check for repeated non-zero signular values

    pick f57ef58 check for repeated non-zero signular values

Author: kshedden

src/MultivariateStats.jl

@@ -1,19 +1,24 @@
 module MultivariateStats
 
-    using LinearAlgebra
-    using SparseArrays
-    using Statistics: middle
-    using Distributions: cdf, FDist
-    using StatsAPI: RegressionModel, HypothesisTest
-    using StatsBase: SimpleCovariance, CovarianceEstimator, AbstractDataTransform,
-                     ConvergenceException, pairwise, pairwise!, CoefTable
-
-    import Statistics: mean, var, cov, covm, cor
-    import Base: length, size, show
-    import StatsAPI: fit, predict, coef, weights, dof, r2, pvalue
-    import LinearAlgebra: eigvals, eigvecs
-
-    export
+using LinearAlgebra
+using SparseArrays
+using Statistics: middle
+using StatsAPI: RegressionModel
+using StatsBase:
+    SimpleCovariance,
+    CovarianceEstimator,
+    AbstractDataTransform,
+    ConvergenceException,
+    pairwise,
+    pairwise!,
+    CoefTable
+
+import Statistics: mean, var, cov, covm, cor
+import Base: length, size, show
+import StatsAPI: fit, predict, coef, weights, dof, r2
+import LinearAlgebra: eigvals, eigvecs
+
+export
 
     ## common
     evaluate,           # evaluate discriminant function values
@@ -38,27 +43,23 @@ module MultivariateStats
 
     # whiten
     Whitening,          # Type: Whitening transformation
-
     invsqrtm,           # Compute inverse of matrix square root, i.e. inv(sqrtm(A))
     cov_whitening,      # Compute a whitening transform based on covariance
     cov_whitening!,     # Compute a whitening transform based on covariance (input will be overwritten)
     invsqrtm,           # Compute C^{-1/2}, i.e. inv(sqrtm(C))
 
     ## pca
     PCA,                # Type: Principal Component Analysis model
-
     pcacov,             # PCA based on covariance
     pcasvd,             # PCA based on singular value decomposition of input data
     principalratio,     # the ratio of variances preserved in the principal subspace
     principalvar,       # the variance along a specific principal direction
     principalvars,      # the variances along all principal directions
-
     tprincipalvar,      # total principal variance, i.e. sum(principalvars(M))
     tresidualvar,       # total residual variance
 
     ## ppca
     PPCA,               # Type: the Probabilistic PCA model
-
     ppcaml,             # Maximum likelihood probabilistic PCA
     ppcaem,             # EM algorithm for probabilistic PCA
     bayespca,           # Bayesian PCA
@@ -67,10 +68,7 @@ module MultivariateStats
     KernelPCA,          # Type: the Kernel PCA model
 
     ## cca
-    CCA,                 # Type: Correlation Component Analysis model
-    WilksLambdaTest,     # Wilks lambda statistics and tests
-    PillaiTraceTest,     # Pillai trace statistics and tests
-    LawleyHotellingTest, # Lawley-Hotelling statistics and tests
+    CCA,                # Type: Correlation Component Analysis model
 
     ccacov,             # CCA based on covariances
     ccasvd,             # CCA based on singular value decomposition of input data
@@ -81,18 +79,17 @@ module MultivariateStats
     MetricMDS,
     classical_mds,      # perform classical MDS over a given distance matrix
     stress,             # stress evaluation
-
-    gram2dmat, gram2dmat!,  # Gram matrix => Distance matrix
-    dmat2gram, dmat2gram!,  # Distance matrix => Gram matrix
+    gram2dmat,
+    gram2dmat!,  # Gram matrix => Distance matrix
+    dmat2gram,
+    dmat2gram!,  # Distance matrix => Gram matrix
 
     ## lda
     LinearDiscriminant,     # Type: Linear Discriminant functional
     MulticlassLDAStats,     # Type: Statistics required for training multi-class LDA
     MulticlassLDA,          # Type: Multi-class LDA model
     SubspaceLDA,            # Type: LDA model for high-dimensional spaces
-
     ldacov,                 # Linear discriminant analysis based on covariances
-
     classweights,           # class-specific weights
     classmeans,             # class-specific means
     withclass_scatter,      # with-class scatter matrix
@@ -103,56 +100,58 @@ module MultivariateStats
 
     ## ica
     ICA,                    # Type: the Fast ICA model
-
     fastica!,               # core algorithm function for the Fast ICA
 
