numEigenMay !minSizeMay !minModMay !items !adjMat =++ if S.rows adjMat > 1+ && hasMultipleClusters clusters+ && ngMod > minMod+ && S.rows left >= minSize+ && S.rows right >= minSize+ then do+ Node { rootLabel = vertex+ , subForest = [ hierarchicalSpectralCluster+ eigenGroup+ numEigenMay+ minSizeMay+ minModMay+ (subsetVector items leftIdxs)+ left+ , hierarchicalSpectralCluster+ eigenGroup+ numEigenMay+ minSizeMay+ minModMay (subsetVector items rightIdxs)+ right+ ]+ }+ else+ Node {rootLabel = vertex, subForest = []}+ where+ clusters = spectralClustering eigenGroup adjMat+ spectralClustering :: EigenGroup -> AdjacencyMatrix -> S.SparseMatrixXd+ spectralClustering SignGroup = spectralClusterNorm+ spectralClustering KMeansGroup = spectralClusterKNorm numEigen 2+ minMod = fromMaybe (Q 0) minModMay+ minSize = fromMaybe 1 minSizeMay+ numEigen = fromMaybe 1 numEigenMay+ vertex = ClusteringVertex { _clusteringItems = items+ , _ngMod = ngMod+ }+ ngMod = getModularity clusters adjMat+ getIdxs val = VS.ifoldr' (\ !i !v !acc -> bool acc (i:acc) $ v == val) []+ . VS.fromList+ . concat+ . S.toDenseList+ leftIdxs = getIdxs 0 clusters+ rightIdxs = getIdxs 1 clusters+ left = S.squareSubset leftIdxs adjMat+ right = S.squareSubset rightIdxs adjMat
+ src/Math/Clustering/Hierarchical/Spectral/Eigen/FeatureMatrix.hs view
@@ -0,0 +1,113 @@+{- Math.Clustering.Hierarchical.Spectral.Eigen.FeatureMatrix+Gregory W. Schwartz++Collects the functions pertaining to hierarchical spectral clustering for+feature matrices.+-}++{-# LANGUAGE BangPatterns #-}++module Math.Clustering.Hierarchical.Spectral.Eigen.FeatureMatrix+ ( hierarchicalSpectralCluster+ , FeatureMatrix (..)+ , B (..)+ , Items (..)+ , ShowB (..)+ ) where++-- Remote+import Data.Bool (bool)+import Data.Clustering.Hierarchical (Dendrogram (..))+import Data.Maybe (fromMaybe)+import Data.Tree (Tree (..))+import Math.Clustering.Spectral.Eigen.FeatureMatrix (B (..), getB, spectralCluster, spectralClusterK)+import Math.Modularity.Eigen.Sparse (getBModularity)+import Math.Modularity.Types (Q (..))+import qualified Data.Foldable as F+import qualified Data.Set as Set+import qualified Data.Eigen.SparseMatrix as S+import qualified Data.Vector as V+import qualified Data.Vector.Storable as VS++-- Local+import Math.Clustering.Hierarchical.Spectral.Types+import Math.Clustering.Hierarchical.Spectral.Utility++type FeatureMatrix = S.SparseMatrixXd+type Items a = V.Vector a+type ShowB = ((Int, Int), [(Int, Int, Double)])+type NormalizeFlag = Bool++-- | Check if there is more than one cluster.+hasMultipleClusters :: S.SparseMatrixXd -> Bool+hasMultipleClusters = (> 1)+ . Set.size+ . Set.fromList+ . concat+ . S.toDenseList++-- | Generates a tree through divisive hierarchical clustering using+-- Newman-Girvan modularity as a stopping criteria. Can use minimum number of+-- observations in a cluster as a stopping criteria. Assumes the feature matrix+-- has column features and row observations. Items correspond to rows. Can+-- use FeatureMatrix or a pre-generated B matrix. See Shu et al., "Efficient+-- Spectral Neighborhood Blocking for Entity Resolution", 2011.