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kprofiles.go
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kprofiles.go
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// Package kprofiles provides an implementation of K-Profiles, a nonlinear
// clustering method for pattern detection in high-dimensional data, which was
// described by Wang et al.
package kprofiles
import (
"bytes"
"fmt"
"math"
"math/rand"
"strconv"
"strings"
"time"
"github.com/gonum/matrix/mat64"
"github.com/senseyeio/roger"
)
// rClient connects to an R Server for calculating the shortest Hamiltonian
// Path when the clusters are reordered
var rClient roger.RClient
// initialization of the connection to the R Server. The function panics if not
// possiblei and expects the server to run on the default port on localhost.
// Also random is seeded.
func init() {
var err error
rClient, err = roger.NewRClient("127.0.0.1", 6311)
if err != nil {
panic("Connection to R Server could not be established")
}
rand.Seed(int64(time.Now().Nanosecond()))
}
// Cluster stores information about the contents of a cluster
type Cluster struct {
// ColumnOrder stores the indices of the actual matrix columns in the order
// of the current cluster
ColumnOrder []int
// Rows holds the indices of the actual matrix that are currently clustered
Rows []int
// current distance of the Hamiltonian Path based on the Manhattan Distance
Distance float64
// the last calculated distance of the Hamiltonian Path
lastDistance float64
}
type Kprofiles struct {
matrix *mat64.Dense // base matrix
nullDistMean []float64 // Means of all rows under the null distribution
nullDistStdDev []float64 // Standard Deviations of all rows under the null distribution
Clusters []*Cluster
}
// NewKprofiles returns a new object with the provided matrix m and the needed
// Cluster objects based on clusterCount
func NewKprofiles(m *mat64.Dense, clusterCount int) (*Kprofiles, error) {
if m == nil {
return nil, fmt.Errorf("Provided matrix is nil")
}
if clusterCount < 2 {
return nil, fmt.Errorf("There have to be at least 2 clusters")
}
rows, columns := m.Dims()
clusters := make([]*Cluster, clusterCount)
for i := 0; i < clusterCount; i++ {
clusters[i] = &Cluster{
ColumnOrder: make([]int, columns),
Rows: make([]int, rows),
Distance: math.MaxFloat64,
lastDistance: 0,
}
clusters[i].initialize()
}
return &Kprofiles{
matrix: m,
nullDistMean: make([]float64, rows),
nullDistStdDev: make([]float64, rows),
Clusters: clusters,
}, nil
}
// NullDistParameters calculates the mean and standard deviation of the dcol
// for each row under the null distribution that there is no dependence
// regarding the order of the values inside a row of the matrix. Each row is
// permuttated p times and the dcol is calculated each time. The results are
// stored in the according arrays of k. Returns an error if one of the
// statistical computations fails.
func (k *Kprofiles) NullDistParameters(p int) error {
rows, _ := k.matrix.Dims()
for i := 0; i < rows; i++ {
// copy the row
row := k.matrix.RawRowView(i)
rowCopy := make([]float64, len(row))
copy(rowCopy, row)
permutatedDcols := make([]float64, p)
for j := 0; j < p; j++ {
// shuffeling the row
for element := range rowCopy {
k := rand.Intn(element + 1)
rowCopy[element], rowCopy[k] = rowCopy[k], rowCopy[element]
}
dcol, err := dcol(rowCopy)
if err != nil {
return err
}
permutatedDcols[j] = dcol
}
var err error
k.nullDistMean[i], err = mean(permutatedDcols)
if err != nil {
return err
}
k.nullDistStdDev[i], err = stdDev(permutatedDcols, k.nullDistMean[i])
if err != nil {
return err
}
}
return nil
}
// Cluster is the core algorithm of K-Profiles. It clusters the rows in its
// base matrix dependent on the order of the columns and the resulting dcol
// values. A row is attached to a cluster where its p-value is minimal and less
// than the current p-value cutoff alpha. Alpha is initialized with sAlpha and
// then in each iteration decreased until it reaches gAlpha. The clustering is
// complete if each cluster is stable or r iterations are done.
