Learning the parts of object by NMF

               

本文为Letters to nature上文章Learning the parts of objects by non-negativematrix factorization的读书笔记，针对如何基于NMF在神经网络中学习一个object的各层part做出理论上的分析，并在人脸part学习和text语义特征学习上做了相应实验。本文不含如何去解NMF，只给出非负约束下矩阵分解的结果。

 

Learning the parts of object by NMF

Rachel Zhang

 

1. Theoretical basis and Motivation

1. Part-based representation

    There is psychological and physiological evidence for parts-based representations in the brain, and certaincomputational theories of object recognition rely on such representations.

2. What is NMF? Why use NFM in NeuralNetwork?

    NMF: non-negative matrix factorization

    Difference: PCA, VQ learn holistic, not part-based representations, NMFdifferent from them via non-negative constrains.

    Virtue in Neural Network:

                1. Firing rates(number of spikes in a window) of neurons are nevernegative. 

                2. Synaptic strengths do not changesign.

 

 

2. Applied Experiments

3. Applied result of PCA, VQ and NMF

    Figure 1 shows the 3 methods learn to represent a face as a linearcombination of basis images.

    VQ: discovers a basisconsisting of whole-face prototypes.

    PCA: discovers a basis of ‘eigenfaces’,some of which resemble distorted versions of wholefaces.

    NMF: discovers a basis consisting localized features that correspond better withintuitive notions of the parts of faces.

Figure 1.Basis of NMF, VQ and PCA

对于图中的encoding，红色表示负数，灰黑表示正数，颜色程度表示大小。

    

 

    4. Matrix Factorization framework

    为什么NMF会得出与PCA和VQ迥然不同的基呢？我们这里将这三种方法展示在Matrix factorizationframework里，首先看一下这个框架。图像数据库用n*m的矩阵V表示，每列包括m张人脸图中一张的n个非负像素值。这三种方法构造近似矩阵分解：V≈WH，or

V_iu≈(WH)_iu≈Σ_aW_iaH_au

    W∈R^n*r中的r列是basis images. H∈R^r*m中的每一列是