+hierarchicalSpectralCluster :: EigenGroup+ -> NormalizeFlag+ -> Maybe NumEigen+ -> Maybe Int+ -> Maybe Q+ -> Items a+ -> Either FeatureMatrix B+ -> ClusteringTree a+hierarchicalSpectralCluster eigenGroup normFlag numEigenMay minSizeMay minModMay initItems initMat =+ go initItems initB+ where+ initB = either (getB normFlag) id $ initMat+ minMod = fromMaybe (Q 0) minModMay+ minSize = fromMaybe 1 minSizeMay+ numEigen = fromMaybe 1 numEigenMay+ go :: Items a -> B -> ClusteringTree a+ go !items !b =+ if (S.rows $ unB b) > 1+ && hasMultipleClusters clusters+ && ngMod > minMod+ && S.rows (unB left) >= minSize+ && S.rows (unB right) >= minSize+ then+ Node { rootLabel = vertex+ , subForest = [ go (subsetVector items leftIdxs) left+ , go (subsetVector items rightIdxs) right+ ]+ }++ else+ Node {rootLabel = vertex, subForest = []}+ where+ vertex = ClusteringVertex+ { _clusteringItems = items+ , _ngMod = ngMod+ }+ clusters :: S.SparseMatrixXd+ clusters = spectralClustering eigenGroup b+ spectralClustering :: EigenGroup -> B -> S.SparseMatrixXd+ spectralClustering SignGroup = spectralCluster+ spectralClustering KMeansGroup = spectralClusterK numEigen 2+ ngMod :: Q+ ngMod = getBModularity clusters b+ getSortedIdxs :: Double -> S.SparseMatrixXd -> [Int]+ getSortedIdxs val = VS.ifoldr' (\ !i !v !acc -> bool acc (i:acc) $ v == val) []+ . VS.fromList+ . concat+ . S.toDenseList+ leftIdxs :: [Int]+ leftIdxs = getSortedIdxs 0 clusters+ rightIdxs :: [Int]+ rightIdxs = getSortedIdxs 1 clusters+ left :: B+ left = B $ extractRows (unB b) leftIdxs+ right :: B+ right = B $ extractRows (unB b) rightIdxs+ extractRows :: S.SparseMatrixXd -> [Int] -> S.SparseMatrixXd+ extractRows mat [] = S.fromList 0 0 []+ extractRows mat xs = S.fromRows . fmap (flip S.getRow mat) $ xs
+ src/Math/Clustering/Hierarchical/Spectral/Load.hs view
@@ -0,0 +1,167 @@+{- Math.Clustering.Hierarchical.Spectral.Load+Gregory W. Schwartz++Collects the functions pertaining to loading a matrix.+-}++{-# LANGUAGE BangPatterns #-}+{-# LANGUAGE OverloadedStrings #-}++module Math.Clustering.Hierarchical.Spectral.Load+ ( readDenseAdjMatrix+ , readSparseAdjMatrix+ , readEigenSparseAdjMatrix+ ) where++-- Remote+import Control.Monad.Except (runExceptT, ExceptT (..))+import Control.Monad.Managed (with, liftIO, Managed (..))+import Data.Maybe (fromMaybe, catMaybes)+import System.IO (Handle (..))+import qualified Data.ByteString.Streaming.Char8 as BS+import qualified Data.Csv as CSV+import qualified Data.Eigen.SparseMatrix as E+import qualified Data.Map.Strict as Map+import qualified Data.Set as Set+import qualified Data.Sparse.Common as SH+import qualified Data.Text as T+import qualified Data.Vector as V+import qualified Numeric.LinearAlgebra as H+import qualified Streaming as S+import qualified Streaming.Cassava as S+import qualified Streaming.Prelude as S+import qualified Streaming.With.Lifted as SW++-- Local+import Math.Clustering.Hierarchical.Spectral.Types++-- | Generic error message.+errorMsg = error "Not correct format (requires row,column,value)"++-- | Parse a row of a label index file.+parseRow :: (T.Text, T.Text, Double) -> ((T.Text, T.Text), Double)+parseRow (i, j, v) = ((i, j), v)++-- | Ignore the disconnected vertices, not used (rather use very small weight).+ignoreDisconnected :: V.Vector T.Text+ -> H.Matrix Double+ -> (V.Vector T.Text, H.Matrix Double)+ignoreDisconnected items mat = (newItems, newMat)+ where+ newItems = V.fromList $ fmap ((V.!) items) valid+ newMat = mat H.?? (H.Pos $ H.idxs valid, H.Pos $ H.idxs valid)+ valid = catMaybes+ . zipWith (\x xs -> if sum xs > 0 then Just x else Nothing) [0..]+ . H.toLists+ $ mat++-- | Ensure symmetry.+symmetric :: [((Int, Int), Double)] -> [((Int, Int), Double)]+symmetric = concatMap (\((!i, !j), v) -> [((i, j), v), ((j, i), v)])++-- | Ensure zeros on diagonal.