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stat: add principal components calculation
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kortschak
81
pca.go
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81
pca.go
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// Copyright ©2016 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package stat
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import (
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"math"
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"github.com/gonum/floats"
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"github.com/gonum/matrix"
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"github.com/gonum/matrix/mat64"
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)
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// PrincipalComponents returns the principal component direction vectors and
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// the column variances of the principle component scores, vecs * a, computed
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// using the singular value decomposition of the input. The input a is an n×d
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// matrix where each row is an observation and each column represents a variable.
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//
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// PrincipalComponents centers the variables but does not scale the variance.
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//
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// The slice weights is used to weight the observations. If weights is nil,
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// each weight is considered to have a value of one, otherwise the length of
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// weights must match the number of observations or PrincipalComponents will
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// panic.
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//
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// On successful completion, the principal component direction vectors are
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// returned in vecs as a d×min(n, d) matrix, and the variances are returned in
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// vars as a min(n, d)-long slice in descending sort order.
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//
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// If no singular value decomposition is possible, vecs and vars are returned
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// nil and ok is returned false.
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func PrincipalComponents(a mat64.Matrix, weights []float64) (vecs *mat64.Dense, vars []float64, ok bool) {
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n, d := a.Dims()
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if weights != nil && len(weights) != n {
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panic("stat: len(weights) != observations")
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}
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centered := mat64.NewDense(n, d, nil)
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col := make([]float64, n)
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for j := 0; j < d; j++ {
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mat64.Col(col, j, a)
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floats.AddConst(-Mean(col, weights), col)
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centered.SetCol(j, col)
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}
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for i, w := range weights {
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floats.Scale(math.Sqrt(w), centered.RawRowView(i))
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}
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kind := matrix.SVDFull
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if n > d {
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kind = matrix.SVDThin
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}
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var svd mat64.SVD
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ok = svd.Factorize(centered, kind)
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if !ok {
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return nil, nil, false
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}
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var v mat64.Dense
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v.VFromSVD(&svd)
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vecs = v.View(0, 0, d, min(n, d)).(*mat64.Dense)
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vars = svd.Values(nil)
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var f float64
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if weights == nil {
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f = 1 / float64(n-1)
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} else {
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f = 1 / (floats.Sum(weights) - 1)
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}
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for i, v := range vars {
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vars[i] = f * v * v
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}
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return vecs, vars, true
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}
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59
pca_example_test.go
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59
pca_example_test.go
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// Copyright ©2016 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package stat_test
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import (
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"fmt"
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"github.com/gonum/matrix/mat64"
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"github.com/gonum/stat"
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)
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func ExamplePrincipalComponents() {
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// iris is a truncated sample of the Fisher's Iris dataset.
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n := 10
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d := 4
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iris := mat64.NewDense(n, d, []float64{
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5.1, 3.5, 1.4, 0.2,
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4.9, 3.0, 1.4, 0.2,
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4.7, 3.2, 1.3, 0.2,
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4.6, 3.1, 1.5, 0.2,
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5.0, 3.6, 1.4, 0.2,
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5.4, 3.9, 1.7, 0.4,
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4.6, 3.4, 1.4, 0.3,
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5.0, 3.4, 1.5, 0.2,
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4.4, 2.9, 1.4, 0.2,
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4.9, 3.1, 1.5, 0.1,
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})
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// Calculate the principal component direction vectors
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// and variances.
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vecs, vars, ok := stat.PrincipalComponents(iris, nil)
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if !ok {
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return
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}
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fmt.Printf("variances = %.4f\n\n", vars)
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// Project the data onto the first 2 principal components.
