Sharlee Climer

Rearrangement Clustering: Pitfalls, Remedies, and Applications

Given a matrix of values in which the rows correspond to objects and the columns correspond to features of the objects, rearrangement clustering is the problem of rearranging the rows of the matrix such that the sum of the similarities between adjacent rows is maximized. Referred to by various names and reinvented several times, this clustering technique has been extensively used in many fields over the last three decades. In this paper, we point out two critical pitfalls that have been previously overlooked. The first pitfall is deleterious when rearrangement clustering is applied to objects that form natural clusters. The second concerns a similarity metric that is commonly used. We present an algorithm that overcomes these pitfalls. This algorithm is based on a variation of the Traveling Salesman Problem. It offers an extra benefit as it automatically determines cluster boundaries. Using this algorithm, we optimally solve four benchmark problems and a 2,467-gene expression data clustering problem. As expected, our new algorithm identifies better clusters than those found by previous approaches in all five cases. Overall, our results demonstrate the benefits of rectifying the pitfalls and exemplify the usefulness of this clustering technique. Our code is available at our websites.

Image database indexing using JPEG coefficients

Abstract Image database indexing is used for efficient retrieval of images in response to a query expressed as an example image. The query image is processed to extract information that is matched against the index to provide pointers to similar images. We present a technique that facilitates content similarity-based retrieval of jpeg -compressed images without first having to uncompress them. The technique is based on an index developed from a subset of jpeg coefficients and a similarity measure to determine the difference between the query image and the images in the database. This method offers substantial efficiency as images are processed in compressed format, information that was derived during the original compression of the images is reused, and extensive early pruning is possible. Initial experiments with the index have provided encouraging results. The system outputs a set of ranked images in the database with respect to the query using the similarity measure, and can be limited to output a specified number of matched images by changing the threshold match.

Local lines: a linear time line detector

This paper introduces LOCAL LINES--a robust, high-resolution line detector that operates in linear time. LOCAL LINES tolerates noisy images well and can be optimized for various specialized applications by adjusting the values of configurable parameters, such as mask values and mask size. As described in this paper, the resolution of LOCAL LINES is the maximum that can be justified for pixelized data. Despite this high resolution, LOCAL LINES is of linear asymptotic complexity in terms of number of pixels in an image. This paper also provides a comparison of LOCAL LINES with the prevalent Hough Transform Line Detector.

Take a walk and cluster genes: a TSP-based approach to optimal rearrangement clustering

Cluster analysis is a fundamental problem and technique in many areas related to machine learning. In this paper, we consider rearrangement clustering, which is the problem of finding sets of objects that share common or similar features by arranging the rows (objects) of a matrix (specifying object features) in such a way that adjacent objects are similar to each other (based on a similarity measure of the features) so as to maximize the overall similarity. Based on formulating this problem as the Traveling Salesman Problem (TSP), we develop a new TSP-based optimal clustering algorithm called TSPCluster. We overcome a flaw that is inherent in previous approaches by relaxing restrictions on dissimilarities between clusters. Our new algorithm has three important features: finding the optimal k clusters for a given k, automatically detecting cluster borders, and ascertaining a set of most viable clustering results that make good balances among maximizing the overall similarity within clusters and dissimilarity between clusters. We apply TSPCluster to cluster and display ~500 genes of flowering plant Arabidopsis which are regulated under various abiotic stress conditions. We compare TSPCluster to the bond energy algorithm and two existing clustering algorithms. Our TSPCluster code is available at (Climer & Zhang, 2004).

A custom correlation coefficient (CCC) approach for fast identification of multi-SNP association patterns in genome-wide SNPs data.

Complex diseases are often associated with sets of multiple interacting genetic factors and possibly with unique sets of the genetic factors in different groups of individuals (genetic heterogeneity). We introduce a novel concept of custom correlation coefficient (CCC) between single nucleotide polymorphisms (SNPs) that address genetic heterogeneity by measuring subset correlations autonomously. It is used to develop a 3‐step process to identify candidate multi‐SNP patterns: (1) pairwise (SNP–SNP) correlations are computed using CCC; (2) clusters of so‐correlated SNPs identified; and (3) frequencies of these clusters in disease cases and controls compared to identify disease‐associated multi‐SNP patterns. This method identified 42 candidate multi‐SNP associations with hypertensive heart disease (HHD), among which one cluster of 22 SNPs (six genes) included 13 in SLC8A1 (aka NCX1, an essential component of cardiac excitation‐contraction coupling) and another of 32 SNPs had 29 from a different segment of SLC8A1. While allele frequencies show little difference between cases and controls, the cluster of 22 associated alleles were found in 20% of controls but no cases and the other in 3% of controls but 20% of cases. These suggest that both protective and risk effects on HHD could be exerted by combinations of variants in different regions of SLC8A1, modified by variants from other genes. The results demonstrate that this new correlation metric identifies disease‐associated multi‐SNP patterns overlooked by commonly used correlation measures. Furthermore, computation time using CCC is a small fraction of that required by other methods, thereby enabling the analyses of large GWAS datasets.

Moving from capstones toward cornerstones: successes and challenges in applying systems biology to identify mechanisms of autism spectrum disorders.