+zeroDiag :: [((Int, Int), Double)] -> [((Int, Int), Double)]+zeroDiag = filter (\((!i, !j), _) -> i /= j)++-- | Get the translated matrix indices.+getNewIndices+ -- :: (Eq a, Ord a)+ -- => [((a, a), Double)] -> [((Int, Int), Double)]+ :: [((T.Text, T.Text), Double)] -> [((Int, Int), Double)]+getNewIndices xs =+ fmap+ (\((!i,!j),!v) ->+ ( ( Map.findWithDefault eMsg i idxMap+ , Map.findWithDefault eMsg j idxMap+ )+ , v+ )+ )+ xs+ where+ eMsg = error "Index not found during index conversion."+ indices = getAllIndices xs+ idxMap = Map.fromList $ zip indices [0 ..]++-- | Get the list of all indices.+getAllIndices :: (Eq a, Ord a) => [((a, a), Double)] -> [a]+getAllIndices xs = Set.toAscList . Set.union (getSet fst) $ getSet snd+ where+ getSet f = Set.fromList . fmap (f . fst) $ xs++-- | Get a dense adjacency matrix from a handle.+readDenseAdjMatrix :: CSV.DecodeOptions+ -> Handle+ -> IO (V.Vector T.Text, H.Matrix Double)+readDenseAdjMatrix decodeOpt handle = flip with return $ do+ let getAssocList = S.toList_ . S.map parseRow++ assocList <-+ fmap (either (error . show) id)+ . runExceptT+ . getAssocList+ . S.decodeWith decodeOpt S.NoHeader+ $ (BS.hGetContents handle :: BS.ByteString (ExceptT S.CsvParseException Managed) ())++ let items = V.fromList $ getAllIndices assocList+ mat = H.assoc (V.length items, V.length items) 0+ . Set.toList+ . Set.fromList -- Ensure no duplicates.+ . symmetric -- Ensure symmetry.+ . zeroDiag -- Ensure zeros on diagonal.+ . getNewIndices -- Only look at present rows by converting indices.+ $ assocList++ return (items, mat)++-- | Get a sparse adjacency matrix from a handle.+readSparseAdjMatrix :: CSV.DecodeOptions+ -> Handle+ -> IO (V.Vector T.Text, SH.SpMatrix Double)+readSparseAdjMatrix decodeOpt handle = flip with return $ do+ let getAssocList = S.toList_ . S.map parseRow++ assocList <-+ fmap (either (error . show) id)+ . runExceptT+ . getAssocList+ . S.decodeWith decodeOpt S.NoHeader+ $ (BS.hGetContents handle :: BS.ByteString (ExceptT S.CsvParseException Managed) ())++ let items = V.fromList $ getAllIndices assocList+ mat = SH.fromListSM (V.length items, V.length items)+ . Set.toList+ . Set.fromList -- Ensure no duplicates.+ . fmap (\((i, j), v) -> (i, j, v))+ . symmetric -- Ensure symmetry.+ . zeroDiag -- Ensure zeros on diagonal.+ . getNewIndices -- Only look at present rows by converting indices.+ $ assocList++ return (items, mat)++-- | Get a sparse adjacency matrix from a handle.+readEigenSparseAdjMatrix :: CSV.DecodeOptions+ -> Handle+ -> IO (V.Vector T.Text, E.SparseMatrixXd)+readEigenSparseAdjMatrix decodeOpt handle = flip with return $ do+ let getAssocList = S.toList_ . S.map parseRow++ assocList <-+ fmap (either (error . show) id)+ . runExceptT+ . getAssocList+ . S.decodeWith decodeOpt S.NoHeader+ $ (BS.hGetContents handle :: BS.ByteString (ExceptT S.CsvParseException Managed) ())++ let items = V.fromList $ getAllIndices assocList+ mat = E.fromList (V.length items) (V.length items)+ . Set.toList+ . Set.fromList -- Ensure no duplicates.+ . fmap (\((i, j), v) -> (i, j, v))+ . symmetric -- Ensure symmetry.+ . zeroDiag -- Ensure zeros on diagonal.+ . getNewIndices -- Only look at present rows by converting indices.+ $ assocList++ return (items, mat)
+ src/Math/Clustering/Hierarchical/Spectral/Sparse.hs view
