Integrated Clustering Approach Research Articles

Spectral Clustering via Adaptive Layer Aggregation for Multi-Layer Networks

One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches based on effective convex layer aggregations. Our aggregation methods are strongly motivated by a delicate asymptotic analysis of the spectral embedding of weighted adjacency matrices and the downstream k-means clustering, in a challenging regime where community detection consistency is impossible. In fact, the methods are shown to estimate the optimal convex aggregation, which minimizes the misclustering error under some specialized multi-layer network models. Our analysis further suggests that clustering using Gaussian mixture models is generally superior to the commonly used k-means in spectral clustering. Extensive numerical studies demonstrate that our adaptive aggregation techniques, together with Gaussian mixture model clustering, make the new spectral clustering remarkably competitive compared to several popularly used methods. Supplementary materials for this article are available online.

Recursive integration of synergised graph representations of multi-omics data for cancer subtypes identification

Cancer subtypes identification is one of the critical steps toward advancing personalized anti-cancerous therapies. Accumulation of a massive amount of multi-platform omics data measured across the same set of samples provides an opportunity to look into this deadly disease from several views simultaneously. Few integrative clustering approaches are developed to capture shared information from all the views to identify cancer subtypes. However, they have certain limitations. The challenge here is identifying the most relevant feature space from each omic view and systematically integrating them. Both the steps should lead toward a global clustering solution with biological significance. In this respect, a novel multi-omics clustering algorithm named RISynG (Recursive Integration of Synergised Graph-representations) is presented in this study. RISynG represents each omic view as two representation matrices that are Gramian and Laplacian. A parameterised combination function is defined to obtain a synergy matrix from these representation matrices. Then a recursive multi-kernel approach is applied to integrate the most relevant, shared, and complementary information captured via the respective synergy matrices. At last, clustering is applied to the integrated subspace. RISynG is benchmarked on five multi-omics cancer datasets taken from The Cancer Genome Atlas. The experimental results demonstrate RISynG’s efficiency over the other approaches in this domain.

Approximate Graph Laplacians for Multimodal Data Clustering.

One of the important approaches of handling data heterogeneity in multimodal data clustering is modeling each modality using a separate similarity graph. Information from the multiple graphs is integrated by combining them into a unified graph. A major challenge here is how to preserve cluster information while removing noise from individual graphs. In this regard, a novel algorithm, termed as CoALa, is proposed that integrates noise-free approximations of multiple similarity graphs. The proposed method first approximates a graph using the most informative eigenpairs of its Laplacian which contain cluster information. The approximate Laplacians are then integrated for the construction of a low-rank subspace that best preserves overall cluster information of multiple graphs. However, this approximate subspace differs from the full-rank subspace which integrates information from all the eigenpairs of each Laplacian. Matrix perturbation theory is used to theoretically evaluate how far approximate subspace deviates from the full-rank one for a given value of approximation rank. Finally, spectral clustering is performed on the approximate subspace to identify the clusters. Experimental results on several real-life cancer and benchmark data sets demonstrate that the proposed algorithm significantly and consistently outperforms state-of-the-art integrative clustering approaches.

Selective Update of Relevant Eigenspaces for Integrative Clustering of Multimodal Data

One of the major problems in cancer subtype discovery from multimodal omic data is that all the available modalities may not encode relevant and homogeneous information about the subtypes. Moreover, the high-dimensional nature of the modalities makes sample clustering computationally expensive. In this regard, a novel algorithm is proposed to extract a low-rank joint subspace of the integrated data matrix. The proposed algorithm first evaluates the quality of subtype information provided by each of the modalities, and then judiciously selects only relevant ones to construct the joint subspace. The problem of incrementally updating the singular value decomposition of a data matrix is formulated for the multimodal data framework. The analytical formulation enables efficient construction of the joint subspace of integrated data from low-rank subspaces of the individual modalities. The construction of joint subspace by the proposed method is shown to be computationally more efficient compared to performing the principal component analysis (PCA) on the integrated data matrix. Some new quantitative indices are introduced to measure theoretically the accuracy of subspace construction by the proposed approach with respect to the principal subspace extracted by the PCA. The efficacy of clustering on the joint subspace constructed by the proposed algorithm is established over existing integrative clustering approaches on several real-life multimodal cancer data sets.

