11module MultivariateStats
22
3- using LinearAlgebra
4- using SparseArrays
5- using Statistics: middle
6- using StatsAPI: RegressionModel
7- using StatsBase:
8- SimpleCovariance,
9- CovarianceEstimator,
10- AbstractDataTransform,
11- ConvergenceException,
12- pairwise,
13- pairwise!,
14- CoefTable
15-
16- import Statistics: mean, var, cov, covm, cor
17- import Base: length, size, show
18- import StatsAPI: fit, predict, coef, weights, dof, r2
19- import LinearAlgebra: eigvals, eigvecs
20-
21- export
3+ using DataFrames
4+ using LinearAlgebra
5+ using SparseArrays
6+ using Statistics: middle
7+ using StatsAPI: RegressionModel
8+ using StatsBase: SimpleCovariance, CovarianceEstimator, AbstractDataTransform,
9+ ConvergenceException, pairwise, pairwise!, CoefTable
10+
11+ import Statistics: mean, var, cov, covm, cor
12+ import Base: length, size, show
13+ import StatsAPI: fit, predict, coef, weights, dof, r2
14+ import LinearAlgebra: eigvals, eigvecs
15+
16+ export
2217
2318 # # common
2419 evaluate, # evaluate discriminant function values
@@ -43,23 +38,27 @@ export
4338
4439 # whiten
4540 Whitening, # Type: Whitening transformation
41+
4642 invsqrtm, # Compute inverse of matrix square root, i.e. inv(sqrtm(A))
4743 cov_whitening, # Compute a whitening transform based on covariance
4844 cov_whitening!, # Compute a whitening transform based on covariance (input will be overwritten)
4945 invsqrtm, # Compute C^{-1/2}, i.e. inv(sqrtm(C))
5046
5147 # # pca
5248 PCA, # Type: Principal Component Analysis model
49+
5350 pcacov, # PCA based on covariance
5451 pcasvd, # PCA based on singular value decomposition of input data
5552 principalratio, # the ratio of variances preserved in the principal subspace
5653 principalvar, # the variance along a specific principal direction
5754 principalvars, # the variances along all principal directions
55+
5856 tprincipalvar, # total principal variance, i.e. sum(principalvars(M))
5957 tresidualvar, # total residual variance
6058
6159 # # ppca
6260 PPCA, # Type: the Probabilistic PCA model
61+
6362 ppcaml, # Maximum likelihood probabilistic PCA
6463 ppcaem, # EM algorithm for probabilistic PCA
6564 bayespca, # Bayesian PCA
@@ -79,17 +78,18 @@ export
7978 MetricMDS,
8079 classical_mds, # perform classical MDS over a given distance matrix
8180 stress, # stress evaluation
82- gram2dmat,
83- gram2dmat!, # Gram matrix => Distance matrix
84- dmat2gram,
85- dmat2gram!, # Distance matrix => Gram matrix
81+
82+ gram2dmat, gram2dmat!, # Gram matrix => Distance matrix
83+ dmat2gram, dmat2gram!, # Distance matrix => Gram matrix
8684
8785 # # lda
8886 LinearDiscriminant, # Type: Linear Discriminant functional
8987 MulticlassLDAStats, # Type: Statistics required for training multi-class LDA
9088 MulticlassLDA, # Type: Multi-class LDA model
9189 SubspaceLDA, # Type: LDA model for high-dimensional spaces
90+
9291 ldacov, # Linear discriminant analysis based on covariances
92+
9393 classweights, # class-specific weights
9494 classmeans, # class-specific means
9595 withclass_scatter, # with-class scatter matrix
@@ -100,58 +100,59 @@ export
100100
101101 # # ica
102102 ICA, # Type: the Fast ICA model
103+
103104 fastica!, # core algorithm function for the Fast ICA
104105
105106 # # fa
106107 FactorAnalysis, # Type: the Factor Analysis model
108+
107109 faem, # EM algorithm for factor analysis
108110 facm, # CM algorithm for factor analysis
109111
110- # # CA, MCA
