Consensus Matrices Research Articles

Fast unsupervised multi-modal hashing based on piecewise learning

Unsupervised hashing has been extensively applied in large-scale multi-modal retrieval by mapping original data from heterogeneous modalities into unified binary codes. However, there still remain challenges especially how to balance the individual modality-specific representations and common representation preserving intrinsic linkages among heterogeneous modalities. In this paper, we propose a novel fast Unsupervised Multi-modal Hashing based on Piecewise Learning, denoted as UMHPL, to deal with the mentioned issue. Initially, we formulate the problem as matrix factorization to derive the individual modality-specific latent representations and common latent representation with consensus matrices in a brief time. To maintain the integrality of multi-modal data, we integrate them by adaptive weight factors and nuclear norm minimization. Subsequently, we establish a connection between the individual modality-specific latent representations and common latent representation based on the piecewise hash learning framework to reinforce the discriminative competency of model, which leads the hash codes more compact. Finally, an effective discrete optimization algorithm in mathematical logic and functional analysis is proposed. Comprehensive experiments on Wiki, MIRFlirck, NUS-WIDE, and MSCOCO datasets demonstrate the superior performance of UMHPL to state-of-the-art hashing methods.

Fuzzy similarity based hierarchical clustering for communities in twitter social networks

The complexity of the Internet has significantly increased along with its expansions. In particular, social networking has resulted in user clusters pertaining to many communities at different levels. Studies of online communities are a growing area of research user preferences can be categorized including dangerous groups. This work uses pre-processing techniques including stemming, stop words removals, and tokenizations of data using unigram, bigram, and 1–3 g representations. TF-IDFs (Term Frequency-Inverse Document Frequencies) and Word Embeds are used in feature Extractions. Perspectives generate hierarchical data structures which are then combined using consensus matrices followed by computations of dissimilarities between observed sets. This work employs FS-HC (fuzzy similarity based Hierarchical Clustering) to generate dendrograms for views. Finally, consensus matrices are generated by integrating several hierarchical agglomerations using transitive consensus matrix generations. They contain representative data of generated dendrograms. Performance metrics including precisions, recalls, f-measures, accuracies, clustering coefficients, conductance, and contractions are used to evaluate outcomes of benchmarked clustering algorithms. The proposed approach attains higher accuracy value of about 92 % when compared to other existing algorithms. The required data for community discoveries in social media were gathered from Twitter.

HCTMFS: A multi-modal feature selection framework with higher-order correlated topological manifold for ESRDaMCI

Background and ObjectiveThe diagnosis of end-stage renal disease associated with mild cognitive impairment (ESRDaMCI) mainly relies on objective cognitive assessment, clinical observation, and neuro-psychological evaluation, while only adopting clinical tools often limits the diagnosis accuracy. MethodsWe proposed a multi-modal feature selection framework with higher-order correlated topological manifold (HCTMFS) to classify ESRDaMCI patients and identify the discriminative brain regions. It constructed brain structural and functional networks with diffuse kurtosis imaging (DKI) and functional magnetic resonance imaging (fMRI) data, and extracted node efficiency and clustering coefficient from the brain networks to construct multi-modal feature matrices. The topological relationship matrices were constructed to measure the lower-order topological correlation between features. Then the consensus matrices were learned to approximate the topological relationship matrices at different confidence levels and eliminate the noise influence of individual matrices. ResultsThe higher-order topological correlation between features was explored by the Laplacian matrix of the hypergraph, which was calculated through the consensus matrix. The new framework achieved an accuracy rate of 93.56 % for classifying ESRDaMCI patients, and outperformed the existing state-of-the-art methods in terms of sensitivity, specificity, and area under the curve. ConclusionsThis study contributes to effectively reflect the functional neural degradation of ESRDaMCI and provide a reference for the diagnosis of ESRDaMCI by selecting discriminative brain regions.