Cluster analysis of core measurements using heterogeneous data sources: An application to complex Miocene reservoirs

An integrated clustering approach is suggested for the interpretation of petrophysical properties measured on core samples. Porosity, carbonate content, bulk and grain density, permeability, irreducible water saturation and capillary pressure curves measured from different sources are processed simultaneously for a more reliable evaluation of hydrocarbon reservoirs. The specialty of the problem is that the input dataset is composed of observations at different boreholes and depth intervals, where the number of rock specimens and measurement types strongly vary. Several statistical methods such as cluster and factor analyses are traditionally used for rock typing, which are either highly limited or not feasible at all for the processing of such incomplete datasets. To overcome this difficulty, the sparse matrix of multivariate observations is fully filled with reliable estimates of petrophysical parameters before cluster analysis. In the first phase, a correlation-based interpolation method is proposed for replacing the missing data with synthetic ones estimated from the available petrophysical information. Then, principal component analysis of the filled data matrix is performed to investigate the relative contribution of different variables to the solution and reduce the large number of measured parameters into fewer variables. In the last step, non-hierarchical cluster analysis of the principal components is made to separate the lithological units and reservoir zones. The suggested statistical workflow is tested in a Hungarian oilfield, where Miocene reservoirs of different lithologies are evaluated using a large amount of laboratory data collected for three decades. When clustering all petrophysical variables in a joint procedure, not just the lithological properties but also the fluid and other reservoir characteristics are taken into account to differentiate the pay zones from unproductive intervals. In addition to the current application, the statistical method may serve as useful tool for improved well log analysis, well-to-well correlation and reservoir modeling on larger scales.

Evaluation of integrative clustering methods for the analysis of multi-omics data.

Recent advances in sequencing, mass spectrometry and cytometry technologies have enabled researchers to collect large-scale omics data from the same set of biological samples. The joint analysis of multiple omics offers the opportunity to uncover coordinated cellular processes acting across different omic layers. In this work, we present a thorough comparison of a selection of recent integrative clustering approaches, including Bayesian (BCC and MDI) and matrix factorization approaches (iCluster, moCluster, JIVE and iNMF). Based on simulations, the methods were evaluated on their sensitivity and their ability to recover both the correct number of clusters and the simulated clustering at the common and data-specific levels. Standard non-integrative approaches were also included to quantify the added value of integrative methods. For most matrix factorization methods and one Bayesian approach (BCC), the shared and specific structures were successfully recovered with high and moderate accuracy, respectively. An opposite behavior was observed on non-integrative approaches, i.e. high performances on specific structures only. Finally, we applied the methods on the Cancer Genome Atlas breast cancer data set to check whether results based on experimental data were consistent with those obtained in the simulations.

Low-Rank Joint Subspace Construction for Cancer Subtype Discovery.

Multimodal data integration is an important framework for cancer subtype discovery as it can blend the inherent properties of individual modalities with their cross-platform correlations to infer clinically relevant subtypes. The main problem here is the appropriate selection of relevant and complementary modalities. Another problem is the 'high dimension-low sample size' nature of each modality. The current research work proposes a novel algorithm to construct a low-rank joint subspace from the low-rank subspaces of individual high-dimensional modalities. Statistical hypothesis testing is introduced to effectively estimate the rank of each modality by separating the signal component from its noise counterpart. Two quantitative indices are proposed to evaluate the quality of different modalities, the first one assesses the degree of relevance of the cluster structure embedded within each modality, while the second measure evaluates the amount of cluster information shared between two modalities. To construct the joint subspace, the algorithm selects the most relevant modalities with maximum shared information. During data integration, the intersection between two subspaces is also considered to select cluster information and filter out the noise from different subspaces. The efficacy of clustering on the joint subspace, extracted by the proposed algorithm, is compared with that of several existing integrative clustering approaches on real-life multimodal data sets. Experimental results show that the identified subtypes have closer resemblance with the clinically established subtypes as compared to the subtypes identified by the existing approaches. Survival analysis has revealed the significant differences between survival profiles of the identified subtypes, while robustness analysis shows that the identified subtypes are not sensitive towards perturbation of the data sets.

