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# Graph-Multi-NMF-Feature-Clustering
Codes for __Feature Extraction via Multi-view Non-negative Matrix Factorization with Local Graph Regularization__

## Introduction

Codes for __Feature Extraction via Multi-view Non-negative Matrix Factorization with Local Graph Regularization__.

Motivated by manifold learning and multi-view Non-negative Matrix Factorization (NMF), we introduce a novel feature extraction method via multi-view NMF with local graph regularization, where the inner-view relatedness between data is taken into consideration. We propose the matrix factorization objective function by constructing a nearest neighbor graph to integrate local geometrical information of each view and apply two iterative updating rules to effectively solve the optimization problem.

Please cite the following information:

```
@inproceedings{wang2015multi,
title={Feature Extraction via Multi-view Non-negative Matrix Factorization with Local Graph Regularization},
author={Wang, Zhenfan and Kong, Xiangwei and Fu, Haiyan and Li, Ming and Zhang, Yujia},
booktitle={Image Processing (ICIP), 2015 IEEE International Conference on},
year={2015},
organization={IEEE}
}
```

## Demo

There is a demo in `GMultiNMF/demo_digit.m` working for hand-written digits recognition. See releases to download the full demo with dataset.

## Results

The accuracy (AC) and normalized mutual information (NMI) of different algorithms on three datasets:

![1](https://cloud.githubusercontent.com/assets/853842/8086601/c6d273f2-0fc8-11e5-8ceb-85c84239ec06.png)

![2](https://cloud.githubusercontent.com/assets/853842/8086602/c70111a8-0fc8-11e5-9f6e-63f4d02a67b7.png)

From the tables, we can see that our proposed algorithm performs better in each dataset in terms of AC and NMI. Although other methods consider multiple feature integration, Co-reguSC and SC-ML use latent data relationship, the results demonstrate that our proposed Multi-view NMF with local graph regularization feature extraction framework can learn a better feature representation.

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