clustering: creates the package and implements DBSCAN

Verified against scikit-learn's implementation (gen_test.py)

base/conversion.go

@@ -0,0 +1,69 @@
+package base
+
+import (
+	"fmt"
+	"github.com/gonum/matrix/mat64"
+)
+
+func checkAllAttributesAreFloat(attrs []Attribute) error {
+	// Check that all the attributes are float
+	for _, a := range attrs {
+		if _, ok := a.(*FloatAttribute); !ok {
+			fmt.Errorf("All []Attributes to this method must be FloatAttributes")
+		}
+	}
+	return nil
+}
+
+// ConvertRowToMat64 takes a list of Attributes, a FixedDataGrid
+// and a row number, and returns the float values of that row
+// in a mat64.Dense format.
+func ConvertRowToMat64(attrs []Attribute, f FixedDataGrid, r int) (*mat64.Dense, error) {
+
+	err := checkAllAttributesAreFloat(attrs)
+	if err != nil {
+		return nil, err
+	}
+
+	// Allocate the return value
+	ret := mat64.NewDense(1, len(attrs), nil)
+
+	// Resolve all the attributes
+	attrSpecs := ResolveAttributes(f, attrs)
+
+	// Get the results
+	for i, a := range attrSpecs {
+		ret.Set(0, i, UnpackBytesToFloat(f.Get(a, r)))
+	}
+
+	// Return the result
+	return ret, nil
+}
+
+// ConvertAllRowsToMat64 takes a list of Attributes and returns a vector
+// of all rows in a mat64.Dense format.
+func ConvertAllRowsToMat64(attrs []Attribute, f FixedDataGrid) ([]*mat64.Dense, error) {
+
+	// Check for floats
+	err := checkAllAttributesAreFloat(attrs)
+	if err != nil {
+		return nil, err
+	}
+
+	// Return value
+	_, rows := f.Size()
+	ret := make([]*mat64.Dense, rows)
+
+	// Resolve all attributes
+	attrSpecs := ResolveAttributes(f, attrs)
+
+	// Set the values in each return value
+	for i := 0; i < rows; i++ {
+		cur := mat64.NewDense(1, len(attrs), nil)
+		for j, a := range attrSpecs {
+			cur.Set(0, j, UnpackBytesToFloat(f.Get(a, i)))
+		}
+		ret[i] = cur
+	}
+	return ret, nil
+}

clustering/cluster_test.go

@@ -0,0 +1,82 @@
+package clustering
+
+import (
+	. "github.com/smartystreets/goconvey/convey"
+	"testing"
+)
+
+func TestClusterEquality(t *testing.T) {
+
+	Convey("Should be able to determine if two cluster maps represent the same thing...", t, func() {
+
+		Convey("When everything's exactly the same...", func() {
+
+			m1 := ClusterMap(make(map[int][]int))
+			m1[0] = []int{1, 2, 3}
+			m1[1] = []int{4, 5}
+
+			m2 := ClusterMap(make(map[int][]int))
+			m2[0] = []int{1, 2, 3}
+			m2[1] = []int{4, 5}
+
+			ret, err := m1.Equals(m2)
+			So(err, ShouldBeNil)
+			So(ret, ShouldBeTrue)
+
+		})
+
+		Convey("With re-labelled clusters...", func() {
+			m1 := ClusterMap(make(map[int][]int))
+			m1[1] = []int{1, 2, 3}
+			m1[0] = []int{4, 5}
+
+			m2 := ClusterMap(make(map[int][]int))
+			m2[1] = []int{1, 2, 3}
+			m2[0] = []int{4, 5}
+
+			ret, err := m1.Equals(m2)
+			So(err, ShouldBeNil)
+			So(ret, ShouldBeTrue)
+		})
+
+		Convey("With missing clusters...", func() {
+			m1 := ClusterMap(make(map[int][]int))
+			m1[1] = []int{1, 2, 3}
+
+			m2 := ClusterMap(make(map[int][]int))
+			m2[1] = []int{1, 2, 3}
+			m2[0] = []int{4, 5}
+
+			_, err := m1.Equals(m2)
+			So(err, ShouldNotBeNil)
+		})
+
+		Convey("With missing points...", func() {
+			m1 := ClusterMap(make(map[int][]int))
+			m1[1] = []int{1, 3}
+			m1[0] = []int{4, 5}
+
+			m2 := ClusterMap(make(map[int][]int))
+			m2[1] = []int{1, 2, 3}
+			m2[0] = []int{4, 5}
+
+			_, err := m1.Equals(m2)
+			So(err, ShouldNotBeNil)
+		})
+
+		Convey("With invalid maps...", func() {
+			m1 := ClusterMap(make(map[int][]int))
+			m1[0] = []int{1, 2, 3}
+			m1[1] = []int{4, 4, 5}
+
+			m2 := ClusterMap(make(map[int][]int))
+			m2[0] = []int{1, 2, 3}
+			m2[1] = []int{4, 5}
+
+			_, err := m1.Equals(m2)
+			So(err, ShouldNotBeNil)
+		})
+
+	})
+
+}