Integrative cancer patient stratification via subspace merging.

Technologies that generate high-throughput omics data are flourishing, creating enormous, publicly available repositories of multi-omics data. As many data repositories continue to grow, there is an urgent need for computational methods that can leverage these data to create comprehensive clusters of patients with a given disease. Our proposed approach creates a patient-to-patient similarity graph for each data type as an intermediate representation of each omics data type and merges the graphs through subspace analysis on a Grassmann manifold. We hypothesize that this approach generates more informative clusters by preserving the complementary information from each level of omics data. We applied our approach to The Cancer Genome Atlas (TCGA) breast cancer dataset and show that by integrating gene expression, microRNA and DNA methylation data, our proposed method can produce clinically useful subtypes of breast cancer. We then investigate the molecular characteristics underlying these subtypes. We discover a highly expressed cluster of genes on chromosome 19p13 that strongly correlates with survival in TCGA breast cancer patients and validate these results in three additional breast cancer datasets. We also compare our approach with previous integrative clustering approaches and obtain comparable or superior results. https://github.com/michaelsharpnack/GrassmannCluster. Supplementary data are available at Bioinformatics online.

Bi-level and Bi-objective p-Median Type Problems for Integrative Clustering: Application to Analysis of Cancer Gene-Expression and Drug-Response Data.

Recent advances in high-throughput technologies have given rise to collecting large amounts of multidimensional heterogeneous data that provide diverse information on the same biological samples. Integrative analysis of such multisource datasets may reveal new biological insights into complex biological mechanisms and therefore remains an important research field in systems biology. Most of the modern integrative clustering approaches rely on independent analysis of each dataset and consensus clustering, probabilistic or statistical modeling, while flexible distance-based integrative clustering techniques are sparsely covered. We propose two distance-based integrative clustering frameworks based on bi-level and bi-objective extensions of the p-median problem. A hybrid branch-and-cut method is developed to find global optimal solutions to the bi-level p-median model. As to the bi-objective problem, an -constraint algorithm is proposed to generate an approximation to the Pareto optimal set. Every solution found by any of the frameworks corresponds to an integrative clustering. We present an application of our approaches to integrative analysis of NCI-60 human tumor cell lines characterized by gene expression and drug activity profiles. We demonstrate that the proposed mathematical optimization-based approaches outperform some state-of-the-art and traditional distance-based integrative and non-integrative clustering techniques.

Integrative Data Analysis of Multi-Platform Cancer Data with a Multimodal Deep Learning Approach.

Identification of cancer subtypes plays an important role in revealing useful insights into disease pathogenesis and advancing personalized therapy. The recent development of high-throughput sequencing technologies has enabled the rapid collection of multi-platform genomic data (e.g., gene expression, miRNA expression, and DNA methylation) for the same set of tumor samples. Although numerous integrative clustering approaches have been developed to analyze cancer data, few of them are particularly designed to exploit both deep intrinsic statistical properties of each input modality and complex cross-modality correlations among multi-platform input data. In this paper, we propose a new machine learning model, called multimodal deep belief network (DBN), to cluster cancer patients from multi-platform observation data. In our integrative clustering framework, relationships among inherent features of each single modality are first encoded into multiple layers of hidden variables, and then a joint latent model is employed to fuse common features derived from multiple input modalities. A practical learning algorithm, called contrastive divergence (CD), is applied to infer the parameters of our multimodal DBN model in an unsupervised manner. Tests on two available cancer datasets show that our integrative data analysis approach can effectively extract a unified representation of latent features to capture both intra- and cross-modality correlations, and identify meaningful disease subtypes from multi-platform cancer data. In addition, our approach can identify key genes and miRNAs that may play distinct roles in the pathogenesis of different cancer subtypes. Among those key miRNAs, we found that the expression level of miR-29a is highly correlated with survival time in ovarian cancer patients. These results indicate that our multimodal DBN based data analysis approach may have practical applications in cancer pathogenesis studies and provide useful guidelines for personalized cancer therapy.

An efficient and scalable graph modeling approach for capturing information at different levels in next generation sequencing reads.

