mirror of
https://github.com/gonum/gonum.git
synced 2025-10-28 01:21:44 +08:00
aa29fc4604
vecs is wide when a is wide, but vectors beyond n are not valid, so clone the result view into vecs. This costs an allocation when it happens, but potentially saves significant space - when n << d.
78 lines
2.2 KiB
Go
78 lines
2.2 KiB
Go
// Copyright ©2016 The gonum Authors. All rights reserved.
|
||
// Use of this source code is governed by a BSD-style
|
||
// license that can be found in the LICENSE file.
|
||
|
||
package stat
|
||
|
||
import (
|
||
"math"
|
||
|
||
"github.com/gonum/floats"
|
||
"github.com/gonum/matrix"
|
||
"github.com/gonum/matrix/mat64"
|
||
)
|
||
|
||
// PrincipalComponents returns the principal component direction vectors and
|
||
// the column variances of the principal component scores, vecs * a, computed
|
||
// using the singular value decomposition of the input. The input a is an n×d
|
||
// matrix where each row is an observation and each column represents a variable.
|
||
//
|
||
// PrincipalComponents centers the variables but does not scale the variance.
|
||
//
|
||
// The slice weights is used to weight the observations. If weights is nil,
|
||
// each weight is considered to have a value of one, otherwise the length of
|
||
// weights must match the number of observations or PrincipalComponents will
|
||
// panic.
|
||
//
|
||
// On successful completion, the principal component direction vectors are
|
||
// returned in vecs as a d×min(n, d) matrix, and the variances are returned in
|
||
// vars as a min(n, d)-long slice in descending sort order.
|
||
//
|
||
// If no singular value decomposition is possible, vecs and vars are returned
|
||
// nil and ok is returned false.
|
||
func PrincipalComponents(a mat64.Matrix, weights []float64) (vecs *mat64.Dense, vars []float64, ok bool) {
|
||
n, d := a.Dims()
|
||
if weights != nil && len(weights) != n {
|
||
panic("stat: len(weights) != observations")
|
||
}
|
||
|
||
centered := mat64.NewDense(n, d, nil)
|
||
col := make([]float64, n)
|
||
for j := 0; j < d; j++ {
|
||
mat64.Col(col, j, a)
|
||
floats.AddConst(-Mean(col, weights), col)
|
||
centered.SetCol(j, col)
|
||
}
|
||
for i, w := range weights {
|
||
floats.Scale(math.Sqrt(w), centered.RawRowView(i))
|
||
}
|
||
|
||
kind := matrix.SVDFull
|
||
if n > d {
|
||
kind = matrix.SVDThin
|
||
}
|
||
var svd mat64.SVD
|
||
ok = svd.Factorize(centered, kind)
|
||
if !ok {
|
||
return nil, nil, false
|
||
}
|
||
|
||
vecs = &mat64.Dense{}
|
||
vecs.VFromSVD(&svd)
|
||
if n < d {
|
||
// Don't retain columns that are not valid direction vectors.
|
||
vecs.Clone(vecs.View(0, 0, d, n))
|
||
}
|
||
vars = svd.Values(nil)
|
||
var f float64
|
||
if weights == nil {
|
||
f = 1 / float64(n-1)
|
||
} else {
|
||
f = 1 / (floats.Sum(weights) - 1)
|
||
}
|
||
for i, v := range vars {
|
||
vars[i] = f * v * v
|
||
}
|
||
return vecs, vars, true
|
||
}
|