@@ -0,0 +1,177 @@+{- Math.Clustering.Hierarchical.Spectral.Sparse+Gregory W. Schwartz++Collects the functions pertaining to hierarchical spectral clustering for sparse+data.+-}++{-# LANGUAGE BangPatterns #-}++module Math.Clustering.Hierarchical.Spectral.Sparse+ ( hierarchicalSpectralCluster+ , hierarchicalSpectralClusterAdj+ , FeatureMatrix (..)+ , B (..)+ , Items (..)+ , ShowB (..)+ ) where++-- Remote+import Data.Bool (bool)+import Data.Clustering.Hierarchical (Dendrogram (..))+import Data.Maybe (fromMaybe)+import Data.Tree (Tree (..))+import Math.Clustering.Spectral.Sparse (B (..), AdjacencyMatrix (..), getB, spectralCluster, spectralClusterK, spectralClusterNorm, spectralClusterKNorm)+import Math.Modularity.Sparse (getBModularity, getModularity)+import Math.Modularity.Types (Q (..))+import qualified Data.Foldable as F+import qualified Data.Set as Set+import qualified Data.Sparse.Common as S+import qualified Data.Vector as V+import qualified Data.Vector.Storable as VS+import qualified Numeric.LinearAlgebra.Sparse as S++-- Local+import Math.Clustering.Hierarchical.Spectral.Types+import Math.Clustering.Hierarchical.Spectral.Utility++type FeatureMatrix = S.SpMatrix Double+type Items a = V.Vector a+type ShowB = ((Int, Int), [(Int, Int, Double)])+type NormalizeFlag = Bool++-- | Check if there is more than one cluster.+hasMultipleClusters :: S.SpVector Double -> Bool+hasMultipleClusters = (> 1) . Set.size . Set.fromList . S.toDenseListSV++-- | Generates a tree through divisive hierarchical clustering using+-- Newman-Girvan modularity as a stopping criteria. Can use minimum number of+-- observations in a cluster as a stopping criteria. Assumes the feature matrix+-- has column features and row observations. Items correspond to rows. Can+-- use FeatureMatrix or a pre-generated B matrix. See Shu et al., "Efficient+-- Spectral Neighborhood Blocking for Entity Resolution", 2011.+hierarchicalSpectralCluster :: EigenGroup+ -> NormalizeFlag+ -> Maybe NumEigen+ -> Maybe Int+ -> Maybe Q+ -> Items a+ -> Either FeatureMatrix B+ -> ClusteringTree a+hierarchicalSpectralCluster eigenGroup normFlag numEigenMay minSizeMay minModMay initItems initMat =+ go initItems initB+ where+ initB = either (getB normFlag) id $ initMat+ minMod = fromMaybe (Q 0) minModMay+ minSize = fromMaybe 1 minSizeMay+ numEigen = fromMaybe 1 numEigenMay+ go :: Items a -> B -> ClusteringTree a+ go !items !b =+ if (S.nrows $ unB b) > 1+ && hasMultipleClusters clusters+ && ngMod > minMod+ && S.nrows (unB left) >= minSize+ && S.nrows (unB right) >= minSize+ then+ Node { rootLabel = vertex+ , subForest = [ go (subsetVector items leftIdxs) left+ , go (subsetVector items rightIdxs) right+ ]+ }++ else+ Node {rootLabel = vertex, subForest = []}+ where+ vertex = ClusteringVertex+ { _clusteringItems = items+ , _ngMod = ngMod+ }+ clusters :: S.SpVector Double+ clusters = spectralClustering eigenGroup b+ spectralClustering :: EigenGroup -> B -> S.SpVector Double+ spectralClustering SignGroup = spectralCluster+ spectralClustering KMeansGroup = spectralClusterK numEigen 2+ ngMod :: Q+ ngMod = getBModularity clusters $ b+ getSortedIdxs :: Double -> S.SpVector Double -> [Int]+ getSortedIdxs val = VS.ifoldr' (\ !i !v !acc -> bool acc (i:acc) $ v == val) []+ . VS.fromList+ . S.toDenseListSV+ leftIdxs :: [Int]+ leftIdxs = getSortedIdxs 0 $ clusters+ rightIdxs :: [Int]+ rightIdxs = getSortedIdxs 1 $ clusters+ left :: B+ left = B $ extractRows (unB b) leftIdxs+ right :: B+ right = B $ extractRows (unB b) rightIdxs+ extractRows :: S.SpMatrix Double -> [Int] -> S.SpMatrix Double+ extractRows mat [] = S.zeroSM 0 0+ extractRows mat xs =+ S.transposeSM . S.fromColsL . fmap (S.extractRow mat) $ xs++-- | Generates a tree through divisive hierarchical clustering using+-- Newman-Girvan modularity as a stopping criteria. Can use minimum number of+-- observations in a cluster as a stopping criteria. Uses an adjacency matrix.