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stat: added CCA
merged PCA in with CCA into pca_cca.go added the helper svdFactorizeCentered, added Boston and Car datasets for use in tests and examples. Comment Improvements go fmt More Improvements. made BostonData bostonData by moving it to stat_test, moved cca_test.go into stat_test as well to accomodate this. Merged pca and cca into pca_cca.go Minor fixes Capitalisation mostly Full Stop CC type also adjusted some of the calculations to require less allocation Updated Tests also moved around some scaling of columns, and updated comments left, right and some shuffling Mostly doc fixes Improvements to documentation tidied comments, and removed approxEqual in exchange for floats.EqualApprox. More documentation improvement also american spelling of centre second pass go fmt CCA description View -> Slice and PrincipalComponents doc correction.
This commit is contained in:
Armadilloa16
183
cca_test.go
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183
cca_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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"testing"
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"github.com/gonum/floats"
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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 TestCanonicalCorrelations(t *testing.T) {
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for i, test := range []struct {
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xdata mat64.Matrix
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ydata mat64.Matrix
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weights []float64
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wantCorrs []float64
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wantpVecs *mat64.Dense
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wantqVecs *mat64.Dense
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wantphiVs *mat64.Dense
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wantpsiVs *mat64.Dense
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epsilon float64
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}{
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// Test results verified using R.
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{ // Truncated iris data, Sepal vs Petal measurements.
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xdata: mat64.NewDense(10, 2, []float64{
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5.1, 3.5,
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4.9, 3.0,
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4.7, 3.2,
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4.6, 3.1,
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5.0, 3.6,
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5.4, 3.9,
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4.6, 3.4,
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5.0, 3.4,
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4.4, 2.9,
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4.9, 3.1,
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}),
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ydata: mat64.NewDense(10, 2, []float64{
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1.4, 0.2,
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1.4, 0.2,
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1.3, 0.2,
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1.5, 0.2,
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1.4, 0.2,
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1.7, 0.4,
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1.4, 0.3,
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1.5, 0.2,
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1.4, 0.2,
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1.5, 0.1,
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}),
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wantCorrs: []float64{0.7250624174504773, 0.5547679185730191},
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wantpVecs: mat64.NewDense(2, 2, []float64{
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0.0765914610875867, 0.9970625597666721,
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0.9970625597666721, -0.0765914610875868,
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}),
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wantqVecs: mat64.NewDense(2, 2, []float64{
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0.3075184850910837, 0.9515421069649439,
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0.9515421069649439, -0.3075184850910837,
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}),
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wantphiVs: mat64.NewDense(2, 2, []float64{
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-1.9794877596804641, 5.2016325219025124,
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4.5211829944066553, -2.7263663170835697,
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}),
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wantpsiVs: mat64.NewDense(2, 2, []float64{
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-0.0613084818030103, 10.8514169865438941,
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12.7209032660734298, -7.6793888180353775,
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}),
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epsilon: 1e-12,
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},
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// Test results compared to those results presented in examples by
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// Koch, Inge. Analysis of multivariate and high-dimensional data.
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// Vol. 32. Cambridge University Press, 2013. ISBN: 9780521887939
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{ // ASA Car Exposition Data of Ramos and Donoho (1983)
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// Displacement, Horsepower, Weight
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xdata: carData.Slice(0, 392, 0, 3),
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// Acceleration, MPG
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ydata: carData.Slice(0, 392, 3, 5),
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wantCorrs: []float64{0.8782187384352336, 0.6328187219216761},
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wantpVecs: mat64.NewDense(3, 2, []float64{
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0.3218296374829181, 0.3947540257657075,
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0.4162807660635797, 0.7573719053303306,
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0.8503740401982725, -0.5201509936144236,
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}),
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wantqVecs: mat64.NewDense(2, 2, []float64{
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-0.5161984172278830, -0.8564690269072364,
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-0.8564690269072364, 0.5161984172278830,
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}),
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wantphiVs: mat64.NewDense(3, 2, []float64{
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0.0025033152994308, 0.0047795464118615,
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0.0201923608080173, 0.0409150208725958,
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-0.0000247374128745, -0.0026766435161875,
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}),
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wantpsiVs: mat64.NewDense(2, 2, []float64{
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-0.1666196759760772, -0.3637393866139658,
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-0.0915512109649727, 0.1077863777929168,
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}),
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epsilon: 1e-12,
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},
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// Test results compared to those results presented in examples by
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// Koch, Inge. Analysis of multivariate and high-dimensional data.
