H-CLAP: hierarchical clustering within a linear array with an application in genetics

2015 ◽  
Vol 14 (2) ◽  
Author(s):  
Samiran Ghosh ◽  
Jeffrey P. Townsend
Keyword(s):  
Hierarchical Clustering ◽  
Clustering Algorithm ◽  
Linear Array ◽  
Recursive Partitioning ◽  
Biological Significance ◽  
Data Sets ◽  
Clustering Methods ◽  
Domain Specific ◽  
Data Points ◽  
Fully Bayesian

AbstractIn most cases where clustering of data is desirable, the underlying data distribution to be clustered is unconstrained. However clustering of site types in a discretely structured linear array, as is often desired in studies of linear sequences such as DNA, RNA or proteins, represents a problem where data points are not necessarily exchangeable and are directionally constrained within the array. Each position in the linear array is fixed, and could be either “marked” (i.e., of interest such as polymorphic or substitute sites) or “non-marked.” Here we describe a method for clustering of those marked sites. Since the cluster-generating process is constrained by discrete locality inside such an array, traditional clustering methods need adjustment to be appropriate. We develop a hierarchical Bayesian approach. We adopt a Markov clustering algorithm, revealing any natural partitioning in the pattern of marked sites. The resulting recursive partitioning and clustering algorithm is named hierarchical clustering in a linear array (H-CLAP). It employs domain-specific directional constraints directly in the likelihood construction. Our method, being fully Bayesian, is more flexible in cluster discovery compared to a standard agglomerative hierarchical clustering algorithm. It not only provides hierarchical clustering, but also cluster boundaries, which may have their own biological significance. We have tested the efficacy of our method on data sets, including two biological and several simulated ones.

scholarly journals Kernel Treelets

2019 ◽  
Vol 11 (03n04) ◽  
pp. 1950006
Author(s):  
Hedi Xia ◽  
Hector D. Ceniceros
Keyword(s):  
Hierarchical Clustering ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Feature Space ◽  
Coefficient Matrix ◽  
Data Sets ◽  
Clustering Methods ◽  
Orthonormal Bases ◽  
Data Points ◽  
General Data

A new method for hierarchical clustering of data points is presented. It combines treelets, a particular multiresolution decomposition of data, with a mapping on a reproducing kernel Hilbert space. The proposed approach, called kernel treelets (KT), uses this mapping to go from a hierarchical clustering over attributes (the natural output of treelets) to a hierarchical clustering over data. KT effectively substitutes the correlation coefficient matrix used in treelets with a symmetric and positive semi-definite matrix efficiently constructed from a symmetric and positive semi-definite kernel function. Unlike most clustering methods, which require data sets to be numeric, KT can be applied to more general data and yields a multiresolution sequence of orthonormal bases on the data directly in feature space. The effectiveness and potential of KT in clustering analysis are illustrated with some examples.

scholarly journals Improved minimum-minimum roughness algorithm for clustering categorical data

2021 ◽  
Vol 8 (10) ◽  
pp. 43-50
Author(s):  
Truong et al. ◽  
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
Hierarchical Clustering ◽  
Categorical Data ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Experimental Results ◽  
Data Sets ◽  
Top Down ◽  
Hierarchical Clustering Algorithm

Clustering is a fundamental technique in data mining and machine learning. Recently, many researchers are interested in the problem of clustering categorical data and several new approaches have been proposed. One of the successful and pioneering clustering algorithms is the Minimum-Minimum Roughness algorithm (MMR) which is a top-down hierarchical clustering algorithm and can handle the uncertainty in clustering categorical data. However, MMR tends to choose the category with less value leaf node with more objects, leading to undesirable clustering results. To overcome such shortcomings, this paper proposes an improved version of the MMR algorithm for clustering categorical data, called IMMR (Improved Minimum-Minimum Roughness). Experimental results on actual data sets taken from UCI show that the IMMR algorithm outperforms MMR in clustering categorical data.

Summary of Affinity Propagation

2011 ◽  
Vol 268-270 ◽  
pp. 811-816
Author(s):  
Yong Zhou ◽  
Yan Xing
Keyword(s):  
Clustering Algorithm ◽  
Large Data ◽  
Large Data Sets ◽  
Affinity Propagation ◽  
Damping Factor ◽  
Data Sets ◽  
Similarity Matrix ◽  
Data Points

Affinity Propagation(AP)is a new clustering algorithm, which is based on the similarity matrix between pairs of data points and messages are exchanged between data points until clustering result emerges. It is efficient and fast , and it can solve the clustering on large data sets. But the traditional Affinity Propagation has many limitations, this paper introduces the Affinity Propagation, and analyzes in depth the advantages and limitations of it, focuses on the improvements of the algorithm — improve the similarity matrix, adjust the preference and the damping-factor, combine with other algorithms. Finally, discusses the development of Affinity Propagation.