+-- Items correspond to rows.+hierarchicalSpectralClusterAdj :: EigenGroup+ -> Maybe NumEigen+ -> Maybe Int+ -> Maybe Q+ -> Items a+ -> AdjacencyMatrix+ -> ClusteringTree a+hierarchicalSpectralClusterAdj eigenGroup numEigenMay minSizeMay minModMay initItems initMat =+ go initItems initMat+ where+ minMod = fromMaybe (Q 0) minModMay+ minSize = fromMaybe 1 minSizeMay+ numEigen = fromMaybe 1 numEigenMay+ go :: Items a -> AdjacencyMatrix -> ClusteringTree a+ go !items !mat =+ if S.nrows mat > 1+ && hasMultipleClusters clusters+ && ngMod > minMod+ && S.nrows left >= minSize+ && S.nrows right >= minSize+ then+ Node { rootLabel = vertex+ , subForest = [ go (subsetVector items leftIdxs) left+ , go (subsetVector items rightIdxs) right+ ]+ }++ else+ Node {rootLabel = vertex, subForest = []}+ where+ vertex = ClusteringVertex+ { _clusteringItems = items+ , _ngMod = ngMod+ }+ clusters :: S.SpVector Double+ clusters = spectralClustering eigenGroup mat+ spectralClustering :: EigenGroup -> AdjacencyMatrix -> S.SpVector Double+ spectralClustering SignGroup = spectralClusterNorm+ spectralClustering KMeansGroup = spectralClusterKNorm numEigen 2+ ngMod :: Q+ ngMod = getModularity clusters mat+ getSortedIdxs :: Double -> S.SpVector Double -> [Int]+ getSortedIdxs val = VS.ifoldr' (\ !i !v !acc -> bool acc (i:acc) $ v == val) []+ . VS.fromList+ . S.toDenseListSV+ leftIdxs :: [Int]+ leftIdxs = getSortedIdxs 0 clusters+ rightIdxs :: [Int]+ rightIdxs = getSortedIdxs 1 clusters+ left :: AdjacencyMatrix+ left = getSubMat mat leftIdxs+ right :: AdjacencyMatrix+ right = getSubMat mat rightIdxs+ getSubMat :: S.SpMatrix Double -> [Int] -> S.SpMatrix Double+ getSubMat mat [] = S.zeroSM 0 0+ getSubMat mat is = S.fromColsL+ . (\x -> fmap (S.extractCol x) is)+ . S.transposeSM+ . S.fromColsL+ . fmap (S.extractRow mat)+ $ is
+ src/Math/Clustering/Hierarchical/Spectral/Test.hs view
@@ -0,0 +1,188 @@+{- Math.Clustering.Hierarchical.Spectral.Test+Gregory W. Schwartz++Collects the functions pertaining to testing hierarchical spectral clustering.+-}++{-# LANGUAGE BangPatterns #-}++module Math.Clustering.Hierarchical.Spectral.Test where++-- Remote+import Data.List (tails)+import Data.Maybe (fromMaybe)+import Data.Monoid ((<>))+import Math.Clustering.Spectral.Sparse (getB, B (..))+import qualified Data.Map.Strict as Map+import qualified Data.Set as Set+import qualified Data.Sparse.Common as S+import qualified Data.Eigen.SparseMatrix as E+import qualified Data.Vector as V+import qualified Math.Clustering.Spectral.Eigen.FeatureMatrix as EF+import qualified Numeric.LinearAlgebra as H++-- Local+import Math.Clustering.Hierarchical.Spectral.Types+import Math.Clustering.Hierarchical.Spectral.Sparse+import qualified Math.Clustering.Hierarchical.Spectral.Dense as Dense+import qualified Math.Clustering.Hierarchical.Spectral.Eigen.FeatureMatrix as EF+import qualified Math.Clustering.Hierarchical.Spectral.Eigen.AdjacencyMatrix as EA++newtype QGram = QGram { unQGram :: String } deriving (Eq, Ord, Read, Show)+newtype QGramMap = QGramMap+ { unQGramMap :: Map.Map QGram Int+ } deriving (Eq,Ord,Read,Show)++exampleData :: [String]+exampleData = [ "600 MOUNTAIN AVENUE"+ , "700 MOUNTAIN AVE"+ , "600-700 MOUNTAIN AVE"+ , "100 DIAMOND HILL RD"+ , "100 DIAMOND HILL ROAD"+ , "123 SPRINGFIELD AVENUE"+ , "123 SPRINFGIELD AVE"+ ]++exampleItems :: V.Vector String+exampleItems = V.fromList exampleData++-- | Add beginning and ending symbols.