Application of nonnegative matrix factorization to improve profile-profile alignment features for fold recognition and remote homolog detection

Background  

Nonnegative matrix factorization (NMF) is a feature extraction method that has the property of intuitive part-based representation of the original features. This unique ability makes NMF a potentially promising method for biological sequence analysis. Here, we apply NMF to fold recognition and remote homolog detection problems. Recent studies have shown that combining support vector machines (SVM) with profile-profile alignments improves performance of fold recognition and remote homolog detection remarkably. However, it is not clear which parts of sequences are essential for the performance improvement.     

Discriminant Projective Non-Negative Matrix Factorization

Projective non-negative matrix factorization (PNMF) projects high-dimensional non-negative examples X onto a lower-dimensional subspace spanned by a non-negative basis W and considers W^T X as their coefficients, i.e., X≈WW^T X. Since PNMF learns the natural parts-based representation Wof X, it has been widely used in many fields such as pattern recognition and computer vision. However, PNMF does not perform well in classification tasks because it completely ignores the label information of the dataset. This paper proposes a Discriminant PNMF method (DPNMF) to overcome this deficiency. In particular, DPNMF exploits Fisher''s criterion to PNMF for utilizing the label information. Similar to PNMF, DPNMF learns a single non-negative basis matrix and needs less computational burden than NMF. In contrast to PNMF, DPNMF maximizes the distance between centers of any two classes of examples meanwhile minimizes the distance between any two examples of the same class in the lower-dimensional subspace and thus has more discriminant power. We develop a multiplicative update rule to solve DPNMF and prove its convergence. Experimental results on four popular face image datasets confirm its effectiveness comparing with the representative NMF and PNMF algorithms.     

应用非负矩阵分解方法提取注意力相关脑电特征

介绍了非负矩阵分解算法(NMF)的基本原理,给出一种利用NMF进行脑电能量谱特征提取的方法。设计试验对10个被试在三种不同注意任务中的脑电信号进行特征提取,并采用人工神经网络作为分类器进行分类测试。结果表明,NMF算法在高维特征空间具有较强的特征选择能力,其分类正确率明显高于主分量分析(PCA)方法和直接法,三种意识任务的分类正确率分别达到84.5、88%和86.5。     

Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis

MOTIVATION: Many practical pattern recognition problems require non-negativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are non-negative. Sparse non-negative matrix factorizations (NMFs) are useful when the degree of sparseness in the non-negative basis matrix or the non-negative coefficient matrix in an NMF needs to be controlled in approximating high-dimensional data in a lower dimensional space. RESULTS: In this article, we introduce a novel formulation of sparse NMF and show how the new formulation leads to a convergent sparse NMF algorithm via alternating non-negativity-constrained least squares. We apply our sparse NMF algorithm to cancer-class discovery and gene expression data analysis and offer biological analysis of the results obtained. Our experimental results illustrate that the proposed sparse NMF algorithm often achieves better clustering performance with shorter computing time compared to other existing NMF algorithms. AVAILABILITY: The software is available as supplementary material.     

Knowledge-based gene expression classification via matrix factorization

MOTIVATION: Modern machine learning methods based on matrix decomposition techniques, like independent component analysis (ICA) or non-negative matrix factorization (NMF), provide new and efficient analysis tools which are currently explored to analyze gene expression profiles. These exploratory feature extraction techniques yield expression modes (ICA) or metagenes (NMF). These extracted features are considered indicative of underlying regulatory processes. They can as well be applied to the classification of gene expression datasets by grouping samples into different categories for diagnostic purposes or group genes into functional categories for further investigation of related metabolic pathways and regulatory networks. RESULTS: In this study we focus on unsupervised matrix factorization techniques and apply ICA and sparse NMF to microarray datasets. The latter monitor the gene expression levels of human peripheral blood cells during differentiation from monocytes to macrophages. We show that these tools are able to identify relevant signatures in the deduced component matrices and extract informative sets of marker genes from these gene expression profiles. The methods rely on the joint discriminative power of a set of marker genes rather than on single marker genes. With these sets of marker genes, corroborated by leave-one-out or random forest cross-validation, the datasets could easily be classified into related diagnostic categories. The latter correspond to either monocytes versus macrophages or healthy vs Niemann Pick C disease patients.     