clustering/clustering.go

@@ -0,0 +1,107 @@
+/* This package implements clustering algorithms */
+package clustering
+
+import (
+	"fmt"
+	"github.com/sjwhitworth/golearn/base"
+	"github.com/sjwhitworth/golearn/metrics/pairwise"
+)
+
+// ClusterParameters takes a number of variables common to all clustering
+// algorithms.
+
+type ClusterParameters struct {
+	// Attributes represents the set of Attributes which
+	// can be used for clustering
+	Attributes []base.Attribute
+
+	// Metric is used to compute pairwise distance
+	Metric pairwise.PairwiseDistanceFunc
+}
+
+// ClusterMap contains the cluster identifier as a key, followed by a vector of point
+// indices that cluster contains.
+type ClusterMap map[int][]int
+
+// Invert returns an alternative form of cluster map where the key represents the point
+// index and the value represents the cluster index it's assigned to
+func (ref ClusterMap) Invert() (map[int]int, error) {
+	ret := make(map[int]int)
+	for c := range ref {
+		for _, p := range ref[c] {
+			if _, ok := ret[p]; ok {
+				return nil, fmt.Errorf("Not a valid cluster map (points appear in more than one cluster)")
+			} else {
+				ret[p] = c
+			}
+		}
+	}
+	return ret, nil
+}
+
+// Equals checks whether a bijection exists between two ClusterMaps (i.e. the clusters in one can
+// be re-labelled to become the clusters of another)
+func (ref ClusterMap) Equals(other ClusterMap) (bool, error) {
+	if len(ref) != len(other) {
+		return false, fmt.Errorf("ref and other do not contain the same number of clusters (%d and %d)", len(ref), len(other))
+	}
+
+	refInv, err := ref.Invert()
+	if err != nil {
+		return false, fmt.Errorf("ref: %s", err)
+	}
+
+	otherInv, err := other.Invert()
+	if err != nil {
+		return false, fmt.Errorf("other: %s", err)
+	}
+
+	clusterIdMap := make(map[int]int)
+
+	// Range through each point index
+	for p := range refInv {
+		c1 := refInv[p]                // Get the cluster index of this point
+		if c2, ok := otherInv[p]; ok { // Check if the other map has this point
+			// if so, c2 is the point's cluster in the other map
+			if c3, ok := clusterIdMap[c2]; ok { // what's our correspondance with c2?
+				if c1 != c3 {
+					// if c1 is not what we've currently got, error out
+					return false, fmt.Errorf("ref point %d (cluster %d) is assigned to a different cluster (%d) in ref %s", p, c2, c1, clusterIdMap)
+				}
+			} else {
+				clusterIdMap[c2] = c1
+			}
+		} else {
+			return false, fmt.Errorf("failed to find reference point %d in src", p)
+		}
+	}
+
+	// Check that after transformation, key contains the same points
+	arraysEqual := func(a1, a2 []int) bool {
+
+		cnt := make(map[int]bool)
+		for _, a := range a1 {
+			cnt[a] = true
+		}
+
+		for _, a := range a2 {
+			if _, ok := cnt[a]; !ok {
+				return false
+			}
+		}
+
+		return true
+
+	}
+	newMap := ClusterMap(make(map[int][]int))
+	for cOld := range other {
+		cNew := clusterIdMap[cOld]
+		if !arraysEqual(ref[cNew], other[cOld]) {
+			return false, fmt.Errorf("Re-labelled cluster %d => %d doesn't contain the same points (%s, %s)", cOld, cNew, ref[cNew], other[cOld])
+		}
+		newMap[cNew] = other[cOld]
+	}
+
+	return true, nil
+
+}