SCM Enables Improved Single-Cell Clustering by Scoring Consensus Matrices

Single-cell clustering facilitates the identification of different cell types, especially the identification of rare cells. Preprocessing and dimensionality reduction are the two most commonly used data-processing methods and are very important for single-cell clustering. However, we found that different preprocessing and dimensionality reduction methods have very different effects on single-cell clustering. In addition, there seems to be no specific combination of preprocessing and dimensionality reduction methods that is applicable to all datasets. In this study, we developed a new algorithm for improving single-cell clustering results, called SCM. It first automatically searched for an optimal combination that corresponds to the best cell type clustering of a given dataset. It then defined a flexible cell-to-cell distance measure with data specificity for cell-type clustering. Experiments on ten benchmark datasets showed that SCM performed better than almost all the other seven popular clustering algorithms. For example, the average ARI improvement of SCM over the second best method SC3 even reached 29.31% on the ten datasets, which demonstrated its great potential in revealing cellular heterogeneity, identifying cell types, depicting cell functional states, inferring cellular dynamics, and other related research areas.

Consensus clustering of single-cell RNA-seq data by enhancing network affinity.

Elucidation of cell subpopulations at high resolution is a key and challenging goal of single-cell ribonucleic acid (RNA) sequencing (scRNA-seq) data analysis. Although unsupervised clustering methods have been proposed for de novo identification of cell populations, their performance and robustness suffer from the high variability, low capture efficiency and high dropout rates which are characteristic of scRNA-seq experiments. Here, we present a novel unsupervised method for Single-cell Clustering by Enhancing Network Affinity (SCENA), which mainly employed three strategies: selecting multiple gene sets, enhancing local affinity among cells and clustering of consensus matrices. Large-scale validations on 13 real scRNA-seq datasets show that SCENA has high accuracy in detecting cell populations and is robust against dropout noise. When we applied SCENA to large-scale scRNA-seq data of mouse brain cells, known cell types were successfully detected, and novel cell types of interneurons were identified with differential expression of gamma-aminobutyric acid receptor subunits and transporters. SCENA is equipped with CPU + GPU (Central Processing Units + Graphics Processing Units) heterogeneous parallel computing to achieve high running speed. The high performance and running speed of SCENA combine into a new and efficient platform for biological discoveries in clustering analysis of large and diverse scRNA-seq datasets.

Concensus-Based ALADIN Method to Faster the Decentralized Estimation of Laplacian Spectrum

With the upcoming fifth Industrial Revolution, humans and collaborative robots will dance together in production. They themselves act as an agent in a connected world, understood as a multi-agent system, in which the Laplacian spectrum plays an important role since it can define the connection of the complex networks as well as depict the robustness. In addition, the Laplacian spectrum can locally check the controllability and observability of a dynamic controlled network, etc. This paper presents a new method, which is based on the Augmented Lagrange based Alternating Direction Inexact Newton (ALADIN) method, to faster the convergence rate of the Laplacian Spectrum Estimation via factorization of the average consensus matrices, that are expressed as Laplacian-based matrices problems. Herein, the non-zero distinct Laplacian eigenvalues are the inverse of the stepsizes {αt,t=1,2,…} of those matrices. Therefore, the problem now is to carry out the agreement on the stepsize values for all agents in the given network while ensuring the factorization of average consensus matrices to be accomplished. Furthermore, in order to obtain the entire Laplacian spectrum, it is necessary to estimate the relevant multiplicities of these distinct eigenvalues. Consequently, a non-convex optimization problem is formed and solved using ALADIN method. The effectiveness of the proposed method is evaluated through the simulation results and the comparison with the Lagrange-based method in advance.