基于LNMF的癌症基因表达谱数据的特征提取

海量数据的存在是现代信息社会的一大特点,如何在成千上万的基因中有效地选出样本的分类特征对癌症的诊治具有重要意义。采用局部非负矩阵分解方法对癌症基因表达谱数据进行特征提取。首先对基因表达谱数据进行筛选,然后构造局部非负矩阵并对其进行分解得到维数低、能充分表征样本的特征向量,最后用支持向量机对特征向量进行分类。结果表明该方法的可行性和有效性。     

Ensemble non-negative matrix factorization methods for clustering protein-protein interactions

MOTIVATION: When working with large-scale protein interaction data, an important analysis task is the assignment of pairs of proteins to groups that correspond to higher order assemblies. Previously a common approach to this problem has been to apply standard hierarchical clustering methods to identify such a groups. Here we propose a new algorithm for aggregating a diverse collection of matrix factorizations to produce a more informative clustering, which takes the form of a 'soft' hierarchy of clusters. RESULTS: We apply the proposed Ensemble non-negative matrix factorization (NMF) algorithm to a high-quality assembly of binary protein interactions derived from two proteome-wide studies in yeast. Our experimental evaluation demonstrates that the algorithm lends itself to discovering small localized structures in this data, which correspond to known functional groupings of complexes. In addition, we show that the algorithm also supports the assignment of putative functions for previously uncharacterized proteins, for instance the protein YNR024W, which may be an uncharacterized component of the exosome.     

An approach for improving repeatability and reliability of non-negative matrix factorization for muscle synergy analysis

The aim of this study was to evaluate non-negative matrix factorization (NMF) and concatenated NMF (CNMF) to analyze and reliably extract muscle synergies. NMF and CNMF were used to extract knee joint muscle synergies from surface EMGs collected during a weight bearing, force matching task. Repeatability and between subject similarity were evaluated for each method using intra-class correlation coefficients (ICCs). High repeatability was found for CNMF (>0.99; 0.99–1.0) compared to NMF (>0.26; range 0.26–0.98). Reasonable consistency across subjects was improved using the CNMF over the NMF approach. CNMF was found to be a more reliable approach than NMF and suitable for between subject comparison of muscle synergies.     

Position-dependent motif characterization using non-negative matrix factorization

MOTIVATION: Cis-acting regulatory elements are frequently constrained by both sequence content and positioning relative to a functional site, such as a splice or polyadenylation site. We describe an approach to regulatory motif analysis based on non-negative matrix factorization (NMF). Whereas existing pattern recognition algorithms commonly focus primarily on sequence content, our method simultaneously characterizes both positioning and sequence content of putative motifs. RESULTS: Tests on artificially generated sequences show that NMF can faithfully reproduce both positioning and content of test motifs. We show how the variation of the residual sum of squares can be used to give a robust estimate of the number of motifs or patterns in a sequence set. Our analysis distinguishes multiple motifs with significant overlap in sequence content and/or positioning. Finally, we demonstrate the use of the NMF approach through characterization of biologically interesting datasets. Specifically, an analysis of mRNA 3'-processing (cleavage and polyadenylation) sites from a broad range of higher eukaryotes reveals a conserved core pattern of three elements.     

Extraction of food consumption systems by nonnegative matrix factorization (NMF) for the assessment of food choices

In Western countries where food supply is satisfactory, consumers organize their diets around a large combination of foods. It is the purpose of this article to examine how recent nonnegative matrix factorization (NMF) techniques can be applied to food consumption data to understand these combinations. Such data are nonnegative by nature and of high dimension. The NMF model provides a representation of consumption data through latent vectors with nonnegative coefficients, that we call consumption systems (CS), in a small number. As the NMF approach may encourage sparsity of the data representation produced, the resulting CS are easily interpretable. Beyond the illustration of its properties we provide through a simple simulation result, the NMF method is applied to data issued from a French consumption survey. The numerical results thus obtained are displayed and thoroughly discussed. A clustering based on the k-means method is also achieved in the resulting latent consumption space, to recover food consumption patterns easily usable for nutritionists.     

Nonnegative tensor factorization for continuous EEG classification

In this paper we present a method for continuous EEG classification, where we employ nonnegative tensor factorization (NTF) to determine discriminative spectral features and use the Viterbi algorithm to continuously classify multiple mental tasks. This is an extension of our previous work on the use of nonnegative matrix factorization (NMF) for EEG classification. Numerical experiments with two data sets in BCI competition, confirm the useful behavior of the method for continuous EEG classification.     

