Structure preserving non-negative matrix factorization for dimensionality reduction

Abstract Single cell RNA-sequencing (scRNA-seq) technology, a powerful tool for analyzing the entire transcriptome at single cell level, is receiving increasing research attention. The presence of dropouts is an important characteristic of scRNA-seq data that may affect the performance of downstream analyses, such as dimensionality reduction and clustering. Cells sequenced to lower depths tend to have more dropouts than those sequenced to greater depths. In this study, we aimed to develop a dimensionality reduction method to address both dropouts and the non-negativity constraints in scRNA-seq data. The developed method simultaneously performs dimensionality reduction and dropout imputation under the non-negative matrix factorization (NMF) framework. The dropouts were modeled as a non-negative sparse matrix. Summation of the observed data matrix and dropout matrix was approximated by NMF. To ensure the sparsity pattern was maintained, a weighted ℓ1 penalty that took into account the dependency of dropouts on the sequencing depth in each cell was imposed. An efficient algorithm was developed to solve the proposed optimization problem. Experiments using both synthetic data and real data showed that dimensionality reduction via the proposed method afforded more robust clustering results compared with those obtained from the existing methods, and that dropout imputation improved the differential expression analysis.

Download Full-text

Robust Structure Preserving Nonnegative Matrix Factorization for Dimensionality Reduction

Mathematical Problems in Engineering ◽

10.1155/2016/7474839 ◽

2016 ◽

Vol 2016 ◽

pp. 1-14

Author(s):

Bingfeng Li ◽

Yandong Tang ◽

Zhi Han

Keyword(s):

Dimensionality Reduction ◽

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Noisy Data ◽

Nonnegative Matrix ◽

Structure Preserving ◽

Structure Preservation ◽

Significant Performance ◽

Linear Dimensionality Reduction ◽

Low Dimensional

As a linear dimensionality reduction method, nonnegative matrix factorization (NMF) has been widely used in many fields, such as machine learning and data mining. However, there are still two major drawbacks for NMF: (a) NMF can only perform semantic factorization in Euclidean space, and it fails to discover the intrinsic geometrical structure of high-dimensional data distribution. (b) NMF suffers from noisy data, which are commonly encountered in real-world applications. To address these issues, in this paper, we present a new robust structure preserving nonnegative matrix factorization (RSPNMF) framework. In RSPNMF, a local affinity graph and a distant repulsion graph are constructed to encode the geometrical information, and noisy data influence is alleviated by characterizing the data reconstruction term of NMF withl2,1-norm instead ofl2-norm. With incorporation of the local and distant structure preservation regularization term into the robust NMF framework, our algorithm can discover a low-dimensional embedding subspace with the nature of structure preservation. RSPNMF is formulated as an optimization problem and solved by an effective iterative multiplicative update algorithm. Experimental results on some facial image datasets clustering show significant performance improvement of RSPNMF in comparison with the state-of-the-art algorithms.

Download Full-text