+addBorders :: String -> String+addBorders x = "##" <> x <> "$$"++-- | Generate qgrams for a string.+getQGrams :: Int -> String -> [QGram]+getQGrams n =+ fmap QGram . filter ((== n) . length) . fmap (take n) . tails . addBorders++-- | Get mapping of qgrams to indices.+getQGramMap :: [QGram] -> QGramMap+getQGramMap = QGramMap . Map.fromList . flip zip [0,1..]++-- | Convert a record to a vector.+recordToRow :: Int -> QGramMap -> String -> S.SpVector Double+recordToRow n (QGramMap qgramMap) = S.fromListSV (Map.size qgramMap)+ . Map.toAscList+ . Map.fromListWith (+)+ . flip zip [1,1..]+ . fromMaybe (error "Invalid qgram.")+ . mapM (flip Map.lookup qgramMap)+ . getQGrams n++-- | Generate the matrix of qgrams from a list of records and qgram length.+exampleMatrix :: Int -> [String] -> S.SpMatrix Double+exampleMatrix n records =+ S.transposeSM . S.fromColsL . fmap (recordToRow n qgramMap) $ records+ where+ qgramMap = getQGramMap+ . Set.toList+ . Set.fromList+ . concatMap (getQGrams n)+ $ records++clusterExample = hierarchicalSpectralCluster+ SignGroup+ True+ Nothing+ Nothing+ Nothing+ exampleItems+ (Left $ exampleMatrix 3 exampleData)++clusterKExample = hierarchicalSpectralCluster+ KMeansGroup+ True+ (Just 2)+ Nothing+ Nothing+ exampleItems+ (Left $ exampleMatrix 3 exampleData)++clusterAdjExample = hierarchicalSpectralClusterAdj+ SignGroup+ Nothing+ Nothing+ Nothing+ exampleItems+ adjacencyExample++clusterKAdjExample = hierarchicalSpectralClusterAdj+ KMeansGroup+ (Just 2)+ Nothing+ Nothing+ exampleItems+ adjacencyExample++adjacencyExample :: S.SpMatrix Double+adjacencyExample = S.filterSM (\i j _ -> i /= j) $ (unB b) S.##^ (unB b)+ where+ b = getB True $ exampleMatrix 3 exampleData++denseAdjacencyExample :: H.Matrix Double+denseAdjacencyExample = H.assoc (S.dimSM adjacencyExample) 0+ . fmap (\(!x, !y, !z) -> if x == y then ((x, y), 0) else ((x, y), z))+ . S.toListSM+ $ adjacencyExample++denseClusterExample = Dense.hierarchicalSpectralCluster+ SignGroup+ Nothing+ Nothing+ Nothing+ exampleItems+ denseAdjacencyExample++denseClusterKExample = Dense.hierarchicalSpectralCluster+ KMeansGroup+ (Just 2)+ Nothing+ Nothing+ exampleItems+ denseAdjacencyExample++-- | Generate the matrix of qgrams from a list of records and qgram length.+exampleEigenMatrix :: Int -> [String] -> E.SparseMatrixXd+exampleEigenMatrix n records = E.fromList (S.nrows mat) (S.ncols mat) . S.toListSM $ mat+ where+ mat = exampleMatrix n records++adjacencyEigenExample :: E.SparseMatrixXd+adjacencyEigenExample = E._imap (\i j v -> if i == j then 0 else v)+ $ (EF.unB b) * E.transpose (EF.unB b)+ where+ b = EF.getB True $ exampleEigenMatrix 3 exampleData++clusterEigenExample = EF.hierarchicalSpectralCluster+ SignGroup+ True+ Nothing+ Nothing+ Nothing+ exampleItems+ (Left $ exampleEigenMatrix 3 exampleData)++clusterKEigenExample = EF.hierarchicalSpectralCluster+ KMeansGroup+ True+ (Just 2)+ Nothing+ Nothing+ exampleItems+ (Left $ exampleEigenMatrix 3 exampleData)++clusterAdjEigenExample = EA.hierarchicalSpectralCluster+ SignGroup+ Nothing+ Nothing+ Nothing+ exampleItems+ adjacencyEigenExample++clusterKAdjEigenExample = EA.hierarchicalSpectralCluster+ KMeansGroup+ (Just 2)+ Nothing+ Nothing+ exampleItems+ adjacencyEigenExample