Improving molecular cancer class discovery through sparse non-negative matrix factorization

MOTIVATION: Identifying different cancer classes or subclasses with similar morphological appearances presents a challenging problem and has important implication in cancer diagnosis and treatment. Clustering based on gene-expression data has been shown to be a powerful method in cancer class discovery. Non-negative matrix factorization is one such method and was shown to be advantageous over other clustering techniques, such as hierarchical clustering or self-organizing maps. In this paper, we investigate the benefit of explicitly enforcing sparseness in the factorization process. RESULTS: We report an improved unsupervised method for cancer classification by the use of gene-expression profile via sparse non-negative matrix factorization. We demonstrate the improvement by direct comparison with classic non-negative matrix factorization on the three well-studied datasets. In addition, we illustrate how to identify a small subset of co-expressed genes that may be directly involved in cancer.     

Clustering of Expression Data in Chronic Lymphocytic Leukemia Reveals New Molecular Subdivisions

Although the identification of inherent structure in chronic lymphocytic leukemia (CLL) gene expression data using class discovery approaches has not been extensively explored, the natural clustering of patient samples can reveal molecular subdivisions that have biological and clinical implications. To explore this, we preprocessed raw gene expression data from two published studies, combined the data to increase the statistical power, and performed unsupervised clustering analysis. The clustering analysis was replicated in 4 independent cohorts. To assess the biological significance of the resultant clusters, we evaluated their prognostic value and identified cluster-specific markers. The clustering analysis revealed two robust and stable subgroups of CLL patients in the pooled dataset. The subgroups were confirmed by different methodological approaches (non-negative matrix factorization NMF clustering and hierarchical clustering) and validated in different cohorts. The subdivisions were related with differential clinical outcomes and markers associated with the microenvironment and the MAPK and BCR signaling pathways. It was also found that the cluster markers were independent of the immunoglobulin heavy chain variable (IGVH) genes mutational status. These findings suggest that the microenvironment can influence the clinical behavior of CLL, contributing to prognostic differences. The workflow followed here provides a new perspective on differences in prognosis and highlights new markers that should be explored in this context.     

Ontogenetic aspects of individual characteristics of functional brain asymmetry in the perception of emotions

Studies have been made on individual variations in perception of speech emotional information by 7-16-year children. Significant differences between subjects from various age groups were found concerning the correct recognition of emotions, the degree of brain asymmetry and domination type. The exactness of emotional recognition increases with age, while the degree of asymmetry becomes lower, the right hemisphere domination becoming more stable in processing of speech emotional information. With age, individual type of asymmetry turns to the specific one, reflecting asymmetry formation during evolution.     

Simultaneous Non-Negative Matrix Factorization for Multiple Large Scale Gene Expression Datasets in Toxicology

Non-negative matrix factorization is a useful tool for reducing the dimension of large datasets. This work considers simultaneous non-negative matrix factorization of multiple sources of data. In particular, we perform the first study that involves more than two datasets. We discuss the algorithmic issues required to convert the approach into a practical computational tool and apply the technique to new gene expression data quantifying the molecular changes in four tissue types due to different dosages of an experimental panPPAR agonist in mouse. This study is of interest in toxicology because, whilst PPARs form potential therapeutic targets for diabetes, it is known that they can induce serious side-effects. Our results show that the practical simultaneous non-negative matrix factorization developed here can add value to the data analysis. In particular, we find that factorizing the data as a single object allows us to distinguish between the four tissue types, but does not correctly reproduce the known dosage level groups. Applying our new approach, which treats the four tissue types as providing distinct, but related, datasets, we find that the dosage level groups are respected. The new algorithm then provides separate gene list orderings that can be studied for each tissue type, and compared with the ordering arising from the single factorization. We find that many of our conclusions can be corroborated with known biological behaviour, and others offer new insights into the toxicological effects. Overall, the algorithm shows promise for early detection of toxicity in the drug discovery process.     

The non-negative matrix factorization toolbox for biological data mining

Background

Non-negative matrix factorization (NMF) has been introduced as an important method for mining biological data. Though there currently exists packages implemented in R and other programming languages, they either provide only a few optimization algorithms or focus on a specific application field. There does not exist a complete NMF package for the bioinformatics community, and in order to perform various data mining tasks on biological data.

Results

We provide a convenient MATLAB toolbox containing both the implementations of various NMF techniques and a variety of NMF-based data mining approaches for analyzing biological data. Data mining approaches implemented within the toolbox include data clustering and bi-clustering, feature extraction and selection, sample classification, missing values imputation, data visualization, and statistical comparison.

Conclusions

A series of analysis such as molecular pattern discovery, biological process identification, dimension reduction, disease prediction, visualization, and statistical comparison can be performed using this toolbox.