Partition Decoupling for Multi-gene Analysis of Gene Expression Profiling Data

We present the extention and application of a new unsupervised statistical learning technique--the Partition Decoupling Method--to gene expression data. Because it has the ability to reveal non-linear and non-convex geometries present in the data, the PDM is an improvement over typical gene expression analysis algorithms, permitting a multi-gene analysis that can reveal phenotypic differences even when the individual genes do not exhibit differential expression. Here, we apply the PDM to publicly-available gene expression data sets, and demonstrate that we are able to identify cell types and treatments with higher accuracy than is obtained through other approaches. By applying it in a pathway-by-pathway fashion, we demonstrate how the PDM may be used to find sets of mechanistically-related genes that discriminate phenotypes.Comment: Revise

Manifold Learning in MR spectroscopy using nonlinear dimensionality reduction and unsupervised clustering

Purpose To investigate whether nonlinear dimensionality reduction improves unsupervised classification of 1H MRS brain tumor data compared with a linear method. Methods In vivo single-voxel 1H magnetic resonance spectroscopy (55 patients) and 1H magnetic resonance spectroscopy imaging (MRSI) (29 patients) data were acquired from histopathologically diagnosed gliomas. Data reduction using Laplacian eigenmaps (LE) or independent component analysis (ICA) was followed by k-means clustering or agglomerative hierarchical clustering (AHC) for unsupervised learning to assess tumor grade and for tissue type segmentation of MRSI data. Results An accuracy of 93% in classification of glioma grade II and grade IV, with 100% accuracy in distinguishing tumor and normal spectra, was obtained by LE with unsupervised clustering, but not with the combination of k-means and ICA. With 1H MRSI data, LE provided a more linear distribution of data for cluster analysis and better cluster stability than ICA. LE combined with k-means or AHC provided 91% accuracy for classifying tumor grade and 100% accuracy for identifying normal tissue voxels. Color-coded visualization of normal brain, tumor core, and infiltration regions was achieved with LE combined with AHC. Conclusion Purpose To investigate whether nonlinear dimensionality reduction improves unsupervised classification of 1H MRS brain tumor data compared with a linear method. Methods In vivo single-voxel 1H magnetic resonance spectroscopy (55 patients) and 1H magnetic resonance spectroscopy imaging (MRSI) (29 patients) data were acquired from histopathologically diagnosed gliomas. Data reduction using Laplacian eigenmaps (LE) or independent component analysis (ICA) was followed by k-means clustering or agglomerative hierarchical clustering (AHC) for unsupervised learning to assess tumor grade and for tissue type segmentation of MRSI data. Results An accuracy of 93% in classification of glioma grade II and grade IV, with 100% accuracy in distinguishing tumor and normal spectra, was obtained by LE with unsupervised clustering, but not with the combination of k-means and ICA. With 1H MRSI data, LE provided a more linear distribution of data for cluster analysis and better cluster stability than ICA. LE combined with k-means or AHC provided 91% accuracy for classifying tumor grade and 100% accuracy for identifying normal tissue voxels. Color-coded visualization of normal brain, tumor core, and infiltration regions was achieved with LE combined with AHC. Conclusion The LE method is promising for unsupervised clustering to separate brain and tumor tissue with automated color-coding for visualization of 1H MRSI data after cluster analysis

UNCLES: Method for the identification of genes differentially consistently co-expressed in a specific subset of datasets

Background: Collective analysis of the increasingly emerging gene expression datasets are required. The recently proposed binarisation of consensus partition matrices (Bi-CoPaM) method can combine clustering results from multiple datasets to identify the subsets of genes which are consistently co-expressed in all of the provided datasets in a tuneable manner. However, results validation and parameter setting are issues that complicate the design of such methods. Moreover, although it is a common practice to test methods by application to synthetic datasets, the mathematical models used to synthesise such datasets are usually based on approximations which may not always be sufficiently representative of real datasets. Results: Here, we propose an unsupervised method for the unification of clustering results from multiple datasets using external specifications (UNCLES). This method has the ability to identify the subsets of genes consistently co-expressed in a subset of datasets while being poorly co-expressed in another subset of datasets, and to identify the subsets of genes consistently co-expressed in all given datasets. We also propose the M-N scatter plots validation technique and adopt it to set the parameters of UNCLES, such as the number of clusters, automatically. Additionally, we propose an approach for the synthesis of gene expression datasets using real data profiles in a way which combines the ground-truth-knowledge of synthetic data and the realistic expression values of real data, and therefore overcomes the problem of faithfulness of synthetic expression data modelling. By application to those datasets, we validate UNCLES while comparing it with other conventional clustering methods, and of particular relevance, biclustering methods. We further validate UNCLES by application to a set of 14 real genome-wide yeast datasets as it produces focused clusters that conform well to known biological facts. Furthermore, in-silico-based hypotheses regarding the function of a few previously unknown genes in those focused clusters are drawn. Conclusions: The UNCLES method, the M-N scatter plots technique, and the expression data synthesis approach will have wide application for the comprehensive analysis of genomic and other sources of multiple complex biological datasets. Moreover, the derived in-silico-based biological hypotheses represent subjects for future functional studies.The National Institute for Health Research (NIHR) under its Programme Grants for Applied Research Programme (Grant Reference Number RP-PG-0310-1004)

