---
title: "Truncated SVD"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Truncated SVD}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
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](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.TruncatedSVD.html).

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.

```{r}
A <- rbind(c(1,3), c(2,-4))

tsvd(A, 1, "auto")
tsvd(A, 1, "sklearn")
tsvd(A, 1, "none")
```

## References

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