Network-based integrative clustering of multiple types of genomic data using non-negative matrix factorization

Identification of novel molecular subtypes of disease using multi-source ‘omics data is an active area of on-going research. Integrative clustering is a powerful approach to identify latent subtype structure inherent in the data sets accounting for both between and within data correlations. We propose a new integrative network-based clustering method using the non-negative matrix factorization, nNMF, for clustering multiple types of interrelated datasets assayed on same tumor-samples. nNMF utilizes the consensus matrices generated using the non-negative matrix factorization (NMF) algorithm on each type of data as networks among the patient samples. The multiple networks are then combined, and a comprehensive network structure is created optimizing the strengths of the relationships. A spectral clustering algorithm is then used on the final network data to determine the cluster groups. nNMF is a non-parametric method and therefore prior assumptions on the statistical distribution of data is not required. The application of the proposed nNMF method has been provided with simulated and the real-life datasets obtained from The Cancer Genome Atlas studies on glioblastoma, lower grade glioma and head and neck cancer. nNMF was found to be working competitively with previous methods and sometimes better as compared to previous NMF or model-based method especially when the signal to noise ratio is small. The novel nNMF method allows researchers to utilize such relationships to identify the latent subtype structure inherent in the data so that further association studies can be carried out. The R program for the nNMF will be available upon request.

AHP-Group Decision Making Based on Consistency

The Precise consistency consensus matrix (PCCM) is a consensus matrix for AHP-group decision making in which the value of each entry belongs, simultaneously, to all the individual consistency stability intervals. This new consensus matrix has shown significantly better behaviour with regards to consistency than other group consensus matrices, but it is slightly worse in terms of compatibility, understood as the discrepancy between the individual positions and the collective position that synthesises them. This paper includes an iterative algorithm for improving the compatibility of the PCCM. The sequence followed to modify the judgments of the PCCM is given by the entries that most contribute to the overall compatibility of the group. The procedure is illustrated by means of its application to a real-life situation (a local context) with three decision makers and four alternatives. The paper also offers, for the first time in the scientific literature, a detailed explanation of the process followed to solve the optimisation problem proposed for the consideration of different weights for the decision makers in the calculation of the PCCM.

A Decision Support System and Visualisation Tools for AHP-GDM

The Precise Consistency Consensus Matrix (PCCM) is a decisional tool for AHP-Group Decision Making (AHP-GDM). Based on the initial pairwise comparison matrices of the individuals, the PCCM constructs a consensus matrix for the group using the concept of consistency. This paper presents a decision support system (PRIOR-PCCM) that facilitates the construction of the PCCM in the context of AHP-GDM, and the calculus of four indicators that allows comparison of the behaviour of group consensus matrices. PRIOR-PCCM incorporates the possibility of considering different weights for the decision makers and includes a module that permits the extension of the initial PCCM which can achieve the minimum number of non-null entries required for deriving priorities or establishing a complete PCCM matrix. It also includes two cardinal indicators for measuring consistency and compatibility and two ordinal indicators for evaluating the number of violations of consistency and priority. The paper introduces some new visualisation tools that improve comprehension of the process followed for obtaining the PCCM matrix and allow the cognitive exploitation of the results. These original contributions are illustrated with a case study.

Clustering stability-based Evolutionary K-Means

Evolutionary K-Means (EKM), which combines K-Means and genetic algorithm, solves K-Means’ initiation problem by selecting parameters automatically through the evolution of partitions. Currently, EKM algorithms usually choose silhouette index as cluster validity index, and they are effective in clustering well-separated clusters. However, their performance of clustering noisy data is often disappointing. On the other hand, clustering stability-based approaches are more robust to noise; yet, they should start intelligently to find some challenging clusters. It is necessary to join EKM with clustering stability-based analysis. In this paper, we present a novel EKM algorithm that uses clustering stability to evaluate partitions. We firstly introduce two weighted aggregated consensus matrices, positive aggregated consensus matrix (PA) and negative aggregated consensus matrix (NA), to store clustering tendency for each pair of instances. Specifically, PA stores the tendency of sharing the same label and NA stores that of having different labels. Based upon the matrices, clusters and partitions can be evaluated from the view of clustering stability. Then, we propose a clustering stability-based EKM algorithm CSEKM that evolves partitions and the aggregated matrices simultaneously. To evaluate the algorithm’s performance, we compare it with an EKM algorithm, two consensus clustering algorithms, a clustering stability-based algorithm and a multi-index-based clustering approach. Experimental results on a series of artificial datasets, two simulated datasets and eight UCI datasets suggest CSEKM is more robust to noise.

