Metadata-Version: 2.1
Name: IncSVD
Version: 0.2.3
Summary: Towards Efficient Updating of Truncated Singular Value Decompostion
Author-email: Haoran Deng <denghaoran@zju.edu.cn>
Project-URL: Homepage, https://github.com/HaoranDeng/IncSVD
Project-URL: Bug Tracker, https://github.com/HaoranDeng/IncSVD/issues
Classifier: Programming Language :: Python :: 3
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Requires-Python: >=3.6
Description-Content-Type: text/markdown
License-File: LICENSE
Requires-Dist: numpy>=1.19
Requires-Dist: scikit-learn>=0.23
Requires-Dist: scipy>=1.5

# IncSVD: A python package for dynamic Truncated SVD

[![PyPI](https://img.shields.io/badge/-PyPI-FFFFFF?style=plastic&logo=pypi&logoColor=3775A9)](https://pypi.org/project/IncSVD/)
[![PyPI](https://img.shields.io/badge/-PyPI-FFFFFF?style=plastic&logo=pypi&logoColor=3775A9)](https://pypi.org/project/IncSVD/)
[![PyPI](https://img.shields.io/badge/-PyPI-FFFFFF?style=plastic&logo=pypi&logoColor=3775A9)](https://pypi.org/project/IncSVD/)
[![PyPI](https://img.shields.io/badge/-PyPI-FFFFFF?style=plastic&logo=pypi&logoColor=3775A9)](https://pypi.org/project/IncSVD/)
[![https://arxiv.org/pdf/2401.09703.pdf](https://img.shields.io/badge/-arXiv-B31B1B?style=plastic&logo=arxiv&logoColor=FFFFFF)](https://arxiv.org/pdf/2401.09703.pdf)
[![https://arxiv.org/pdf/2401.09703.pdf](https://img.shields.io/badge/-arXiv-B31B1B?style=plastic&logo=arxiv&logoColor=FFFFFF)](https://arxiv.org/pdf/2401.09703.pdf)
[![https://arxiv.org/pdf/2401.09703.pdf](https://img.shields.io/badge/-arXiv-B31B1B?style=plastic&logo=arxiv&logoColor=FFFFFF)](https://arxiv.org/pdf/2401.09703.pdf)
[![https://arxiv.org/pdf/2401.09703.pdf](https://img.shields.io/badge/-arXiv-B31B1B?style=plastic&logo=arxiv&logoColor=FFFFFF)](https://arxiv.org/pdf/2401.09703.pdf)

**IncSVD** is a python package capable of dynamically maintaining the incremental Truncated Singular Value Decomposition (Truncated SVD) of evolving matrices.

This is the code implementation of the paper "Fast Updating Truncated SVD for Representation Learning with Sparse Matrices" (ICLR'24).

## Install and Setup.

It is recommended to use python 3.8 or higher and install **IncSVD** with the following command.

```shell
pip install IncSVD
```

## User Guide

Initialize the **IncSVD** using an $m \times n$ matrix `data_init` given the rank (dimension) `k` for which the truncated SVD needs to be computed. Here is an example to initialize a $1000 \times 1000$ matrix with truncated dimension $k = 64$.

***class EvolvingMatrix(data, k, sparse = True, method = "RPI")***
- **data: data matrix**
  Data matrix used to initialize truncated SVD.
  The format of this initial matrix can be `np.ndarray` or `scipy.sparse`.
- **k: *int***
  Truncated dimension in the maintained SVD.
  It should be a positive integer not greater than the length of the sides of the original matrix.
- **sparse: *bool, default=True*** 
  Set true implies the update process will employ the proposed acceleration methods [1].
  Set false implies using the original methods (ZhaSimon's [2], Vecharynski's [3], Yamazaki's [4]).
- **method: {'ZhaSimon', 'GKL', 'RPI'}, default='RPI'**
  Method for SVD update.
  It can be chosen from `['ZhaSimon', 'GKL', 'RPI']`. 


```python
import scipy.sparse
import IncSVD.EvolvingMatrix as EM
m, n, k = 1000, 1000, 64

# data_init = scipy.sparse.rand(m, n, density=0.005).tocsr()
M = EM.EvolvingMatrix(data_init, k, sparse=True, method="ZhaSimon")
```

> [!TIP]
>
> We recommend using `GKL` or `RPI` when the rank of each update matrix (e.g. adding many rows at once) is large.


