Normalized dimensionality reduction using nonnegative matrix factorization
Normalized dimensionality reduction using nonnegative matrix factorization
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DOI：
10.1016/j.neucom.2009.11.046
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发表时间：
2010-06
期刊：
影响因子：
6
通讯作者：
Zhenfeng Zhu;Yue-Fei Guo;Xingquan Zhu;X. Xue
中科院分区：
文献类型：
--
作者：
Zhenfeng Zhu;Yue-Fei Guo;Xingquan Zhu;X. Xue
本文提出了一种利用非负矩阵分解（NCMF）进行降维的迭代归一化压缩方法。为了将实例矩阵X分解为C×M，定义了一个目标函数来对基矩阵C和系数矩阵m施加归一化约束。我们认为，在许多应用中，实例通常以一种方式或另一种方式进行归一化。通过将数据归一化约束整合到目标函数中，并对实例矩阵进行转置，可以直接发现不同维度之间的关系，并设计出有效的矩阵分解过程。本文假设实例矩阵中的特征维数是归一化的，提出了一种迭代解NCMF，实现了快速的矩阵分解降维。因此，基矩阵可以看作是压缩矩阵，系数矩阵可以看作是映射矩阵。NCMF简单、有效，只需要初始化映射矩阵。在文本、生物和图像数据上的实验对比表明，NCMF的计算时间减少了21.02%，映射矩阵的稀疏度提高了39.60%，聚类精度提高了8.59%。
In this paper, we propose an iterative normalized compression method for dimensionality reduction using non-negative matrix factorization (NCMF). To factorize the instance matrix X into C×M, an objective function is defined to impose the normalization constraints to the basis matrix C and the coefficient matrix M. We argue that in many applications, instances are often normalized in one way or the other. By integrating data normalization constraints into the objective function and transposing the instance matrix, one can directly discover relations among different dimensions and devise effective and efficient procedure for matrix factorization. In the paper, we assume that feature dimensions in instance matrix are normalized, and propose an iterative solution NCMF to achieve rapid matrix factorization for dimensionality reduction. As a result, the basis matrix can be viewed as a compression matrix and the coefficient matrix becomes a mapping matrix. NCMF is simple, effective, and only needs to initialize the mapping matrix. Experimental comparisons on text, biological and image data demonstrate that NCMF gains 21.02% computational time reduction, 39.60% sparsity improvement for mapping matrix, and 8.59% clustering accuracy improvement.