<italic>Consensus+Innovations</italic> Distributed Kalman Filter With Optimized Gains

In this paper, we address the distributed filtering and prediction of time-varying random fields represented by linear time-invariant (LTI) dynamical systems. The field is observed by a sparsely connected network of agents/sensors collaborating among themselves. We develop a Kalman filter type consensus+innovations distributed linear estimator of the dynamic field termed as Consensus+Innovations Kalman Filter. We analyze the convergence properties of this distributed estimator. We prove that the mean-squared error of the estimator asymptotically converges if the degree of instability of the field dynamics is within a pre-specified threshold defined as tracking capacity of the estimator. The tracking capacity is a function of the local observation models and the agent communication network. We design the optimal consensus and innovation gain matrices yielding distributed estimates with minimized mean-squared error. Through numerical evaluations, we show that, the distributed estimator with optimal gains converges faster and with approximately 3dB better mean-squared error performance than previous distributed estimators.

A two-layer integration framework for protein complex detection.

BackgroundProtein complexes carry out nearly all signaling and functional processes within cells. The study of protein complexes is an effective strategy to analyze cellular functions and biological processes. With the increasing availability of proteomics data, various computational methods have recently been developed to predict protein complexes. However, different computational methods are based on their own assumptions and designed to work on different data sources, and various biological screening methods have their unique experiment conditions, and are often different in scale and noise level. Therefore, a single computational method on a specific data source is generally not able to generate comprehensive and reliable prediction results.ResultsIn this paper, we develop a novel Two-layer INtegrative Complex Detection (TINCD) model to detect protein complexes, leveraging the information from both clustering results and raw data sources. In particular, we first integrate various clustering results to construct consensus matrices for proteins to measure their overall co-complex propensity. Second, we combine these consensus matrices with the co-complex score matrix derived from Tandem Affinity Purification/Mass Spectrometry (TAP) data and obtain an integrated co-complex similarity network via an unsupervised metric fusion method. Finally, a novel graph regularized doubly stochastic matrix decomposition model is proposed to detect overlapping protein complexes from the integrated similarity network.ConclusionsExtensive experimental results demonstrate that TINCD performs much better than 21 state-of-the-art complex detection techniques, including ensemble clustering and data integration techniques.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-0939-3) contains supplementary material, which is available to authorized users.

Convergence Results for the Linear Consensus Problem under Markovian Random Graphs

This paper discusses the linear asymptotic consensus problem for a network of dynamic agents whose communication network is modeled by a randomly switching graph. The switching is determined by a finite state Markov process, each topology corresponding to a state of the process. We address the cases where the dynamics of the agents is expressed both in continuous time and in discrete time. We show that, if the consensus matrices are doubly stochastic, average consensus is achieved in the mean square sense and the almost sure sense if and only if the graph resulting from the union of graphs corresponding to the states of the Markov process is strongly connected. The aim of this paper is to show how techniques from the theory of Markovian jump linear systems, in conjunction with results inspired by matrix and graph theory, can be used to prove convergence results for stochastic consensus problems.

Distributed Change Detection Based on a Consensus Algorithm

In this paper a novel distributed recursive algorithm is proposed for real time change detection using sensor networks. The algorithm is based on a combination of geometric moving average control charts generating local statistics and a global consensus strategy; it does not require any fusion center, so that the final decision is made by testing the state of any node in the network with respect to a given common threshold. The mean-square error with respect to the centralized solution defined by a weighted sum of the local statistics is analyzed in the case of constant asymmetric consensus matrices with constant and time varying forgetting factors in the underlying recursions, assuming spatially and temporally correlated data. These results are consistently extended to the case of time varying random consensus matrices, encompassing asymmetric gossip schemes, lossy networks and intermittent measurements, proving that the algorithm can be an efficient tool for practice. The given simulation results illustrate the main characteristics of the proposed algorithm, including the consensus matrix design, the mean square error with respect to the centralized solution as a function of the forgetting factor, the obtained detection quality expressed using deflection and estimation of the instant of parameter change.