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// Vol. 32. Cambridge University Press, 2013. ISBN: 9780521887939
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{ // Boston Housing Data of Harrison and Rubinfeld (1978)
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// Per capita crime rate by town,
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// Proportion of non-retail business acres per town,
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// Nitric oxide concentration (parts per 10 million),
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// Weighted distances to Boston employment centres,
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// Index of accessibility to radial highways,
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// Pupil-teacher ratio by town, Proportion of blacks by town
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xdata: bostonData.Slice(0, 506, 0, 7),
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// Average number of rooms per dwelling,
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// Proportion of owner-occupied units built prior to 1940,
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// Full-value property-tax rate per $10000,
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// Median value of owner-occupied homes in $1000s
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ydata: bostonData.Slice(0, 506, 7, 11),
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wantCorrs: []float64{0.9451239443886021, 0.6786622733370654, 0.5714338361583764, 0.2009739704710440},
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wantpVecs: mat64.NewDense(7, 4, []float64{
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-0.2574391924541903, 0.0158477516621194, 0.2122169934631024, -0.0945733803894706,
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-0.4836594430018478, 0.3837101908138468, 0.1474448317415911, 0.6597324886718275,
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-0.0800776365873296, 0.3493556742809252, 0.3287336458109373, -0.2862040444334655,
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0.1277586360386374, -0.7337427663667596, 0.4851134819037011, 0.2247964865970192,
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-0.6969432006136684, -0.4341748776002893, -0.3602872887636357, 0.0290661608626292,
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-0.0990903250057199, 0.0503411215453873, 0.6384330631742202, 0.1022367136218303,
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0.4260459963765036, 0.0323334351308141, -0.2289527516030810, 0.6419232947608805,
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}),
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wantqVecs: mat64.NewDense(4, 4, []float64{
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0.0181660502363264, -0.1583489460479038, -0.0066723577642883, -0.9871935400650649,
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-0.2347699045986119, 0.9483314614936594, -0.1462420505631345, -0.1554470767919033,
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-0.9700704038477141, -0.2406071741000039, -0.0251838984227037, 0.0209134074358349,
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0.0593000682318482, -0.1330460003097728, -0.9889057151969489, 0.0291161494720761,
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}),
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wantphiVs: mat64.NewDense(7, 4, []float64{
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-0.0027462234108197, 0.0093444513500898, 0.0489643932714296, -0.0154967189805819,
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-0.0428564455279537, -0.0241708702119420, 0.0360723472093996, 0.1838983230588095,
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-1.2248435648802380, 5.6030921364723980, 5.8094144583797025, -4.7926812190419676,
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-0.0043684825094649, -0.3424101164977618, 0.4469961215717917, 0.1150161814353696,
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-0.0741534069521954, -0.1193135794923700, -0.1115518305471460, 0.0021638758323088,
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-0.0233270323101624, 0.1046330818178399, 0.3853045975077387, -0.0160927870102877,
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0.0001293051387859, 0.0004540746921446, -0.0030296315865440, 0.0081895477974654,
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}),
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wantpsiVs: mat64.NewDense(4, 4, []float64{
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0.0301593362017375, -0.3002219289647127, 0.0878217377593682, -1.9583226531517062,
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-0.0065483104073892, 0.0392212086716247, -0.0117570776209991, -0.0061113064481860,
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-0.0052075523350125, -0.0045770200452960, -0.0022762313289592, 0.0008441873006821,
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0.0020111735096327, 0.0037352799829930, -0.1292578071621794, 0.1037709056329765,
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}),
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epsilon: 1e-12,
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},
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} {
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cc, err := stat.CanonicalCorrelations(test.xdata, test.ydata, test.weights)
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if err != nil {
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t.Errorf("%d: unexpected error: %v", i, err)
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continue
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}
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corrs := cc.Corrs(nil)
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pVecs := cc.Left(true)
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qVecs := cc.Right(true)
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phiVs := cc.Left(false)
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psiVs := cc.Right(false)
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if !floats.EqualApprox(corrs, test.wantCorrs, test.epsilon) {
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t.Errorf("%d: unexpected variance result got:%v, want:%v", i, corrs, test.wantCorrs)
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}
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if !mat64.EqualApprox(pVecs, test.wantpVecs, test.epsilon) {
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t.Errorf("%d: unexpected CCA result got:\n%v\nwant:\n%v",
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i, mat64.Formatted(pVecs), mat64.Formatted(test.wantpVecs))
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}
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if !mat64.EqualApprox(qVecs, test.wantqVecs, test.epsilon) {
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t.Errorf("%d: unexpected CCA result got:\n%v\nwant:\n%v",
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i, mat64.Formatted(qVecs), mat64.Formatted(test.wantqVecs))
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}
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if !mat64.EqualApprox(phiVs, test.wantphiVs, test.epsilon) {
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t.Errorf("%d: unexpected CCA result got:\n%v\nwant:\n%v",
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i, mat64.Formatted(phiVs), mat64.Formatted(test.wantphiVs))
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}
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if !mat64.EqualApprox(psiVs, test.wantpsiVs, test.epsilon) {
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t.Errorf("%d: unexpected CCA result got:\n%v\nwant:\n%v",
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i, mat64.Formatted(psiVs), mat64.Formatted(test.wantpsiVs))
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}
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}
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}
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