New approaches for clustering high dimensional data

Clustering is one of the most effective methods for analyzing datasets that contain a large number of objects with numerous attributes. Clustering seeks to identify groups, or clusters, of similar objects. In low dimensional space, the similarity between objects is often evaluated by summing the difference across all of their attributes. High dimensional data, however, may contain irrelevant attributes which mask the existence of clusters. The discovery of groups of objects that are highly similar within some subsets of relevant attributes becomes an important but challenging task. My thesis focuses on various models and algorithms for this task. We first present a flexible clustering model, namely OP-Cluster (Order Preserving Cluster). Under this model, two objects are similar on a subset of attributes if the values of these two objects induce the same relative ordering of these attributes. OPClustering algorithm has demonstrated to be useful to identify co-regulated genes in gene expression data. We also propose a semi-supervised approach to discover biologically meaningful OP-Clusters by incorporating existing gene function classifications into the clustering process. This semi-supervised algorithm yields only OP-clusters that are significantly enriched by genes from specific functional categories. Real datasets are often noisy. We propose a noise-tolerant clustering algorithm for mining frequently occuring itemsets. This algorithm is called approximate frequent itemsets (AFI). Both the theoretical and experimental results demonstrate that our AFI mining algorithm has higher recoverability of real clusters than any other existing itemset mining approaches. Pair-wise dissimilarities are often derived from original data to reduce the complexities of high dimensional data. Traditional clustering algorithms taking pair-wise dissimilarities as input often generate disjoint clusters from pair-wise dissimilarities. It is well known that the classification model represented by disjoint clusters is inconsistent with many real classifications, such gene function classifications. We develop a Poclustering algorithm, which generates overlapping clusters from pair-wise dissimilarities. We prove that by allowing overlapping clusters, Poclustering fully preserves the information of any dissimilarity matrices while traditional partitioning algorithms may cause significant information loss

Fuzzy-Granular Based Data Mining for Effective Decision Support in Biomedical Applications

Due to complexity of biomedical problems, adaptive and intelligent knowledge discovery and data mining systems are highly needed to help humans to understand the inherent mechanism of diseases. For biomedical classification problems, typically it is impossible to build a perfect classifier with 100% prediction accuracy. Hence a more realistic target is to build an effective Decision Support System (DSS). In this dissertation, a novel adaptive Fuzzy Association Rules (FARs) mining algorithm, named FARM-DS, is proposed to build such a DSS for binary classification problems in the biomedical domain. Empirical studies show that FARM-DS is competitive to state-of-the-art classifiers in terms of prediction accuracy. More importantly, FARs can provide strong decision support on disease diagnoses due to their easy interpretability. This dissertation also proposes a fuzzy-granular method to select informative and discriminative genes from huge microarray gene expression data. With fuzzy granulation, information loss in the process of gene selection is decreased. As a result, more informative genes for cancer classification are selected and more accurate classifiers can be modeled. Empirical studies show that the proposed method is more accurate than traditional algorithms for cancer classification. And hence we expect that genes being selected can be more helpful for further biological studies

Preparation and characterization of magnetite (Fe3O4) nanoparticles By Sol-Gel method

The magnetite (Fe3O4) nanoparticles were successfully synthesized and annealed under vacuum at different temperature. The Fe3O4 nanoparticles prepared via sol-gel assisted method and annealed at 200-400ºC were characterized by Fourier Transformation Infrared Spectroscopy (FTIR), X-ray Diffraction spectra (XRD), Field Emission Scanning Electron Microscope (FESEM) and Atomic Force Microscopy (AFM). The XRD result indicate the presence of Fe3O4 nanoparticles, and the Scherer`s Formula calculated the mean particles size in range of 2-25 nm. The FESEM result shows that the morphologies of the particles annealed at 400ºC are more spherical and partially agglomerated, while the EDS result indicates the presence of Fe3O4 by showing Fe-O group of elements. AFM analyzed the 3D and roughness of the sample; the Fe3O4 nanoparticles have a minimum diameter of 79.04 nm, which is in agreement with FESEM result. In many cases, the synthesis of Fe3O4 nanoparticles using FeCl3 and FeCl2 has not been achieved, according to some literatures, but this research was able to obtained Fe3O4 nanoparticles base on the characterization results

Significance and recovery of blocks structures in binary and real-valued matrices with noise