Convergence results for the agreement problem on Markovian random topologies

AbstractWe study the linear distributed asymptotic agreement(consensus) problem for a network of dynamic agents whose communication network is modeled by a randomly switching graph. The switching is determined by a finite state, Markov process, each topology corresponding to a state of the process. We address both the cases where the dynamics of the agents is expressed in continuous and discrete time. We show that, if the consensus matrices are doubly stochastic, convergence to average consensus is achieved in the mean square and almost sure sense, if and only if the graph resulted from the union of graphs corresponding to the states of the Markov process is strongly connected. The aim of this paper is to show how techniques from the theory of Markovian jump linear systems, in conjunction with results inspired by matrix and graph theory, can be used to prove convergence results for stochastic consensus problems.

Aggregation of preferences in participatory forest planning with multiple criteria: an application to the urban forest in Lycksele, Sweden

A promising approach for participatory forest management planning is the combination of multiple-criteria decision-making and group decision making. A crucial part of the participatory multiple-criteria decision-making process is the aggregation of individual stakeholder preferences into a collective preference. In this study, an approach based on the determination of cardinal compromise consensus was applied to a real case of participatory forest planning. Consensus matrices for four different social groups were established from stakeholder preferences in the form of pairwise comparisons of different sets of criteria. Criteria weights were obtained for each social group and used to determine rankings of 12 forest management plans. The rankings of the social groups were aggregated to determine consensus solutions for the choice of the best forest management plan from a collective perspective. In the procedure, control parameters and a distance metric were employed to find solutions that balance the points of view of the majority and the minority. This approach makes it possible to aggregate preferences of different stakeholders and produces a range of different solutions. Furthermore, certain values of the control parameters and the distance metric generate solutions that are promising to present in a participatory situation where stakeholders have very differing preferences.

Some new tools for visualising multi-way sensory data

In this paper we propose some new plots for three-way analysis of sensory data. One of the plots is called “Manhattan plot” and offers an alternative way of presenting explained variances, while the “Hiding plot” provides information about how the different axes in the consensus space are related to the original measurements. Correlation loadings plots exhibit correlations between the common scores acquired from the consensus matrix and the variables in the original multi-way data. For the computation of the consensus matrices we propose a new tool that bridges Generalised Canonical Analysis and Tucker-1 by defining intermediate combinations of the two. This is accomplished by altering a parameter in a more general model that covers these two methods. Three-way sensory profiling data from cheese are used as input for this general model to compute consensus matrices at different values for the parameter. External validation is pointed out as a useful tool for indicating which of the two statistical methods is most appropriate for computing a consensus matrix representing all assessors.

Nucleotide variation of regulatory motifs may lead to distinct expression patterns

Current methodologies for the selection of putative transcription factor binding sites (TFBS) rely on various assumptions such as over-representation of motifs occurring on gene promoters, and the use of motif descriptions such as consensus or position-specific scoring matrices (PSSMs). In order to avoid bias introduced by such assumptions, we apply an unsupervised motif extraction (MEX) algorithm to sequences of promoters. The extracted motifs are assessed for their likely cis-regulatory function by calculating the expression coherence (EC) of the corresponding genes, across a set of biological conditions. Applying MEX to all Saccharomyces cerevisiae promoters, followed by EC analysis across 40 biological conditions, we obtained a high percentage of putative cis-regulatory motifs. We clustered motifs that obtained highly significant EC scores, based on both their sequence similarity and similarity in the biological conditions these motifs appear to regulate. We describe 20 clusters, some of which regroup known TFBS. The clusters display different mRNA expression profiles, correlated with typical changes in the nucleotide composition of their relevant motifs. In several cases, a variation of a single nucleotide is shown to lead to distinct differences in expression patterns. These results are confronted with additional information, such as binding of transcription factors to groups of genes. Detailed analysis is presented for clusters related to MCB/SCB, STRE and PAC. In the first two cases, we provide evidence for different binding mechanisms of different clusters of motifs. For PAC-related motifs we uncover a new cluster that has so far been overshadowed by the stronger effects of known PAC motifs. Supplementary data are available at http://adios.tau.ac.il/regmotifs and at Bioinformatics online.