     ## fa
     FactorAnalysis,         # Type: the Factor Analysis model
-
     faem,                   # EM algorithm for factor analysis
     facm,                   # CM algorithm for factor analysis
 
     ## CA, MCA
-    CA,
-    MCA,
-    objectscores,
-    variablescores,
-    inertia
-
-    ## source files
-    include("types.jl")
-    include("common.jl")
-    include("lreg.jl")
-    include("whiten.jl")
-    include("pca.jl")
-    include("ppca.jl")
-    include("kpca.jl")
-    include("cca.jl")
-    include("cmds.jl")
-    include("mmds.jl")
-    include("lda.jl")
-    include("ica.jl")
-    include("fa.jl")
-    include("mca.jl")
-
-    ## deprecations
-    @deprecate indim(f) size(f,1)
-    @deprecate outdim(f) size(f,2)
-    @deprecate transform(f, x) predict(f, x)
-    @deprecate indim(f::Whitening) length(f::Whitening)
-    @deprecate outdim(f::Whitening) length(f::Whitening)
-    @deprecate tvar(f::PCA) var(f::PCA)
-    @deprecate classical_mds(D::AbstractMatrix, p::Int) predict(fit(MDS, D, maxoutdim=p, distances=true))
-    @deprecate transform(f::MDS) predict(f::MDS)
-    @deprecate xindim(M::CCA) size(M,1)
-    @deprecate yindim(M::CCA) size(M,2)
-    @deprecate outdim(M::CCA) size(M,3)
-    @deprecate correlations(M::CCA) cor(M)
-    @deprecate xmean(M::CCA) mean(M, :x)
-    @deprecate ymean(M::CCA) mean(M, :y)
-    @deprecate xprojection(M::CCA) projection(M, :x)
-    @deprecate yprojection(M::CCA) projection(M, :y)
-    @deprecate xtransform(M::CCA, x) predict(M, x, :x)
-    @deprecate ytransform(M::CCA, y) predict(M, y, :y)
+    CA,                     # Type: correspondence analysis
+    MCA,                    # Type: multiple correspondence analysis
+    ca,                     # fit and return a correspondence analysis
+    mca,                    # fit and return a multiple correspondence analysis
+    objectscores,           # return the object scores or coordinates from CA or MCA
+    variablescores,         # return the variable/category scores or coordinates from CA or MCA
+    inertia                 # return the inertia (derived from eigenvalues) for CA
+
+## source files
+include("types.jl")
+include("common.jl")
+include("lreg.jl")
+include("whiten.jl")
+include("pca.jl")
+include("ppca.jl")
+include("kpca.jl")
+include("cca.jl")
+include("cmds.jl")
+include("mmds.jl")
+include("lda.jl")
+include("ica.jl")
+include("fa.jl")
+include("mca.jl")
+
+## deprecations
+@deprecate indim(f) size(f, 1)
+@deprecate outdim(f) size(f, 2)
+@deprecate transform(f, x) predict(f, x)
+@deprecate indim(f::Whitening) length(f::Whitening)
+@deprecate outdim(f::Whitening) length(f::Whitening)
+@deprecate tvar(f::PCA) var(f::PCA)
+@deprecate classical_mds(D::AbstractMatrix, p::Int) predict(
+    fit(MDS, D, maxoutdim = p, distances = true),
+)
+@deprecate transform(f::MDS) predict(f::MDS)
+@deprecate xindim(M::CCA) size(M, 1)
+@deprecate yindim(M::CCA) size(M, 2)
+@deprecate outdim(M::CCA) size(M, 3)
+@deprecate correlations(M::CCA) cor(M)
+@deprecate xmean(M::CCA) mean(M, :x)
+@deprecate ymean(M::CCA) mean(M, :y)
+@deprecate xprojection(M::CCA) projection(M, :x)
+@deprecate yprojection(M::CCA) projection(M, :y)
+@deprecate xtransform(M::CCA, x) predict(M, x, :x)
+@deprecate ytransform(M::CCA, y) predict(M, y, :y)
 
 end # module

src/mca.jl

@@ -70,6 +70,12 @@ function fit!(ca::CA, d::Int)
     P, D, Q = svd(ca.SR)
     Dq = Diagonal(D)[:, 1:d]
 
+    # Check that there are no repeated non-zero eigenvalues.
+    d = diff(D[D .> 1e-10])
+    if maximum(d) >= -1e-10
+        @warn("The indicator matrix has repeated non-zero eigenvalues")
+    end
+
     Wr = Diagonal(sqrt.(ca.rm))
     Wc = Diagonal(sqrt.(ca.cm))
     ca.F = Wr \ P * Dq