The substantial progress in the last few years toward uncovering genetic causes and risk factors for autism spectrum disorders (ASDs) has opened new experimental avenues for identifying the underlying neurobiological mechanism of the condition. The bounty of genetic findings has led to a variety of data-driven exploratory analyses aimed at deriving new insights about the shared features of these genes. These approaches leverage data from a variety of different sources such as co-expression in transcriptomic studies, protein–protein interaction networks, gene ontologies (GOs) annotations, or multi-level combinations of all of these. Here, we review the recurrent themes emerging from these analyses and highlight some of the challenges going forward. Themes include findings that ASD associated genes discovered by a variety of methods have been shown to contain disproportionate amounts of neurite outgrowth/cytoskeletal, synaptic, and more recently Wnt-related and chromatin modifying genes. Expression studies have highlighted a disproportionate expression of ASD gene sets during mid fetal cortical development, particularly for rare variants, with multiple analyses highlighting the striatum and cortical projection and interneurons as well. While these explorations have highlighted potentially interesting relationships among these ASD-related genes, there are challenges in how to best transition these insights into empirically testable hypotheses. Nonetheless, defining shared molecular or cellular pathology downstream of the diverse genes associated with ASDs could provide the cornerstones needed to build toward broadly applicable therapeutic approaches.

Allele-specific network reveals combinatorial interaction that transcends small effects in psoriasis GWAS.

Hundreds of genetic markers have shown associations with various complex diseases, yet the “missing heritability” remains alarmingly elusive. Combinatorial interactions may account for a substantial portion of this missing heritability, but their discoveries have been impeded by computational complexity and genetic heterogeneity. We present BlocBuster, a novel systems-level approach that efficiently constructs genome-wide, allele-specific networks that accurately segregate homogenous combinations of genetic factors, tests the associations of these combinations with the given phenotype, and rigorously validates the results using a series of unbiased validation methods. BlocBuster employs a correlation measure that is customized for single nucleotide polymorphisms and returns a multi-faceted collection of values that captures genetic heterogeneity. We applied BlocBuster to analyze psoriasis, discovering a combinatorial pattern with an odds ratio of 3.64 and Bonferroni-corrected p-value of 5.01×10−16. This pattern was replicated in independent data, reflecting robustness of the method. In addition to improving prediction of disease susceptibility and broadening our understanding of the pathogenesis underlying psoriasis, these results demonstrate BlocBusters potential for discovering combinatorial genetic associations within heterogeneous genome-wide data, thereby transcending the limiting “small effects” produced by individual markers examined in isolation.

How frugal is mother nature with haplotypes

MOTIVATION Inference of haplotypes from genotype data is crucial and challenging for many vitally important studies. The first, and most critical step, is the ascertainment of a biologically sound model to be optimized. Many models that have been proposed rely partially or entirely on reducing the number of unique haplotypes in the solution. RESULTS This article examines the parsimony of haplotypes using known haplotypes as well as genotypes from the HapMap project. Our study reveals that there are relatively few unique haplotypes, but not always the least possible, for the datasets with known solutions. Furthermore, we show that there are frequently very large numbers of parsimonious solutions, and the number increases exponentially with increasing cardinality. Moreover, these solutions are quite varied, most of which are not consistent with the true solutions. These results quantify the limitations of the Pure Parsimony model and demonstrate the imperative need to consider additional properties for haplotype inference models. At a higher level, and with broad applicability, this article illustrates the power of combinatorial methods to tease out imperfections in a given biological model.

Latitudinal Clines of the Human Vitamin D Receptor and Skin Color Genes

The well-documented latitudinal clines of genes affecting human skin color presumably arise from the need for protection from intense ultraviolet radiation (UVR) vs. the need to use UVR for vitamin D synthesis. Sampling 751 subjects from a broad range of latitudes and skin colors, we investigated possible multilocus correlated adaptation of skin color genes with the vitamin D receptor gene (VDR), using a vector correlation metric and network method called BlocBuster. We discovered two multilocus networks involving VDR promoter and skin color genes that display strong latitudinal clines as multilocus networks, even though many of their single gene components do not. Considered one by one, the VDR components of these networks show diverse patterns: no cline, a weak declining latitudinal cline outside of Africa, and a strong in- vs. out-of-Africa frequency pattern. We confirmed these results with independent data from HapMap. Standard linkage disequilibrium analyses did not detect these networks. We applied BlocBuster across the entire genome, showing that our networks are significant outliers for interchromosomal disequilibrium that overlap with environmental variation relevant to the genes’ functions. These results suggest that these multilocus correlations most likely arose from a combination of parallel selective responses to a common environmental variable and coadaptation, given the known Mendelian epistasis among VDR and the skin color genes.

Complete Parsimony Haplotype Inference Problem and Algorithms

Haplotype inference by pure parsimony (HIPP) is a well-known paradigm for haplotype inference. In order to assess the biological significance of this paradigm, we generalize the problem of HIPP to the problem of finding all optimal solutions, which we call complete HIPP. We study intrinsic haplotype features, such as backbone haplotypes and fat genotypes as well as equal columns and decomposability. We explicitly exploit these features in three computational approaches which are based on integer linear programming, depth-first branch-and-bound, and a hybrid algorithm that draws on the diverse strengths of the first two approaches. Our experimental analysis shows that our optimized algorithms are significantly superior to the baseline algorithms, often with orders of magnitude faster running time. Finally, our experiments provide some useful insights to the intrinsic features of this interesting problem.