Evolution of a “Conserved” Amino Acid Sequence: a Model Study of an In Silico Investigation of the Phylogenesis of Some Immune Receptors

In this paper we analyze a 55-amino acid (aa) sequence which is relatively well conserved in several seven-transmembrane receptor families (from Insects to Mammals) and in some Viruses. This sequence, which covers the second transmembrane domain, the first extracellular loop and the third transmembrane domain, appears in its complete configuration in most of the seven-transmembrane receptor families, as well as in the protein products of some viruses. Other seven-transmembrane receptors and viruses exhibit reduced configurations of the conserved sequence, lacking either aa 31 or aa 30-31. 53-aa configurations are typically found in most chemokine receptor (CKR) subfamilies, as well as in some viral protein products. However, the CCR1, CCR3, and CCR6 subfamilies comprise a 54-aa configuration and the CKR-related protein products, ChemR23 and RDC1, include the complete 55-aa sequence. For each CKR subfamily the "modal sequence" of the conserved segment was constructed by selecting the most frequently occurring aa at each position. Then, pairwise alignments were made between: (i) the modal CKR sequences, and (ii) the sequence (53-aa) of the Yaba-like disease virus - 7L protein. From the alignments two consensus matrices were derived: (i) the consensus 1 matrix with reference to the whole conserved segment, and (ii) the consensus 2 matrix with reference to aa 22-29, which appear to be the most variable segment of the sequence. Based on the obtained consensus values and with reference to this specific conserved segment, the following conclusions are proposed: (1) ChemR23 and RDC1 are probably the more primitive CKR forms; (2) CCR1 and CCR3 may be grouped in a single cluster; (3) CCRs 2, 4, and 5 are closely related to each other and may be grouped in a cluster; CCR7 is likely to be evolutionarily related to this cluster; (4) CXCRs 2, 3, and 4 and CCX CKR appear to be evolutionarily related to each other and very likely derived from an CCR6-like gene; (5) CCR2/4/5 and CCR7 may have derived either from CCR1/3-like or CCR6-like genes; (6). The Yaba-like disease virus--7L protein most likely derived, through "molecular piracy", from a CCR8-like gene. We also discuss possible, more remote, evolutionary links between CKRs, formylpeptide receptors, and possibly the highly conserved 18S rRNA genes.

Identification of Estrogen-responsive Genes Using a Genome-wide Analysis of Promoter Elements for Transcription Factor Binding Sites

We developed a pipeline to identify novel genes regulated by the steroid hormone-dependent transcription factor, estrogen receptor, through a systematic analysis of upstream regions of all human and mouse genes. We built a data base of putative promoter regions for 23,077 human and 19,984 mouse transcripts from National Center for Biotechnology Information annotation and 8793 human and 6785 mouse promoters from the Data Base of Transcriptional Start Sites. We used this data base of putative promoters to identify potential targets of estrogen receptor by identifying estrogen response elements (EREs) in their promoters. Our program correctly identified EREs in genes known to be regulated by estrogen in addition to several new genes whose putative promoters contained EREs. We validated six genes (KIAA1243, NRIP1, MADH9, NME3, TPD52L, and ABCG2) to be estrogen-responsive in MCF7 cells using reverse transcription PCR. To allow for extensibility of our program in identifying targets of other transcription factors, we have built a Web interface to access our data base and programs. Our Web-based program for Promoter Analysis of Genome, PAGen@UIC, allows a user to identify putative target genes for vertebrate transcription factors through the analysis of their upstream sequences. The interface allows the user to search the human and mouse promoter data bases for potential target genes containing one or more listed transcription factor binding sites (TFBSs) in their upstream elements, using either regular expression-based consensus or position weight matrices. The data base can also be searched for promoters harboring user-defined TFBSs given as a consensus or a position weight matrix. Furthermore, the user can retrieve putative promoter sequences for any given gene together with identified TFBSs located on its promoter. Orthologous promoters are also analyzed to determine conserved elements.