BackgroundNext generation sequencing technologies have greatly advanced many research areas of the biomedical sciences through their capability to generate massive amounts of genetic information at unprecedented rates. The advent of next generation sequencing has led to the development of numerous computational tools to analyze and assemble the millions to billions of short sequencing reads produced by these technologies. While these tools filled an important gap, current approaches for storing, processing, and analyzing short read datasets generally have remained simple and lack the complexity needed to efficiently model the produced reads and assemble them correctly.ResultsPreviously, we presented an overlap graph coarsening scheme for modeling read overlap relationships on multiple levels. Most current read assembly and analysis approaches use a single graph or set of clusters to represent the relationships among a read dataset. Instead, we use a series of graphs to represent the reads and their overlap relationships across a spectrum of information granularity. At each information level our algorithm is capable of generating clusters of reads from the reduced graph, forming an integrated graph modeling and clustering approach for read analysis and assembly. Previously we applied our algorithm to simulated and real 454 datasets to assess its ability to efficiently model and cluster next generation sequencing data. In this paper we extend our algorithm to large simulated and real Illumina datasets to demonstrate that our algorithm is practical for both sequencing technologies.ConclusionsOur overlap graph theoretic algorithm is able to model next generation sequencing reads at various levels of granularity through the process of graph coarsening. Additionally, our model allows for efficient representation of the read overlap relationships, is scalable for large datasets, and is practical for both Illumina and 454 sequencing technologies.

Locally discriminative spectral clustering with composite manifold

A large number of data are generated in many real-world applications, e.g., photos of albums in social networks. Discovering meaningful patterns from them is desirable and still remains a big challenge. To this end, spectral clustering has established itself as a very useful tool for data analysis. It considers the manifold geometrical structure of the data and desires to estimate the intrinsic manifold. However, there exists no principled way for estimating such manifold. Thus, the clustering performance might even degrade seriously when the estimated manifold deviates far from the intrinsic manifold. To address this problem, we propose to employ composite manifold to approximate the intrinsic manifold as much as possible. This composite manifold is derived from a convex combination of some pre-given candidate manifolds in a convex hull. The diversity nature of these manifolds provides richer structure information, which is helpful to maximally estimate the intrinsic manifold. Besides, traditional spectral clustering neglects the discriminant information latent in the data space, so we incorporate the locally discriminative structure into the partition matrix by explicitly using local linear regression, for better clustering. Therefore, in this paper, we present an integrated clustering approach named Spectral Clustering via Composite manifold and Local discriminant learning, referred to as SCCL for short, which addresses the aforementioned two problems. To optimize the objective function, an alternating optimization framework is adopted to derive both the cluster membership matrix and the composite manifold coefficient. Extensive experiments are carried out on several real-world databases. Results have validated the efficacy of the proposed algorithm.

Integrated Clustering Approach to Developing Technology for Functional Feature and Engineering Specification-based Reference Design Retrieval

Engineering design is a complex activity, and is heavily reliant on the know-how of engineering designers. Hence, capturing, storing, and reusing design information, design intent, and underlining design knowledge to support design activities is a key issue in engineering knowledge management. To meet the demand for engineering designers regarding functional feature and engineering specification-based knowledge resources, this study proposes a novel scheme for functional feature and engineering specification-based reference design retrieval using an integrated clustering approach for providing engineering designers with easy access to relevant reference design and associated knowledge. The research objectives can be achieved by performing the following five tasks: (i) designing a functional feature and engineering specificationbased reference design retrieval process, (ii) developing a functional feature and engineering specification representation, (iii) investigating and integrating ART1 (adaptive resonance theory 1) neural network, GA (genetic algorithm), and fuzzy ART (fuzzy adaptive resonance theory) clustering techniques, and (iv) implementing a functional feature and engineering specification-based reference design retrieval mechanism and experimenting with an example. The retrieval process involves three steps: functional feature and engineering specification-based query, similar design case search and retrieval, and similar design case ranking. The techniques involved include: (i) a binary code-based representation for functional feature and an EXPRESS language-based representation for engineering specification, (ii) ART1 neural network and genetic algorithm for functional feature-based similar design case clustering, (iii) fuzzy ART for engineering specification-based similar design case clustering, (iv) similarity calculation for ranking similar design cases, and (v) a case-based representation for designed entities.