### Row / Column Update

Expand the original matrix in row or column dimensions and update the corresponding SVD results.

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alt=""/>

***add_row(update_matrix, l=None, t=None)***
- **update_matrix: data matrix**
  Data matrix to be appended. 
  This matrix should have the same number of **columns** as the original matrix. If type `sparse` is True, this matrix should be in `scipy.sparse._csr.csr_matrix`.
- **l: {*int, None*}**
  Approximate dimension for the update matrix.
  When using GKL or RPI, two methods that require an approximation space, it is necessary to set `l`. The update matrix of rank `s` will be approximated with a smaller space of rank `l` for further speedup. Set to `None` when GKL and RPI is not applied.
- **t: {*int, None*}**
  The number of iterations to perform in the random power iteration.
  It needs to be set when using the RPI. This approximation is more accurate when `t` is larger, while the computational overhead is larger. Set to `None` when RPI is not applied.

***add_column(update_matrix, l=None, t=None)***
- **update_matrix: data matrix**
  Data matrix to be appended. 
  This matrix should have the same number of **rows** as the original matrix. If type `sparse` is True, this matrix should be in `scipy.sparse._csc.csc_matrix`.
- **l: {*int, None*}**
  Approximate dimension for the update matrix.
  Set to `None` when GKL and RPI is not applied.
- **t: {*int, None*}**
  The number of iterations to perform in the random power iteration.
  Set to `None` when RPI is not applied.


```python
''' Add rows '''
# data_append_row = scipy.sparse.rand(m, 10, density=0.005).tocsr() * 10
M.add_row(data_append_row)

''' Add columns '''
# data_append_col = scipy.sparse.rand(n, 10, density=0.005).tocsc() * 10
M.add_column(data_append_col)
```


> [!NOTE]
>
> If type `sparse` is True.
>
> - [Add row] The input `data_append_row`  is required to have the same number of columns as the original matrix columns and be in `scipy.sparse._csr.csr_matrix` type.
> - [Add column] The input `data_append_col` is required to have the same number of rows as the original matrix rows and be in `scipy.sparse._csc.csc_matrix` type.

### Low-rank Update.

Perform low-rank update $\overline{\mathbf{A}} = \mathbf{A} + \mathbf{D}_m \cdot \mathbf{E}_m^{\top}$, where $\mathbf{A}$ is the original matrix, $\mathbf{D}_m \in \mathbb{R}^{m \times s}$ and $\mathbf{E}_m \in \mathbb{R}^{n \times s}$.

