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Truncated SVD

library(rwig) |> suppressPackageStartupMessages()

Truncated Singular Value Decomposition (TSVD) is commonly used in machine learning for dimension reduction, for example it is implemented in scikit-learn.

However, a well known issue in SVD is the “sign indeterminacy”, meaning that the result columns might have different signs depending on how SVD is computed.

I implemented two versions: one as in scikit-learn, and another from Bro et al. (2008). The scikit-learn version specifies the maximum entry (in absolute value) should always be positive, and Bro et al. (2008) entails a specific algorithm for resolving the signs.

A <- rbind(c(1,3), c(2,-4))

tsvd(A, 1, "auto")
#>           [,1]
#> [1,] -2.689994
#> [2,]  4.352502
tsvd(A, 1, "sklearn")
#>           [,1]
#> [1,] -2.689994
#> [2,]  4.352502
tsvd(A, 1, "none")
#>           [,1]
#> [1,] -2.689994
#> [2,]  4.352502

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