+ src/Math/Clustering/Hierarchical/Spectral/Types.hs view
@@ -0,0 +1,90 @@+{- Math.Clustering.Hierarchical.Types+Gregory W. Schwartz++Collects the types used in hierarchical clustering.+-}++{-# LANGUAGE BangPatterns #-}+{-# LANGUAGE DeriveGeneric #-}+{-# LANGUAGE StandaloneDeriving #-}++module Math.Clustering.Hierarchical.Spectral.Types+ ( ClusteringTree (..)+ , ClusteringVertex (..)+ , EigenGroup (..)+ , clusteringTreeToDendrogram+ , clusteringTreeToDendrogramCumulative+ , getClusterItemsDend+ , getClusterItemsTree+ , Q (..)+ , NumEigen (..)+ ) where++-- Remote+import Data.Clustering.Hierarchical (Dendrogram (..))+import Data.Monoid ((<>))+import Data.Tree (Tree (..))+import GHC.Generics (Generic)+import Math.Modularity.Types (Q (..))+import Math.TreeFun.Tree (leaves)+import qualified Data.Aeson as A+import qualified Data.Foldable as F+import qualified Data.Vector as V++-- Local++type Items a = V.Vector a+type ClusteringTree a = Tree (ClusteringVertex a)+type NumEigen = Int++data EigenGroup = SignGroup | KMeansGroup deriving (Read, Show, Generic)++data ClusteringVertex a = ClusteringVertex+ { _clusteringItems :: !(Items a)+ , _ngMod :: !Q+ } deriving (Eq, Ord, Read, Show, Generic)++-- | Convert a ClusteringTree to a Dendrogram. Modularity is the distance.+clusteringTreeToDendrogram :: ClusteringTree a -> Dendrogram (Items a)+clusteringTreeToDendrogram = go+ where+ go (Node { rootLabel = !n, subForest = []}) = Leaf $ _clusteringItems n+ go (Node { rootLabel = !n, subForest = [x, y]}) =+ Branch (unQ . _ngMod $ n) (go x) (go y)+ go (Node { subForest = xs}) =+ error $ "Clustering tree has "+ <> (show $ length xs)+ <> " children. Requires two or none."++-- | Convert a ClusteringTree to a Dendrogram. Modularity is the distance, such+-- that the distance is the modularity plus the maximum distance of each branch.+clusteringTreeToDendrogramCumulative :: ClusteringTree a -> Dendrogram (Items a)+clusteringTreeToDendrogramCumulative = fst . go+ where+ go (Node { rootLabel = !n, subForest = []}) =+ (Leaf (_clusteringItems n), 0)+ go (Node { rootLabel = !n, subForest = [x, y]}) =+ (Branch newD l r, newD)+ where+ newD = (unQ . _ngMod $ n) + max lDist rDist+ (!l, !lDist) = go x+ (!r, !rDist) = go y+ go (Node { subForest = xs}) =+ error $ "Clustering tree has "+ <> (show $ length xs)+ <> " children. Requires two or none."++-- | Gather clusters (leaves) from the dendrogram.+getClusterItemsDend :: Foldable t => t (Items a) -> [Items a]+getClusterItemsDend = F.toList++-- | Gather clusters (leaves) from the tree.+getClusterItemsTree :: ClusteringTree a -> [Items a]+getClusterItemsTree = fmap _clusteringItems . leaves++deriving instance (Read a) => Read (Dendrogram a)+deriving instance Generic (Dendrogram a)++instance (A.ToJSON a) => A.ToJSON (Dendrogram a) where+ toEncoding = A.genericToEncoding A.defaultOptions+instance (A.FromJSON a) => A.FromJSON (Dendrogram a)
+ src/Math/Clustering/Hierarchical/Spectral/Utility.hs view
@@ -0,0 +1,28 @@+{- Math.Clustering.Hierarchical.Spectral.Utility+Gregory W. Schwartz++Collects utility functions for the clustering section of the program.+-}++{-# LANGUAGE BangPatterns #-}++module Math.Clustering.Hierarchical.Spectral.Utility+ ( subsetVector+ ) where++-- Remote+import Data.Maybe (fromMaybe)+import qualified Data.Foldable as F+import qualified Data.Vector as V++-- Local+++subsetVector :: V.Vector a -> [Int] -> V.Vector a+subsetVector xs =+ V.fromList+ . F.foldr' (\ !i !acc+ -> ( fromMaybe (error "Out of bounds in subsetVector.")+ $ xs V.!? i+ ) : acc+ ) []