<img 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K8byo6jzpw8eW0JMgNAOdIMgsVZZoh5WhtlTu8DAAAAwGoTZAYAAAAAAKqQokkAAAAAfaQZBAAwjBQoAcqWznop0vcAAMuXgszHnH9tvHZZZpcgMwDQVZpB0N+u3Ts7x5jb69qAcnvPuvZ/r0v3bKTdI70XAAAAAKtNkBkAAAAAAKhCiiYBAAAA9JFmEADAMFKgBChbOuulSN8DACxfCjI/5k2fi9cuy+wSZAYAukozCPppY8gpkjytjTBvJprchpm7Bp5baQ8AAAAAVp8gMwAAAAAAUIUUTQIAAADoI80gAIBhpEAJULZ01kuRvgcAWL4UZP7+554Ur12W2SXIDAB0lWYQ9LNROLn9+3RfF22YOe05rc/+AAAAAIxLkBkAAAAAAKhCiiYBAAAA9JFmEADAMFKgBChbOuulSN8DACxfCjKn65ZpdgkyAwBdpRkEW7dRMHkRseSNntH+fboPAAAAgNUnyAwAAAAAAFQhRZMAAAAA+kgzCABgGClQApQtnfVSpO8BAJZvNsh89Y23xuuWaXYJMgMAXaUZBFuXAsnT0j1b0Yad0/4tQWYAAACAcgkyAwAAAAAAVUjRJAAAAIA+0gwCABhGCpQAZUtnvRTpewCA5ZsNMl/61Vvidcs0uwSZAYCu0gyCrWlDyCmQvG6RoeRdu3fGZ7Tav0v3AAAAALD6BJkBAAAAAIAqpGgSAAAAQB9pBgEADCMFSoCypbNeivQ9AMDyCTLfnSAzAJQrzSDYmhRHnrbIIHMrPaOVrgUAAACgDILMAAAAAABAFVI0CQAAAKCPNIMAAIaRAiVA2dJZL0X6HgBg+QSZ706QGQDKlWYQbE2KI0/btXtnvG+rduw44G7PaP8sXQsAAABAGQSZAQAAAACAKqRoEgAAAEAfaQYBAAwjBUqAsqWzXor0PQDA8q1ikPnOOycvM1mCzABAV2kGwea1seXZOPKsRQeZ0zMPOfSgeC0AAAAAZRBkBgAAAAAAqpCiSQAAAAB9pBkEADCMFCgBypbOeinS9wAAy7eKQebb7vjGIrMgMwDQVZpBsHmCzAAAAAAsgiAzAAAAAABQhRRNAgAAAOgjzSAAgGGkQAlQtnTWS5G+BwBYvlUMMu+7XZAZANiaNINg87oEmcWSAQAAANiIIDMAAAAAAFCFFE0CAAAA6CPNIACAYaRACVC2dNZLkb4HAFi+VQwy33zbHZO3WVuCzABAV2kGweZ1CTLv2HFAvBcAAAAA1gkyAwAAAAAAVUjRJAAAAIA+0gwCABhGCpQAZUtnvRTpewCA5VvFIPPefYLMAMDWpBkEm9clyNw65NCD4v0AAAAA0BJkBgAAAAAAqpCiSQAAAAB9pBkEADCMFCgBypbOeinS9wAAy7eKQebrb7l98jZrS5AZAOgqzSDYmhRgTtp4c7ofAAAAAASZAQAAAACAKqRoEgAAAEAfaQYBAAwjBUqAsqWzXor0PQDA8q1ikPnam2+bvM3aWnaQ+WFHnTF58trac8XeeB0AsHrSDIKt2bHjgBhgTg459KC4BwAAAADbmyAzAAAAAABQhRRNAgAAAOgjzSAAgGGkQAlQtnTWS5G+BwBYvlUMMt+47/bJ26ytb37SMfG6ofzESwWZAaBUaQbB1uzavTPGl+cRZQYAAABgliAzAAAAAABQhRRNAgAAAOgjzSAAgGGkQAlQtnTWS5G+BwBYvlUMMs+ub3/qsfG6oTz0JadPnry2BJkBoBxpBsHW7dhxQIwvzyPKDAAAAMA0QWYAAAAAAKAKKZoEAAAA0EeaQQAAw0iBEqBs6ayXIn0PALB8qxZk/tdPP27yJl9f93rm8fHaoTzkrwSZAaBUaQZBPym8vBFhZgAAAABagswAAAAAAEAVUjQJAAAAoI80gwAAhpECJUDZ0lkvRfoeAGD5Vi3IfL/nnzx5k6+vH3/xafHaoTzoSEFmAChVmkHQz67dO2N0eSOizAAAAAAIMgMAAAAAAFVI0SQAAACAPtIMAgAYRgqUAGVLZ70U6XsAgOVbtSDzr73+nMmbfH095k2fi9cO5YCXnDF58toSZAaAcqQZBP21ceUUXe5CmBkAAABg+xJkBgAAAAAAqpCiSQAAAAB9pBkEADCMFCgBypbOeinS9wAAyzcbZP7y9fvidcvy0k9+cfImX18vOeaL8dqh/OzLPj158toSZAaAcqQZBIuxa/fOGFzuYseOA+66P+0LAAAAQL0EmQEAAAAAgCqkaBIAAABAH2kGAQAMIwVKgLKls16K9D0AwPLNBplvvf3OeN2yXH79vsmbfH2dd9VN8dqh/PJrzp48eW0JMgNAOdIMgsVq48oputzFIYceFPcEAAAAoE6CzAAAAAAAQBVSNAkAAACgjzSDAACGkQIlQNnSWS9F+h4AYPlmg8zt+o6nHhevHdrzPnrJ5A3uvn79DefEe4bwu28/d/LUtSXIDADlSDMIFq8NK6fgcheizAAAAADbhyAzAAAAAABQhRRNAgAAAOgjzSAAgGGkQAlQtnTWS5G+BwBYvhRk/k9HnBKvHdIz/+GiydPzuvDqm5sfe9Gp8d5Fe8Y/XDh56toSZAaAcqQZBMPYtXtns2PHATG6vJH2vvb+tC8AAAAA9RBkBgAAAAAAqpCiSQAAAAB9pBkEADCMFCgBypbOeinS9wAAy5eCzI947dnx2qEctPOCyZP3v/bdfmfzW2/+XNxjkV523GWTJ64tQWYAKEeaQTCsQw49KEaXuxBlBgAAAKibIDMAAAAAAFCFFE0CAAAA6CPNIACAYaRACVC2dNZLkb4HAFi+FGQ+fNcl8dpF+aHnndz82uvPuSt8fOHVN0+e2n21geSD339B86AjT4/79/XhPddMnrS2BJkBoBxpBsFybCXMvGPHAXEvAAAAAOogyAwAAAAAAFQhRZMAAAAA+kgzCABgGClQApQtnfVSpO8BAJYvBZlPvPi6eG0fbzv9yuaML97Q7N13x+Qpi1nX7L2tOfvyG5tPnP/V5pCjL4rP3ox/8/TjJjt/fQkyA0A50gyC5RFlBgAAAGCaIDMAAAAAAFCFFE0CAAAA6CPNIACAYaRACVC2dNZLkb4HAFi++z3/5LXq8Mz6pVd/Jl6/Vftuv3Oy83DrTadeEZ+9GS877rLJbl9fgswAUI40g2D5Nhtm3rV7Z9wHAAAAgLIJMgMAAAAAAFVI0SQAAACAPtIMAgAYRgqUAGVLZ70U6XsAgOWbF2T+8J5r4vVbdfD7Lxjcb775c/HZXT3sqDMmX/+NS5AZAMqRZhCMYzNR5h07Doh7AAAAAFA2QWYAAAAAAKAKKZoEAAAA0EeaQQAAw0iBEqBs6ayXIn0PALB884LM7frdt58b76nRjqPObK668dbJl3/jEmQGgHKkGQTj2UyUedfunXEPAAAAAMolyAwAAAAAAFQhRZMAAAAA+kgzCABgGClQApQtnfVSpO8BAJZvf0Hmdh3wkjPifTX51dd/trnjzskHhyXIDADlSDMIxtU1yizIDAAAAFAfQWYAAAAAAKAKKZoEAAAA0EeaQQAAw0iBEqBs6ayXIn0PALB89z18/0Hmz195U3PvQ06I95bsR444tTnwvec3J11y/eRL5y9BZgAoR5pBML4UYJ61Y8cB8V4AAAAAyiXIDAAAAAAAVCFFkwAAAAD6SDMIAGAYKVAClC2d9VKk7wEAlm+jIHO72ijzA158Wry/FPd65vHNf3vlWc2hH7yoOeGi6yZf1m0JMgNAOdIMgvEdcuhBMcI8TZAZAAAAoD6CzAAAAAAAQBVSNAkAAACgjzSDAACGkQIlQNnSWS9F+h4AYPm6BJnbtXffHc2jXvfZuMeq23HUmZOv2NoSZAaAcqQZBOPbtXtnjDBPE2QGAAAAqI8gMwAAAAAAUIUUTQIAAADoI80gAIBhpEAJULZ01kuRvgcAWL5/edAnm9ef/OW18nCHdfiuS+I+q2x/QeZ9t9/ZXHHDrc3nr7ypOfmS65uPnntN884zr2xe86nLmxd9/NLmmUdf1Dzh3efFfQGA1ZNmEMzXhpIPOfSgb5CuW4QUYZ4myAwAAABQH0FmAAAAAACgCimaBAAAANBHmkEAAMNIgRKgbOmslyJ9DwAwrl9+zdl3xYg3Wsecf23z0JecHvdYVf/3809p/u2zPtX8q4OPjX8PANQhzSCYrw0wz4aR03WLMPucWYLMAAAAAPURZAYAAAAAAKqQokkAAAAAfaQZBAAwjBQoAcqWznop0vcAAKvj115/TnP0OV9ZKzDPWS/++KXNtx4kcAwArI40g2C+NoI8G0ZO1y3C7HNmtXHodB8AAAAA5RJkBgAAAAAAqpCiSQAAAAB9pBkEADCMFCgBypbOeinS9wAAq+dbnnRM89i37Gk+dfF1axXmmfXVm25rnvaBC+O9AADLlmYQzJfCyLt274zX9pWeNU2QGQAAAKA+gswAAAAAAEAVUjQJAAAAoI80gwAAhpECJUDZ0lkvRfoeAGC1fcdTj2ue8O7zmj1X7F2rMU+ty6/f1/zIEafG+wAAliXNIMja8HIKI48VZB7quQAAAACMR5AZAAAAAACoQoomAQAAAPSRZhAAwDBSoAQoWzrrpUjfAwCU496HnNAc+sGLmituuHWtyPy19ZMvPSNeCwCwLGkGQXbIoQfFMPKOHQfE6/uY96xp6T4AAAAAyibIDAAAAAAAVCFFkwAAAAD6SDMIAGAYKVAClC2d9VKk7wEAynSf557UHPmJSwWZAYDRpRkE2f4iybt274z3bFV6xrT2XdJ9AAAAAJRNkBkAAAAAAKhCiiYBAAAA9JFmEADAMFKgBChbOuulSN8DAAAA0EeaQZClMPK0dM9W7C/8vC7dBwAAAED5BJkBAAAAAIAqpGgSAAAAQB9pBgEADCMFSoCypbNeivQ9AAAAAH2kGQRZCiNP27HjgHjfZnSJMbfXpHsBAAAAKJ8gMwAAAAAAUIUUTQIAAADoI80gAIBhpEAJULZ01kuRvgcAAACgjzSD4O66hJLXbSWYvGv3z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***update_weight(self, update_matrix_B, update_matrix_C, l=None, t=None):***