clustering/dbscan.csv

@@ -0,0 +1,750 @@
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+0.368550995255,0.768785338289
+0.674247371136,-0.335924019381
+-1.79245127675,-1.4045223247
+-1.87656067,-0.476116371583
+0.493448265324,-0.820792271427
+-1.60183922321,-0.868539405266
+0.505927093362,1.21392675643
+-1.64046095603,-0.469972586457
+-0.0571387622957,-0.909261054305
+-1.1693940706,0.0395969246032
+0.263229511513,-0.926499490699

clustering/dbscan.go

@@ -0,0 +1,188 @@
+package clustering
+
+import (
+	"github.com/gonum/matrix/mat64"
+	"github.com/sjwhitworth/golearn/base"
+	"github.com/sjwhitworth/golearn/metrics/pairwise"
+	"math/big"
+)
+
+// DBSCANParameters describes the parameters of the density-based
+// clustering algorithm DBSCAN
+type DBSCANParameters struct {
+	ClusterParameters
+
+	// Eps represents the "reachability", or the maximum
+	// distance any point can be before being considered for
+	// inclusion.
+	Eps float64
+
+	// MinCount represents how many points need to be
+	// in a cluster before it is considered one.
+	MinCount int
+}
+
+func regionQuery(p int, ret *big.Int, dist *mat64.Dense, eps float64) *big.Int {
+	rows, _ := dist.Dims()
+	// Return any points within the Eps neighbourhood
+	for i := 0; i < rows; i++ {
+		if dist.At(p, i) <= eps {
+			ret = ret.SetBit(ret, i, 1) // Mark as neighbour
+		}
+	}
+	return ret
+}
+
+func computePairwiseDistances(inst base.FixedDataGrid, attrs []base.Attribute, metric pairwise.PairwiseDistanceFunc) (*mat64.Dense, error) {
+	// Compute pair-wise distances
+	// First convert everything to floats
+	mats, err := base.ConvertAllRowsToMat64(attrs, inst)
+	if err != nil {
+		return nil, err
+	}
+
+	// Next, do an n^2 computation of all pairwise distances
+	_, rows := inst.Size()
+	dist := mat64.NewDense(rows, rows, nil)
+	for i := 0; i < rows; i++ {
+		for j := i + 1; j < rows; j++ {
+			d := metric.Distance(mats[i], mats[j])
+			dist.Set(i, j, d)
+			dist.Set(j, i, d)
+		}
+	}
+	return dist, nil
+}
+
+// DBSCAN clusters inst using the parameters allowed in and produces a ClusterId->[RowId] map
+func DBSCAN(inst base.FixedDataGrid, params DBSCANParameters) (ClusterMap, error) {
+
+	// Compute the distances between each possible point
+	dist, err := computePairwiseDistances(inst, params.Attributes, params.Metric)
+	if err != nil {
+		return nil, err
+	}
+
+	_, rows := inst.Size()
+
+	clusterMap := make(map[int][]int)
+	visited := big.NewInt(0)
+	clustered := big.NewInt(0)
+	// expandCluster adds P to a cluster C, visiting any neighbours
+	expandCluster := func(p int, neighbours *big.Int, c int) {
+		if clustered.Bit(p) == 1 {