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

Hierarchical information clustering by means of topologically embedded graphs

We introduce a graph-theoretic approach to extract clusters and hierarchies in complex data-sets in an unsupervised and deterministic manner, without the use of any prior information. This is achieved by building topologically embedded networks containing the subset of most significant links and analyzing the network structure. For a planar embedding, this method provides both the intra-cluster hierarchy, which describes the way clusters are composed, and the inter-cluster hierarchy which describes how clusters gather together. We discuss performance, robustness and reliability of this method by first investigating several artificial data-sets, finding that it can outperform significantly other established approaches. Then we show that our method can successfully differentiate meaningful clusters and hierarchies in a variety of real data-sets. In particular, we find that the application to gene expression patterns of lymphoma samples uncovers biologically significant groups of genes which play key-roles in diagnosis, prognosis and treatment of some of the most relevant human lymphoid malignancies

Detection of regulator genes and eQTLs in gene networks

Genetic differences between individuals associated to quantitative phenotypic traits, including disease states, are usually found in non-coding genomic regions. These genetic variants are often also associated to differences in expression levels of nearby genes (they are "expression quantitative trait loci" or eQTLs for short) and presumably play a gene regulatory role, affecting the status of molecular networks of interacting genes, proteins and metabolites. Computational systems biology approaches to reconstruct causal gene networks from large-scale omics data have therefore become essential to understand the structure of networks controlled by eQTLs together with other regulatory genes, and to generate detailed hypotheses about the molecular mechanisms that lead from genotype to phenotype. Here we review the main analytical methods and softwares to identify eQTLs and their associated genes, to reconstruct co-expression networks and modules, to reconstruct causal Bayesian gene and module networks, and to validate predicted networks in silico.Comment: minor revision with typos corrected; review article; 24 pages, 2 figure

Identifying cell types with single cell sequencing data

Single-cell RNA sequencing (scRNA-seq) techniques, which examine the genetic information of individual cells, provide an unparalleled resolution to discern deeply into cellular heterogeneity. On the contrary, traditional RNA sequencing technologies (bulk RNA sequencing technologies), measure the average RNA expression level of a large number of input cells, which are insufficient for studying heterogeneous systems. Hence, scRNA-seq technologies make it possible to tackle many inaccessible problems, such as rare cell types identification, cancer evolution and cell lineage relationship inference. Cell population identification is the fundamental of the analysis of scRNA-seq data. Generally, the workflow of scRNA-seq analysis includes data processing, dropout imputation, feature selection, dimensionality reduction, similarity matrix construction and unsupervised clustering. Many single-cell clustering algorithms rely on similarity matrices of cells, but many existing studies have not received the expectant results. There are some unique challenges in analyzing scRNA-seq data sets, including a significant level of biological and technical noise, so similarity matrix construction still deserves further study. In my study, I present a new method, named Learning Sparse Similarity Matrices (LSSM), to construct cell-cell similarity matrices, and then several clustering methods are used to identify cell populations respectively with scRNA-seq data. Firstly, based on sparse subspace theory, the relationship between a cell and the other cells in the same cell type is expressed by a linear combination. Secondly, I construct a convex optimization objective function to find the similarity matrix, which is consist of the corresponding coefficients of the linear combinations mentioned above. Thirdly, I design an algorithm with column-wise learning and greedy algorithm to solve the objective function. As a result, the large optimization problem on the similarity matrix can be decomposed into a series of smaller optimization problems on the single column of the similarity matrix respectively, and the sparsity of the whole matrix can be ensured by the sparsity of each column. Fourthly, in order to pick an optimal clustering method for identifying cell populations based on the similarity matrix developed by LSSM, I use several clustering methods separately based on the similarity matrix calculated by LSSM from eight scRNA-seq data sets. The clustering results show that my method performs the best when combined with spectral clustering (Laplacian eigenmaps + k-means clustering). In addition, compared with five state-of-the-art methods, my method outperforms most competing methods on eight data sets. Finally, I combine LSSM with t-Distributed Stochastic Neighbor Embedding (t-SNE) to visualize the data points of scRNA-seq data in the two-dimensional space. The results show that for most data points, in the same cell types they are close, while from different cell clusters, they are separated