- **update_matrix_B: data matrix**
  Data matrix to be appended. 
  This matrix should have the same number of **columns** as the original matrix. If type `sparse` is True, this matrix should be in `scipy.sparse._csc.csc_matrix`.
- **update_matrix_C: data matrix**
  Data matrix to be appended. 
  This matrix should have the same number of **columns** as the original matrix. If type `sparse` is True, this matrix should be in `scipy.sparse._csc.csc_matrix`.
- **l: {*int, None*}**
  Approximate dimension for the update matrix.
  Set to `None` when GKL and RPI is not applied.
- **t: {*int, None*}**
  The number of iterations to perform in the random power iteration. 
  Set to `None` when RPI is not applied.


```python
''' Low-rank update '''
# data_dm = scipy.sparse.rand(m, 10, density=0.005).tocsc() * 10
# data_em = scipy.sparse.rand(n, 10, density=0.005).tocsc() * 10
M.update_weight(data_dm, data_em)
```

> [!NOTE]
>
> If type `sparse` is True, the input `data_dm` and `data_em`  is required to be in `scipy.sparse._csc.csc_matrix` type.

### Get the result.

Queries the current SVD result.

```python
''' Get the result. '''
Uk, Sigmak, Vk = M.Uk, M.Sigmak, M.Vk

''' Get a row of singular vectors. '''
# i = 0
Uk0, Vk0 = M.Uki(i), M.Vki(i)

''' A low-rank approximation of data matrix can be obtained from. '''
Ak = Uk @ np.diag(Sigmak) @ Vk.T
```

## Contact Us    

If you have any questions about this code repository, feel free to `raise an issue` or email `denghaoran@zju.edu.cn`.


## Citations.

If you find our work useful, please consider citing the following paper:

```
@inproceedings{deng2024incsvd,
title={Fast Updating Truncated {SVD} for Representation Learning with Sparse Matrices},
author={Haoran Deng and Yang Yang and Jiahe Li and Cheng Chen and Weihao Jiang and Shiliang Pu},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=CX2RgsS29V}
}
```