Biclustering algorithms have been of recent interest in the field of Data Mining, particularly in the analysis of high dimensional data. Most biclustering problems can be stated in the following form: given a rectangular data matrix with real or categorical entries, find every submatrix satisfying a given criterion. In this dissertation, we study the statistical properties of several commonly used biclustering algorithms under appropriate random matrix models. For binary data, we establish a three-point concentration result, and several related probability bounds, for the size of the largest square submatrix of 1s in a square Bernoulli matrix, and extend these results to non-square matrices and submatrices with fixed aspect ratios. We then consider the noise sensitivity of frequent itemset mining under a simple binary additive noise model, and show that, even at small noise levels, large blocks of 1s leave behind fragments of only logarithmic size. As a result, standard FIM algorithms that search only for submatrices of 1s cannot directly recover such blocks when noise is present. On the positive side, we show that an error-tolerant frequent itemset criterion can recover a submatrix of 1s against a background of 0s plus noise, even when the size of the submatrix of 1s is very small. For data matrices with real-valued entries, we establish a concentration result for the size of the largest square submatrix with high average in a square Gaussian matrix. Probability upper bounds on the size of the largest non-square high average submatrix with a fixed row/column aspect ratio in a non-square real-valued matrix with fixed row/column aspect ratio are also established when the entries of the matrix follow appropriate distributions. For biclustering algorithms targeting submatrices with low ANOVA residuals, we show how to assess the significance of the resulting submatrices. Lastly, we study the recoverability of submatrices with high average under an additive Gaussian noise model

Combinatorial chromatin modification patterns in the human genome revealed by subspace clustering

Chromatin modifications, such as post-translational modification of histone proteins and incorporation of histone variants, play an important role in regulating gene expression. Joint analyses of multiple histone modification maps are starting to reveal combinatorial patterns of modifications that are associated with functional DNA elements, providing support to the ‘histone code’ hypothesis. However, due to the lack of analytical methods, only a small number of chromatin modification patterns have been discovered so far. Here, we introduce a scalable subspace clustering algorithm, coherent and shifted bicluster identification (CoSBI), to exhaustively identify the set of combinatorial modification patterns across a given epigenome. Performance comparisons demonstrate that CoSBI can generate biclusters with higher intra-cluster coherency and biological relevance. We apply our algorithm to a compendium of 39 genome-wide chromatin modification maps in human CD4+ T cells. We identify 843 combinatorial patterns that recur at >0.1% of the genome. A total of 19 chromatin modifications are observed in the combinatorial patterns, 10 of which occur in more than half of the patterns. We also identify combinatorial modification signatures for eight classes of functional DNA elements. Application of CoSBI to epigenome maps of different cells and developmental stages will aid in understanding how chromatin structure helps regulate gene expression

Multipartite Graph Algorithms for the Analysis of Heterogeneous Data

The explosive growth in the rate of data generation in recent years threatens to outpace the growth in computer power, motivating the need for new, scalable algorithms and big data analytic techniques. No field may be more emblematic of this data deluge than the life sciences, where technologies such as high-throughput mRNA arrays and next generation genome sequencing are routinely used to generate datasets of extreme scale. Data from experiments in genomics, transcriptomics, metabolomics and proteomics are continuously being added to existing repositories. A goal of exploratory analysis of such omics data is to illuminate the functions and relationships of biomolecules within an organism. This dissertation describes the design, implementation and application of graph algorithms, with the goal of seeking dense structure in data derived from omics experiments in order to detect latent associations between often heterogeneous entities, such as genes, diseases and phenotypes. Exact combinatorial solutions are developed and implemented, rather than relying on approximations or heuristics, even when problems are exceedingly large and/or difficult. Datasets on which the algorithms are applied include time series transcriptomic data from an experiment on the developing mouse cerebellum, gene expression data measuring acute ethanol response in the prefrontal cortex, and the analysis of a predicted protein-protein interaction network. A bipartite graph model is used to integrate heterogeneous data types, such as genes with phenotypes and microbes with mouse strains. The techniques are then extended to a multipartite algorithm to enumerate dense substructure in multipartite graphs, constructed using data from three or more heterogeneous sources, with applications to functional genomics. Several new theoretical results are given regarding multipartite graphs and the multipartite enumeration algorithm. In all cases, practical implementations are demonstrated to expand the frontier of computational feasibility