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,] 4.352502References
Bro, R., Acar, E., & Kolda, T. G. (2008). Resolving the sign ambiguity in the singular value decomposition. Journal of Chemometrics, 22(2), 135–140. https://doi.org/10.1002/cem.1122