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k := 2
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var proj mat64.Dense
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proj.Mul(iris, vecs.View(0, 0, d, k))
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fmt.Printf("proj = %.4f", mat64.Formatted(&proj, mat64.Prefix(" ")))
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// Output:
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// variances = [0.1666 0.0207 0.0079 0.0019]
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//
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// proj = ⎡-6.1686 1.4659⎤
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// ⎢-5.6767 1.6459⎥
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// ⎢-5.6699 1.3642⎥
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// ⎢-5.5643 1.3816⎥
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// ⎢-6.1734 1.3309⎥
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// ⎢-6.7278 1.4021⎥
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// ⎢-5.7743 1.1498⎥
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// ⎢-6.0466 1.4714⎥
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// ⎢-5.2709 1.3570⎥
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// ⎣-5.7533 1.6207⎦
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}
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159
pca_test.go
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159
pca_test.go
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@@ -0,0 +1,159 @@
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// Copyright ©2016 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package stat
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import (
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"testing"
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"github.com/gonum/floats"
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"github.com/gonum/matrix/mat64"
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)
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func TestPrincipalComponents(t *testing.T) {
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for i, test := range []struct {
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data mat64.Matrix
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weights []float64
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wantVecs *mat64.Dense
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wantVars []float64
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epsilon float64
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}{
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// Test results verified using R.
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{
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data: mat64.NewDense(3, 3, []float64{
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1, 2, 3,
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4, 5, 6,
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7, 8, 9,
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}),
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wantVecs: mat64.NewDense(3, 3, []float64{
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0.5773502691896258, 0.8164965809277261, 0,
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0.577350269189626, -0.4082482904638632, -0.7071067811865476,
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0.5773502691896258, -0.4082482904638631, 0.7071067811865475,
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}),
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wantVars: []float64{27, 0, 0},
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epsilon: 1e-12,
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},
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{ // Truncated iris data.
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data: mat64.NewDense(10, 4, []float64{
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5.1, 3.5, 1.4, 0.2,
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4.9, 3.0, 1.4, 0.2,
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4.7, 3.2, 1.3, 0.2,
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4.6, 3.1, 1.5, 0.2,
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5.0, 3.6, 1.4, 0.2,
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5.4, 3.9, 1.7, 0.4,
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4.6, 3.4, 1.4, 0.3,
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5.0, 3.4, 1.5, 0.2,
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4.4, 2.9, 1.4, 0.2,
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4.9, 3.1, 1.5, 0.1,
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}),
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wantVecs: mat64.NewDense(4, 4, []float64{
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-0.6681110197952722, 0.7064764857539533, -0.14026590216895132, -0.18666578956412125,
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-0.7166344774801547, -0.6427036135482664, -0.135650285905254, 0.23444848208629923,
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-0.164411275166307, 0.11898477441068218, 0.9136367900709548, 0.35224901970831746,
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-0.11415613655453069, -0.2714141920887426, 0.35664028439226514, -0.8866286823515034,
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}),
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wantVars: []float64{0.1665786313282786, 0.02065509475412993, 0.007944620317765855, 0.0019327647109368329},
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epsilon: 1e-12,
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},
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{ // Truncated iris data transposed to check for operation on fat input.
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data: mat64.NewDense(10, 4, []float64{
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5.1, 3.5, 1.4, 0.2,
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4.9, 3.0, 1.4, 0.2,
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4.7, 3.2, 1.3, 0.2,
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4.6, 3.1, 1.5, 0.2,
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5.0, 3.6, 1.4, 0.2,
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5.4, 3.9, 1.7, 0.4,
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4.6, 3.4, 1.4, 0.3,
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5.0, 3.4, 1.5, 0.2,
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4.4, 2.9, 1.4, 0.2,
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4.9, 3.1, 1.5, 0.1,
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}).T(),
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wantVecs: mat64.NewDense(10, 4, []float64{
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-0.3366602459946619, -0.1373634006401213, 0.3465102523547623, -0.10290179303893479,
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-0.31381852053861975, 0.5197145790632827, 0.5567296129086686, -0.15923062170153618,
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-0.30857197637565165, -0.07670930360819002, 0.36159923003337235, 0.3342301027853355,
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-0.29527124351656137, 0.16885455995353074, -0.5056204762881208, 0.32580913261444344,
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-0.3327611073694004, -0.39365834489416474, 0.04900050959307464, 0.46812879383236555,
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-0.34445484362044815, -0.2985206914561878, -0.1009714701361799, -0.16803618186050803,
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-0.2986246350957691, -0.4222037823717799, -0.11838613462182519, -0.580283530375069,
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-0.325911246223126, 0.024366468758217238, -0.12082035131864265, 0.16756027181337868,
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-0.2814284432361538, 0.240812316260054, -0.24061437569068145, -0.365034616264623,
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-0.31906138507685167, 0.4423912824105986, -0.2906412122303604, 0.027551046870337714,
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}),
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wantVars: []float64{41.8851906634233, 0.07762619213464989, 0.010516477775373585, 0},
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epsilon: 1e-12,
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},
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{ // Truncated iris data unitary weights.