112+ # # ca, mca
111113 CA, # Type: correspondence analysis
114+
112115 MCA, # Type: multiple correspondence analysis
113116 ca, # fit and return a correspondence analysis
114117 mca, # fit and return a multiple correspondence analysis
115118 objectscores, # return the object scores or coordinates from CA or MCA
116119 variablescores, # return the variable/category scores or coordinates from CA or MCA
117120 inertia # return the inertia (derived from eigenvalues) for CA
118121
119- # # source files
120- include (" types.jl" )
121- include (" common.jl" )
122- include (" lreg.jl" )
123- include (" whiten.jl" )
124- include (" pca.jl" )
125- include (" ppca.jl" )
126- include (" kpca.jl" )
127- include (" cca.jl" )
128- include (" cmds.jl" )
129- include (" mmds.jl" )
130- include (" lda.jl" )
131- include (" ica.jl" )
132- include (" fa.jl" )
133- include (" mca.jl" )
134-
135- # # deprecations
136- @deprecate indim (f) size (f, 1 )
137- @deprecate outdim (f) size (f, 2 )
138- @deprecate transform (f, x) predict (f, x)
139- @deprecate indim (f:: Whitening ) length (f:: Whitening )
140- @deprecate outdim (f:: Whitening ) length (f:: Whitening )
141- @deprecate tvar (f:: PCA ) var (f:: PCA )
142- @deprecate classical_mds (D:: AbstractMatrix , p:: Int ) predict (
143- fit (MDS, D, maxoutdim = p, distances = true ),
144- )
145- @deprecate transform (f:: MDS ) predict (f:: MDS )
146- @deprecate xindim (M:: CCA ) size (M, 1 )
147- @deprecate yindim (M:: CCA ) size (M, 2 )
148- @deprecate outdim (M:: CCA ) size (M, 3 )
149- @deprecate correlations (M:: CCA ) cor (M)
150- @deprecate xmean (M:: CCA ) mean (M, :x )
151- @deprecate ymean (M:: CCA ) mean (M, :y )
152- @deprecate xprojection (M:: CCA ) projection (M, :x )
153- @deprecate yprojection (M:: CCA ) projection (M, :y )
154- @deprecate xtransform (M:: CCA , x) predict (M, x, :x )
155- @deprecate ytransform (M:: CCA , y) predict (M, y, :y )
122+ # # source files
123+ include (" types.jl" )
124+ include (" common.jl" )
125+ include (" lreg.jl" )
126+ include (" whiten.jl" )
127+ include (" pca.jl" )
128+ include (" ppca.jl" )
129+ include (" kpca.jl" )
130+ include (" cca.jl" )
131+ include (" cmds.jl" )
132+ include (" mmds.jl" )
133+ include (" lda.jl" )
134+ include (" ica.jl" )
135+ include (" fa.jl" )
136+ include (" mca.jl" )
137+
138+ # # deprecations
139+ @deprecate indim (f) size (f,1 )
140+ @deprecate outdim (f) size (f,2 )
141+ @deprecate transform (f, x) predict (f, x)
142+ @deprecate indim (f:: Whitening ) length (f:: Whitening )
143+ @deprecate outdim (f:: Whitening ) length (f:: Whitening )
144+ @deprecate tvar (f:: PCA ) var (f:: PCA )
145+ @deprecate classical_mds (D:: AbstractMatrix , p:: Int ) predict (fit (MDS, D, maxoutdim= p, distances= true ))
146+ @deprecate transform (f:: MDS ) predict (f:: MDS )
147+ @deprecate xindim (M:: CCA ) size (M,1 )
148+ @deprecate yindim (M:: CCA ) size (M,2 )
149+ @deprecate outdim (M:: CCA ) size (M,3 )
150+ @deprecate correlations (M:: CCA ) cor (M)
151+ @deprecate xmean (M:: CCA ) mean (M, :x )
152+ @deprecate ymean (M:: CCA ) mean (M, :y )
153+ @deprecate xprojection (M:: CCA ) projection (M, :x )
154+ @deprecate yprojection (M:: CCA ) projection (M, :y )
155+ @deprecate xtransform (M:: CCA , x) predict (M, x, :x )
156+ @deprecate ytransform (M:: CCA , y) predict (M, y, :y )
156157
157158end # module
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