+ src/Math/Graph/Components.hs view
@@ -0,0 +1,37 @@+{- Math.Graph.Components+Gregory W. Schwartz++Find connected components of matrices.+-}++{-# LANGUAGE BangPatterns #-}++module Math.Graph.Components+ ( getComponentMats+ , getComponentMatsItems+ ) where++-- Remote+import Data.List (sort)+import qualified Data.Graph.Inductive as G+import qualified Data.Vector as V++-- Local+import Math.Graph.Types+import Math.Clustering.Hierarchical.Spectral.Utility++-- | Get the components of a graphable object, an adjacency matrix.+getComponentMats :: (Graphable a) => a -> [a]+getComponentMats mat = fmap (fromGraph . flip G.subgraph gr) . G.components $ gr+ where+ gr = toGraph mat++-- | Get the components of a graphable object, an adjacency matrix with the+-- associated items.+getComponentMatsItems :: (Graphable b) => V.Vector a -> b -> [(V.Vector a, b)]+getComponentMatsItems items mat =+ fmap (\ !xs -> (subsetVector items . sort $ xs, fromGraph . G.subgraph xs $ gr))+ . G.components+ $ gr+ where+ gr = toGraph mat
+ src/Math/Graph/Types.hs view
@@ -0,0 +1,71 @@+{- Math.Graph.Types+Gregory W. Schwartz++Types used for graph sections of the program.+-}++{-# LANGUAGE BangPatterns #-}+{-# LANGUAGE TypeSynonymInstances #-}+{-# LANGUAGE FlexibleInstances #-}++module Math.Graph.Types where++-- Remote+import Data.List (sort)+import qualified Data.Eigen.SparseMatrix as E+import qualified Data.Map.Strict as Map+import qualified Data.Graph.Inductive as G+import qualified Data.Sparse.Common as S+import qualified Data.Vector.Unboxed as V+import qualified Math.Clustering.Spectral.Dense as D+import qualified Numeric.LinearAlgebra as H+import qualified Numeric.LinearAlgebra.Sparse as S++-- Local+import qualified Math.Clustering.Spectral.Dense as D+import qualified Math.Clustering.Spectral.Eigen.AdjacencyMatrix as E+import qualified Math.Clustering.Spectral.Sparse as S++-- | Get a re-mapped edge list with nodes ordered from 0 to the number of nodes+-- in the graph.+orderedEdges :: G.Gr Int a -> [(Int, Int, a)]+orderedEdges gr =+ fmap (\(!i, !j, !v) -> (getUpdate i, getUpdate j, v)) . G.labEdges $ gr+ where+ nodeMap = Map.fromList . flip zip [0..] . sort . G.nodes $ gr+ getUpdate = flip ( Map.findWithDefault+ (error "Unexpected missing node in orderedEdges.")+ )+ nodeMap++-- | Graphable class for converting matrices to and from a graph.+class Graphable a where+ toGraph :: a -> G.Gr Int Double+ fromGraph :: G.Gr Int Double -> a++instance Graphable D.AdjacencyMatrix where+ toGraph mat = G.mkGraph (zip [0 .. H.rows mat - 1] [0 .. H.rows mat - 1])+ . filter (\(_, _, x) -> x /= 0)+ . concatMap (\(!i, !xs) -> fmap (\(!j, !v) -> (i, j, v)) xs)+ . zip [0..]+ . fmap (zip [0..] . H.toList)+ . H.toRows+ $ mat+ fromGraph gr = H.assoc (G.noNodes gr, G.noNodes gr) 0+ . fmap (\(!i, !j, !v) -> ((i, j), v))+ . orderedEdges+ $ gr++instance Graphable S.AdjacencyMatrix where+ toGraph mat = G.mkGraph (zip [0 .. S.nrows mat - 1] [0 .. S.nrows mat - 1])+ . filter (\(_, _, x) -> x /= 0)+ . S.toListSM+ $ mat+ fromGraph gr = S.fromListSM (G.noNodes gr, G.noNodes gr) . orderedEdges $ gr++instance Graphable E.AdjacencyMatrix where+ toGraph mat = G.mkGraph (zip [0 .. E.rows mat - 1] [0 .. E.rows mat - 1])+ . filter (\(_, _, x) -> x /= 0)+ . E.toList+ $ mat+ fromGraph gr = E.fromList (G.noNodes gr) (G.noNodes gr) . orderedEdges $ gr