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data: mat64.NewDense(10, 4, []float64{
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5.1, 3.5, 1.4, 0.2,
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4.9, 3.0, 1.4, 0.2,
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4.7, 3.2, 1.3, 0.2,
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4.6, 3.1, 1.5, 0.2,
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5.0, 3.6, 1.4, 0.2,
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5.4, 3.9, 1.7, 0.4,
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4.6, 3.4, 1.4, 0.3,
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5.0, 3.4, 1.5, 0.2,
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4.4, 2.9, 1.4, 0.2,
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4.9, 3.1, 1.5, 0.1,
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}),
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weights: []float64{1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
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wantVecs: mat64.NewDense(4, 4, []float64{
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-0.6681110197952722, 0.7064764857539533, -0.14026590216895132, -0.18666578956412125,
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-0.7166344774801547, -0.6427036135482664, -0.135650285905254, 0.23444848208629923,
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-0.164411275166307, 0.11898477441068218, 0.9136367900709548, 0.35224901970831746,
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-0.11415613655453069, -0.2714141920887426, 0.35664028439226514, -0.8866286823515034,
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}),
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wantVars: []float64{0.1665786313282786, 0.02065509475412993, 0.007944620317765855, 0.0019327647109368329},
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epsilon: 1e-12,
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},
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{ // Truncated iris data non-unitary weights.
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data: mat64.NewDense(10, 4, []float64{
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5.1, 3.5, 1.4, 0.2,
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4.9, 3.0, 1.4, 0.2,
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4.7, 3.2, 1.3, 0.2,
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4.6, 3.1, 1.5, 0.2,
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5.0, 3.6, 1.4, 0.2,
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5.4, 3.9, 1.7, 0.4,
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4.6, 3.4, 1.4, 0.3,
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5.0, 3.4, 1.5, 0.2,
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4.4, 2.9, 1.4, 0.2,
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4.9, 3.1, 1.5, 0.1,
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}),
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weights: []float64{2, 3, 1, 1, 1, 1, 1, 1, 1, 2},
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wantVecs: mat64.NewDense(4, 4, []float64{
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-0.618936145422414, 0.763069301531647, 0.124857741232537, 0.138035623677211,
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-0.763958271606519, -0.603881770702898, 0.118267155321333, -0.194184052457746,
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-0.143552119754944, 0.090014599564871, -0.942209377020044, -0.289018426115945,
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-0.112599271966947, -0.212012782487076, -0.287515067921680, 0.927203898682805,
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}),
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wantVars: []float64{0.129621985550623, 0.022417487771598, 0.006454461065715, 0.002495076601075},
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epsilon: 1e-12,
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},
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} {
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vecs, vars, ok := PrincipalComponents(test.data, test.weights)
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if !ok {
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t.Errorf("unexpected SVD failure for test %d", i)
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continue
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}
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if !mat64.EqualApprox(vecs, test.wantVecs, test.epsilon) {
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t.Errorf("%d: unexpected PCA result got:\n%v\nwant:\n%v",
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i, mat64.Formatted(vecs), mat64.Formatted(test.wantVecs))
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}
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if !approxEqual(vars, test.wantVars, test.epsilon) {
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t.Errorf("%d: unexpected variance result got:%v, want:%v", i, vars, test.wantVars)
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}
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}
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}
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func approxEqual(a, b []float64, epsilon float64) bool {
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if len(a) != len(b) {
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return false
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}
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for i, v := range a {
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if !floats.EqualWithinAbsOrRel(v, b[i], epsilon, epsilon) {
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return false
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}
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}
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return true
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}
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