Analysis and Integration of Biological Data

2010 ◽  
pp. 287-314
Author(s):  
Diego Milone ◽  
Georgina Stegmayer ◽  
Matías Gerard ◽  
Laura Kamenetzky ◽  
Mariana López ◽  
...  
Keyword(s):  
Data Integration ◽  
New Technologies ◽  
Biological Significance ◽  
Neural Model ◽  
Biological Data ◽  
Data Sets ◽  
Clustering Methods ◽  
Gene Expressions ◽  
Internal Coherence ◽  
Biological Data Integration

The volume of information derived from post genomic technologies is rapidly increasing. Due to the amount of involved data, novel computational methods are needed for the analysis and knowledge discovery into the massive data sets produced by these new technologies. Furthermore, data integration is also gaining attention for merging signals from different sources in order to discover unknown relations. This chapter presents a pipeline for biological data integration and discovery of a priori unknown relationships between gene expressions and metabolite accumulations. In this pipeline, two standard clustering methods are compared against a novel neural network approach. The neural model provides a simple visualization interface for identification of coordinated patterns variations, independently of the number of produced clusters. Several quality measurements have been defined for the evaluation of the clustering results obtained on a case study involving transcriptomic and metabolomic profiles from tomato fruits. Moreover, a method is proposed for the evaluation of the biological significance of the clusters found. The neural model has shown a high performance in most of the quality measures, with internal coherence in all the identified clusters and better visualization capabilities.

scholarly journals DETERMINISTIC INITIALIZATION OF THE K-MEANS ALGORITHM USING HIERARCHICAL CLUSTERING

2012 ◽  
Vol 26 (07) ◽  
pp. 1250018 ◽  
Author(s):  
M. EMRE CELEBI ◽  
HASSAN A. KINGRAVI
Keyword(s):  
Clustering Algorithm ◽  
Large Data ◽  
Large Data Sets ◽  
Data Sets ◽  
Partitional Clustering ◽  
Highly Sensitive ◽  
Data Points ◽  
Initial Placement ◽  
Random Initialization ◽  
Common Deficiency

K-means is undoubtedly the most widely used partitional clustering algorithm. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initial placement of the cluster centers. Numerous initialization methods have been proposed to address this problem. Many of these methods, however, have superlinear complexity in the number of data points, making them impractical for large data sets. On the other hand, linear methods are often random and/or order-sensitive, which renders their results unrepeatable. Recently, Su and Dy proposed two highly successful hierarchical initialization methods named Var-Part and PCA-Part that are not only linear, but also deterministic (nonrandom) and order-invariant. In this paper, we propose a discriminant analysis based approach that addresses a common deficiency of these two methods. Experiments on a large and diverse collection of data sets from the UCI machine learning repository demonstrate that Var-Part and PCA-Part are highly competitive with one of the best random initialization methods to date, i.e. k-means++, and that the proposed approach significantly improves the performance of both hierarchical methods.

On Fuzzy Non-Metric Model for Data with Tolerance and its Application to Incomplete Data Clustering

2016 ◽  
Vol 20 (4) ◽  
pp. 571-579 ◽  
Author(s):  
Yasunori Endo ◽  
◽  
Tomoyuki Suzuki ◽  
Naohiko Kinoshita ◽  
Yukihiro Hamasuna ◽  
...  
Keyword(s):  
Data Clustering ◽  
Incomplete Data ◽  
Clustering Algorithm ◽  
Uncertain Data ◽  
Data Sets ◽  
Membership Degree ◽  
Clustering Methods ◽  
Clustering Method ◽  
Numerical Examples ◽  
Metric Model

The fuzzy non-metric model (FNM) is a representative non-hierarchical clustering method, which is very useful because the belongingness or the membership degree of each datum to each cluster can be calculated directly from the dissimilarities between data and the cluster centers are not used. However, the original FNM cannot handle data with uncertainty. In this study, we refer to the data with uncertainty as “uncertain data,” e.g., incomplete data or data that have errors. Previously, a methods was proposed based on the concept of a tolerance vector for handling uncertain data and some clustering methods were constructed according to this concept, e.g. fuzzyc-means for data with tolerance. These methods can handle uncertain data in the framework of optimization. Thus, in the present study, we apply the concept to FNM. First, we propose a new clustering algorithm based on FNM using the concept of tolerance, which we refer to as the fuzzy non-metric model for data with tolerance. Second, we show that the proposed algorithm can handle incomplete data sets. Third, we verify the effectiveness of the proposed algorithm based on comparisons with conventional methods for incomplete data sets in some numerical examples.