+			panic("Shouldn't happen!")
+		}
+		// Add this point to cluster C
+		if _, ok := clusterMap[c]; !ok {
+			clusterMap[c] = make([]int, 0)
+		}
+		clusterMap[c] = append(clusterMap[c], p)
+		clustered.SetBit(clustered, p, 1)
+		visited.SetBit(visited, p, 1)
+
+		for i := 0; i < rows; i++ {
+			reset := false
+			if neighbours.Bit(i) == 0 {
+				// Not a neighbour, so skip
+				continue
+			}
+			if visited.Bit(i) == 0 {
+				// not yet visited
+				visited = visited.SetBit(visited, i, 1) // Mark as visited
+				newNeighbours := big.NewInt(0)
+				newNeighbours = regionQuery(i, newNeighbours, dist, params.Eps)
+				if BitCount(newNeighbours) >= params.MinCount {
+					neighbours = neighbours.Or(neighbours, newNeighbours)
+					reset = true
+				}
+			} else {
+				continue
+			}
+			if clustered.Bit(i) == 0 {
+				clusterMap[c] = append(clusterMap[c], i)
+				clustered = clustered.SetBit(clustered, i, 1)
+			}
+			if reset {
+				i = 0
+			}
+		}
+	}
+
+	c := 0
+	for i := 0; i < rows; i++ {
+		if visited.Bit(i) == 1 {
+			continue // Already visited here
+		}
+		visited.SetBit(visited, i, 1)
+		neighbours := big.NewInt(0)
+		neighbours = regionQuery(i, neighbours, dist, params.Eps)
+		if BitCount(neighbours) < params.MinCount {
+			// Noise, cluster 0
+			clustered = clustered.Or(clustered, neighbours)
+			continue
+		}
+		c = c + 1 // Increment cluster count
+		expandCluster(i, neighbours, c)
+	}
+
+	// Remove anything from the map which doesn't make
+	// minimum points
+	rmKeys := make([]int, 0)
+	for id := range clusterMap {
+		if len(clusterMap[id]) < params.MinCount {
+			rmKeys = append(rmKeys, id)
+		}
+	}
+	for _, r := range rmKeys {
+		delete(clusterMap, r)
+	}
+
+	return ClusterMap(clusterMap), nil
+}
+
+// How many bits?
+func BitCount(n *big.Int) int {
+	var count int = 0
+	for _, b := range n.Bytes() {
+		count += int(bitCounts[b])
+	}
+	return count
+}
+
+// The bit counts for each byte value (0 - 255).
+var bitCounts = []int8{
+	// Generated by Java BitCount of all values from 0 to 255
+	0, 1, 1, 2, 1, 2, 2, 3,
+	1, 2, 2, 3, 2, 3, 3, 4,
+	1, 2, 2, 3, 2, 3, 3, 4,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	1, 2, 2, 3, 2, 3, 3, 4,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	1, 2, 2, 3, 2, 3, 3, 4,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	4, 5, 5, 6, 5, 6, 6, 7,
+	1, 2, 2, 3, 2, 3, 3, 4,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	4, 5, 5, 6, 5, 6, 6, 7,
+	2, 3, 3, 4, 3, 4, 4, 5,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	4, 5, 5, 6, 5, 6, 6, 7,
+	3, 4, 4, 5, 4, 5, 5, 6,
+	4, 5, 5, 6, 5, 6, 6, 7,
+	4, 5, 5, 6, 5, 6, 6, 7,
+	5, 6, 6, 7, 6, 7, 7, 8,
+}