func (k *Kprofiles) Cluster(sAlpha, gAlpha float64, r int) error {
if sAlpha < gAlpha {
return fmt.Errorf("The start value of alpha is smaller than the goal value")
}
alpha := sAlpha
for rounds := 0; !clustersStable(k.Clusters) && rounds < r; rounds++ {
rows, _ := k.matrix.Dims()
k.resetClusters()
for i := 0; i < rows; i++ {
row := k.matrix.RawRowView(i)
var bestCluster *Cluster
bestPvalue := math.MaxFloat64
for _, c := range k.Clusters {
clusterRow, err := getOrderedRow(row, c.ColumnOrder)
if err != nil {
return err
}
dcol, err := dcol(clusterRow)
if err != nil {
return err
}
pvalue := pvalue(dcol, k.nullDistMean[i], k.nullDistStdDev[i])
// check if the calculated p-value is statistically
// signinficant and store the current cluster as the best if
// there hasn't been a better p-value
if pvalue <= alpha && pvalue <= bestPvalue {
bestPvalue = pvalue
bestCluster = c
}
}
// attach the row to the best fitting cluster regarding the p-value
// if it is statistically signinficant
if bestCluster != nil {
bestCluster.Rows = append(bestCluster.Rows, i)
}
}
var err error
alpha, err = sidak(alpha, gAlpha, len(k.Clusters))
if err != nil {
return err
}
for _, c := range k.Clusters {
if len(c.Rows) > 0 {
err = c.reorder(k.matrix)
if err != nil {
return err
}
}
}
}
return nil
}
func (k *Kprofiles) resetClusters() {
for _, c := range k.Clusters {
c.resetRows()
}
}
// reorder uses the R TSP library to reorder the columns based on the currently
// clustered rows.
func (c *Cluster) reorder(matrix *mat64.Dense) error {
var value interface{}
var err error
session, err := rClient.GetSession()
if err != nil {
return fmt.Errorf("R: Session could not be established: " + err.Error())
}
defer session.Close()
value, err = session.Eval("library(\"TSP\")")
if err != nil {
return fmt.Errorf("R: TSP library could not be loaded: " + err.Error())
}
var buffer bytes.Buffer
// R matrices are column based, therefore the row- and column-counts
// are exchanged so that we directly have the transposed.
buffer.WriteString("A <- matrix(c(" + c.valuesAsString(matrix) + ")")
buffer.WriteString(",nrow=" + strconv.Itoa(len(c.ColumnOrder)))
buffer.WriteString(",ncol=" + strconv.Itoa(len(c.Rows)) + ");")
buffer.WriteString("d<-dist(A,method=\"man\");")
buffer.WriteString("tsp<-TSP(d);")
buffer.WriteString("tsp<-insert_dummy(tsp, label=\"cut\");")
buffer.WriteString("tour<-solve_TSP(tsp,method=\"nn\");")
buffer.WriteString("path<-cut_tour(tour,\"cut\");")
buffer.WriteString("path;")
value, err = session.Eval(buffer.String())
if err != nil {
return fmt.Errorf("R: tsp could not be solved: " + err.Error())
} else {
if newOrder, ok := value.([]int32); ok {
c.ColumnOrder = c.ColumnOrder[:0]
for i := range newOrder {
c.ColumnOrder = append(c.ColumnOrder, int(newOrder[i])-1)
}
} else {
return fmt.Errorf("R: returned path is not an int array")
}
}
value, err = session.Eval("attributes(tour)$tour_length")
if err != nil {
return fmt.Errorf("R: tour distance could not be get: " + err.Error())
} else {
if newDistance, ok := value.(float64); ok {
c.lastDistance = c.Distance
c.Distance = newDistance
} else {
return fmt.Errorf("R: returned distance is not a float64 value")
}
}
return nil
}
// initialize sets a intial random order for each cluster in k and puts
// every row in every cluster for the initial p-value calculation
func (c *Cluster) initialize() {
c.ColumnOrder = rand.Perm(len(c.ColumnOrder))
for i, _ := range c.Rows {
c.Rows[i] = i
}
}
func (c *Cluster) resetRows() {
c.Rows = c.Rows[:0]
}
// valuesAsString returns the values of a cluster as comma-seperated row-based
// string.
func (c *Cluster) valuesAsString(matrix *mat64.Dense) string {
stringArray := make([]string, 0)
for _, v := range c.Rows {
for j := 0; j < len(c.ColumnOrder); j++ {
stringArray = append(stringArray, strconv.FormatFloat(matrix.At(v, j), 'f', -1, 64))
}
}
return strings.Join(stringArray, ",")
}
// getOrderedRow returns a copy of baseRow ordered by the mapping of order
func getOrderedRow(baseRow []float64, order []int) ([]float64, error) {
if len(baseRow) != len(order) {
return nil, fmt.Errorf("Row couldn't be ordered. baseRow has length %d, order array has length %d", len(baseRow), len(order))
}
orderedRow := make([]float64, len(baseRow))
for i := 0; i < len(baseRow); i++ {
orderedRow[i] = baseRow[order[i]]
}
return orderedRow, nil
}
// clustersStable reports if it is no longer possible to make further progress in the
// calculation of the clusters. Returns true, if all clusters are empty (no
// rows get attached to any cluster) or no cluster made progress regarding the
// Hamiltonian Length in the last cluster round.
func clustersStable(clusters []*Cluster) bool {
allClustersEmpty := true
noDistanceProgress := true
for _, c := range clusters {
if len(c.Rows) != 0 {
allClustersEmpty = false
}
if c.Distance != c.lastDistance {
noDistanceProgress = false
}
}
return allClustersEmpty || noDistanceProgress
}