Research on NMF Based Hierarchical Clustering Methods

2010 ◽  
Vol 439-440 ◽  
pp. 1306-1311
Author(s):  
Fang Li ◽  
Qun Xiong Zhu
Keyword(s):  
Hierarchical Clustering ◽  
Clustering Algorithm ◽  
Clustering Methods ◽  
Agglomerative Clustering ◽  
Clustering Method ◽  
Hierarchical Agglomerative Clustering ◽  
Hierarchical Clustering Methods

LSI based hierarchical agglomerative clustering algorithm is studied. Aiming to the problems of LSI based hierarchical agglomerative clustering method, NMF based hierarchical clustering method is proposed and analyzed. Two ways of implementing NMF based method are introduced. Finally the result of two groups of experiment based on the TanCorp document corpora show that the method proposed is effective.

CLUSTERING USING SIMULATED ANNEALING WITH PROBABILISTIC REDISTRIBUTION

2001 ◽  
Vol 15 (02) ◽  
pp. 269-285 ◽  
Author(s):  
SANGHAMITRA BANDYOPADHYAY ◽  
UJJWAL MAULIK ◽  
MALAY KUMAR PAKHIRA
Keyword(s):  
Simulated Annealing ◽  
Clustering Algorithm ◽  
Minimum Energy ◽  
Real Life ◽  
Feature Space ◽  
Cluster Center ◽  
Data Sets ◽  
Partitional Clustering ◽  
Real Life Data ◽  
Data Points

An efficient partitional clustering technique, called SAKM-clustering, that integrates the power of simulated annealing for obtaining minimum energy configuration, and the searching capability of K-means algorithm is proposed in this article. The clustering methodology is used to search for appropriate clusters in multidimensional feature space such that a similarity metric of the resulting clusters is optimized. Data points are redistributed among the clusters probabilistically, so that points that are farther away from the cluster center have higher probabilities of migrating to other clusters than those which are closer to it. The superiority of the SAKM-clustering algorithm over the widely used K-means algorithm is extensively demonstrated for artificial and real life data sets.

SPSM: A NEW HYBRID DATA CLUSTERING ALGORITHM FOR NONLINEAR DATA ANALYSIS

2009 ◽  
Vol 23 (08) ◽  
pp. 1701-1737 ◽  
Author(s):  
UREERAT WATTANACHON ◽  
CHIDCHANOK LURSINSAP
Keyword(s):  
Clustering Algorithm ◽  
Color Image ◽  
Clustering Algorithms ◽  
Noisy Data ◽  
Second Phase ◽  
Data Sets ◽  
Data Set ◽  
Cluster Distance ◽  
Data Points ◽  
Hybrid Data

Existing clustering algorithms, such as single-link clustering, k-means, CURE, and CSM are designed to find clusters based on predefined parameters specified by users. These algorithms may be unsuccessful if the choice of parameters is inappropriate with respect to the data set being clustered. Most of these algorithms work very well for compact and hyper-spherical clusters. In this paper, a new hybrid clustering algorithm called Self-Partition and Self-Merging (SPSM) is proposed. The SPSM algorithm partitions the input data set into several subclusters in the first phase and, then, removes the noisy data in the second phase. In the third phase, the normal subclusters are continuously merged to form the larger clusters based on the inter-cluster distance and intra-cluster distance criteria. From the experimental results, the SPSM algorithm is very efficient to handle the noisy data set, and to cluster the data sets of arbitrary shapes of different density. Several examples for color image show the versatility of the proposed method and compare with results described in the literature for the same images. The computational complexity of the SPSM algorithm is O(N2), where N is the number of data points.

scholarly journals Detecting heterogeneity in single-cell RNA-Seq data by non-negative matrix factorization

2016 ◽  
Author(s):  
Xun Zhu ◽  
Travers Ching ◽  
Xinghua Pan ◽  
Sherman Weissman ◽  
Lana Garmire
Keyword(s):  
Single Cell ◽  
Hierarchical Clustering ◽  
Matrix Factorization ◽  
New Technology ◽  
Data Sets ◽  
Biological Processes ◽  
Rna Seq ◽  
Clustering Methods ◽  
Hematopoietic Stem ◽  
Non Negative Matrix Factorization

Single-cell RNA-Sequencing (scRNA-Seq) is a cutting edge technology that enables the understanding of biological processes at an unprecedentedly high resolution. However, well suited bioinformatics tools to analyze the data generated from this new technology are still lacking. Here we have investigated the performance of non-negative matrix factorization (NMF) method to analyze a wide variety of scRNA-Seq data sets, ranging from mouse hematopoietic stem cells to human glioblastoma data. In comparison to other unsupervised clustering methods including K-means and hierarchical clustering, NMF has higher accuracy even when the clustering results of K-means and hierarchical clustering are enhanced by t-SNE. Moreover, NMF successfully detect the subpopulations, such as those in a single glioblastoma patient. Furthermore, in conjugation with the modularity detection method FEM, it reveals unique modules that are indicative of clinical subtypes. In summary, we propose that NMF is a desirable method to analyze heterogeneous single-cell RNA-Seq data, and the NMFEM pipeline is suitable for modularity detection among single-cell RNA-Seq data.

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