clustering/dbscan_labels.csv

@@ -0,0 +1,750 @@
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+1

clustering/dbscan_test.go

@@ -0,0 +1,150 @@
+package clustering
+
+import (
+	"bufio"
+	"github.com/gonum/matrix/mat64"
+	"github.com/sjwhitworth/golearn/base"
+	"github.com/sjwhitworth/golearn/metrics/pairwise"
+	. "github.com/smartystreets/goconvey/convey"
+	"math"
+	"math/big"
+	"os"
+	"strconv"
+	"testing"
+)
+
+func TestDBSCANDistanceQuery(t *testing.T) {
+
+	Convey("Should be able to determine which points are in range...", t, func() {
+
+		// Read in the synthetic test data
+		inst, err := base.ParseCSVToInstances("synthetic.csv", false)
+		So(err, ShouldBeNil)
+
+		// Create a neighbours vector
+		neighbours := big.NewInt(0)
+
+		// Compute pairwise distances
+		dist, err := computePairwiseDistances(inst, inst.AllAttributes(), pairwise.NewEuclidean())
+		So(dist.At(0, 0), ShouldAlmostEqual, 0)
+		So(dist.At(0, 1), ShouldAlmostEqual, 1)
+		So(dist.At(1, 0), ShouldAlmostEqual, 1)
+		So(dist.At(0, 2), ShouldAlmostEqual, math.Sqrt(5))
+		So(dist.At(2, 0), ShouldAlmostEqual, math.Sqrt(5))
+		So(err, ShouldBeNil)
+
+		// Do the region query
+		neighbours = regionQuery(0, neighbours, dist, 1)
+		So(neighbours.Bit(0), ShouldEqual, 1)
+		So(neighbours.Bit(1), ShouldEqual, 1)
+		So(neighbours.Bit(2), ShouldEqual, 0)
+		So(neighbours.Bit(3), ShouldEqual, 0)
+		So(neighbours.Bit(4), ShouldEqual, 0)
+
+	})
+
+}
+
+func TestDBSCANSynthetic(t *testing.T) {
+	Convey("Synthetic DBSCAN test should work...", t, func() {
+
+		inst, err := base.ParseCSVToInstances("synthetic.csv", false)
+		So(err, ShouldBeNil)
+
+		p := DBSCANParameters{
+			ClusterParameters{
+				inst.AllAttributes(),
+				pairwise.NewEuclidean(),
+			},
+			1,
+			1,
+		}
+
+		m, err := DBSCAN(inst, p)
+		So(err, ShouldBeNil)
+
+		So(len(m), ShouldEqual, 2)
+		So(m[1], ShouldContain, 0)
+		So(m[1], ShouldContain, 1)
+		So(m[1], ShouldContain, 2)
+		So(m[1], ShouldContain, 3)
+
+	})
+}
+
+func TestDBSCANDistanceMetric(t *testing.T) {
+
+	Convey("Check the distance function is sane...", t, func() {
+
+		d1 := mat64.NewDense(1, 2, nil)
+		d2 := mat64.NewDense(1, 2, nil)
+
+		d1.Set(0, 0, 0.494260967249)
+		d1.Set(0, 1, 1.45106696541)
+		d2.Set(0, 0, -1.42808099324)
+		d2.Set(0, 1, -0.83706376669)
+
+		e := pairwise.NewEuclidean()
+		So(e.Distance(d1, d2), ShouldAlmostEqual, 2.9882, 0.001)
+
+	})
+
+}
+
+func TestDBSCAN(t *testing.T) {
+
+	Convey("Loading some data and labels...", t, func() {
+
+		inst, err := base.ParseCSVToInstances("dbscan.csv", false)
+		So(err, ShouldBeNil)
+
+		file, err := os.Open("dbscan_labels.csv")
+		defer file.Close()
+		So(err, ShouldBeNil)
+
+		clusterMap := ClusterMap(make(map[int][]int))
+
+		scanner := bufio.NewScanner(file)
+		line := -1
+		for scanner.Scan() {
+			line = line + 1
+			v, err := strconv.ParseInt(scanner.Text(), 10, 64)
+			if err != nil {
+				panic(err)
+			}
+			v = v + 1 // -1 are noise in scikit-learn's DBSCAN
+			c := int(v)
+			if c == 0 {
+				continue
+			}
+			if _, ok := clusterMap[c]; !ok {
+				clusterMap[c] = make([]int, 0)
+			}
+			clusterMap[c] = append(clusterMap[c], line)
+		}
+
+		Convey("Our DBSCAN implementation should match...", func() {
+			p := DBSCANParameters{
+				ClusterParameters{
+					inst.AllAttributes(),
+					pairwise.NewEuclidean(),
+				},
+				0.3,
+				10,
+			}
+			m, err := DBSCAN(inst, p)
+			Convey("There should be nothing in the result that's smaller than MinPts", func() {
+
+				for id := range m {
+					So(len(m[id]), ShouldBeGreaterThanOrEqualTo, 10)
+				}
+
+			})
+			So(err, ShouldBeNil)
+			eq, err := clusterMap.Equals(m)
+			So(err, ShouldBeNil)
+			So(eq, ShouldBeTrue)
+		})
+	})
+
+}

clustering/gen_test.py

@@ -0,0 +1,30 @@
+#
+# Generate sample data for the DBSCAN test 
+# 
+# Lifted from http://scikit-learn.org/stable/auto_examples/cluster/plot_dbscan.html#example-cluster-plot-dbscan-py
+#
+
+import numpy as np
+
+from sklearn.cluster import DBSCAN
+from sklearn import metrics
+from sklearn.datasets.samples_generator import make_blobs
+from sklearn.preprocessing import StandardScaler
+
+centers = [[1, 1], [-1, -1], [1, -1]]
+X, labels_true = make_blobs(n_samples=750, centers=centers, cluster_std=0.4,
+    random_state=0)
+
+X = StandardScaler().fit_transform(X)
+X = X.astype(np.float64)
+db = DBSCAN(eps=0.3, min_samples=10, metric='l2', algorithm='brute').fit(X)
+core_samples_mask = np.zeros_like(db.labels_, dtype=bool)
+core_samples_mask[db.core_sample_indices_] = True
+labels = db.labels_
+
+with open('dbscan.csv', 'w') as fscanout:
+    with open('dbscan_labels.csv', 'w') as fscanlabout:
+        for i in range(750):
+            fscanout.write(",".join([str(x) for x in X[i,:]]) + "\n")
+            fscanlabout.write(str(labels[i]) + "\n")
+

clustering/synthetic.csv

@@ -0,0 +1,5 @@
+0,4
+1,4
+2,3
+2,4
+3,1