Dynamic range-based distance measure for microarray expressions and a fast gene-ordering algorithm

An introduction to new robust linear and monotonic correlation coefficients

BACKGROUND

The most common measure of association between two continuous variables is the Pearson correlation (Maronna et al. in Safari an OMC. Robust statistics, 2019. https://login.proxy.bib.uottawa.ca/login?url=https://learning.oreilly.com/library/view/-/9781119214687/?ar&orpq&email=^u). When outliers are present, Pearson does not accurately measure association and robust measures are needed. This article introduces three new robust measures of correlation: Taba (T), TabWil (TW), and TabWil rank (TWR). The correlation estimators T and TW measure a linear association between two continuous or ordinal variables; whereas TWR measures a monotonic association. The robustness of these proposed measures in comparison with Pearson (P), Spearman (S), Quadrant (Q), Median (M), and Minimum Covariance Determinant (MCD) are examined through simulation. Taba distance is used to analyze genes, and statistical tests were used to identify those genes most significantly associated with Williams Syndrome (WS).

RESULTS

Based on the root mean square error (RMSE) and bias, the three proposed correlation measures are highly competitive when compared to classical measures such as P and S as well as robust measures such as Q, M, and MCD. Our findings indicate TBL2 was the most significant gene among patients diagnosed with WS and had the most significant reduction in gene expression level when compared with control (P value = 6.37E-05).

CONCLUSIONS

Overall, when the distribution is bivariate Log-Normal or bivariate Weibull, TWR performs best in terms of bias and T performs best with respect to RMSE. Under the Normal distribution, MCD performs well with respect to bias and RMSE; but TW, TWR, T, S, and P correlations were in close proximity. The identification of TBL2 may serve as a diagnostic tool for WS patients. A Taba R package has been developed and is available for use to perform all necessary computations for the proposed methods.

Genetic algorithm for assigning weights to gene expressions using functional annotations

A method, named genetic algorithm for assigning weights to gene expressions using functional annotations (GAAWGEFA), is developed to assign proper weights to the gene expressions at each time point. The weights are estimated using functional annotations of the genes in a genetic algorithm framework. The method shows gene similarity in an improved manner as compared with other existing methods because it takes advantage of the existing functional annotations of the genes. The weight combination for the expressions at different time points is determined by maximizing the fitness function of GAAWGEFA in terms of the positive predictive value (PPV) for the top 10,000 gene pairs. The performance of the proposed method is primarily compared with Biweight mid correlation (BICOR) and original expression values for the six Saccharomyces cerevisiae datasets and one Bacillus subtilis dataset. The utility of GAAWGEFA is shown in predicting the functions of 48 unclassified genes (using p-value cutoff 10^-13) from Saccharomyces cerevisiae microarray data where the expressions are weighted using GAAWGEFA and are clustered using k-medoids algorithm. The related code along with various parameters is available at http://sampa.droppages.com/GAAWGEFA.html.

A supervised weighted similarity measure for gene expressions using biological knowledge

A supervised similarity measure for Saccharomyces cerevisiae gene expressions is developed which can capture the gene similarity when multiple types of experimental conditions like cell cycle, heat shock are available for all the genes. The measure is called Weighted Pearson correlation (WPC), where the weights are systematically determined for each type of experiment by maximizing the positive predictive value for gene pairs having Pearson correlation greater than 0.80. The positive predictive value is computed by using the annotation information available from yeast GO-Slim process annotations in Saccharomyces Genome Database (SGD). Genes are then clustered by k-medoid algorithm using the newly computed WPC, and functions of 135 unclassified genes are predicted with a p-value cutoff 10^-5 using Munich Information for Protein Sequences (MIPS) annotations. Out of these genes, functional categories of 55 gene are predicted with p-value cutoff greater than 10^-10 and reported in this investigation. The superiority of WPC as compared to some existing similarity measures like Pearson correlation and Euclidean distance is demonstrated using positive predictive (PPV) values of gene pairs for different Saccharomyces cerevisiae data sets. The related code is available at http://www.sampa.droppages.com/WPC.html.

A Granular Self-Organizing Map for Clustering and Gene Selection in Microarray Data

A new granular self-organizing map (GSOM) is developed by integrating the concept of a fuzzy rough set with the SOM. While training the GSOM, the weights of a winning neuron and the neighborhood neurons are updated through a modified learning procedure. The neighborhood is newly defined using the fuzzy rough sets. The clusters (granules) evolved by the GSOM are presented to a decision table as its decision classes. Based on the decision table, a method of gene selection is developed. The effectiveness of the GSOM is shown in both clustering samples and developing an unsupervised fuzzy rough feature selection (UFRFS) method for gene selection in microarray data. While the superior results of the GSOM, as compared with the related clustering methods, are provided in terms of β -index, DB-index, Dunn-index, and fuzzy rough entropy, the genes selected by the UFRFS are not only better in terms of classification accuracy and a feature evaluation index, but also statistically more significant than the related unsupervised methods. The C-codes of the GSOM and UFRFS are available online at http://avatharamg.webs.com/software-code.

Fast and accurate hashing via iterative nearest neighbors expansion

Recently, the hashing techniques have been widely applied to approximate the nearest neighbor search problem in many real applications. The basic idea of these approaches is to generate binary codes for data points which can preserve the similarity between any two of them. Given a query, instead of performing a linear scan of the entire data base, the hashing method can perform a linear scan of the points whose hamming distance to the query is not greater than rh , where rh is a constant. However, in order to find the true nearest neighbors, both the locating time and the linear scan time are proportional to O(∑i=0(rh)(c || i)) ( c is the code length), which increase exponentially as rh increases. To address this limitation, we propose a novel algorithm named iterative expanding hashing in this paper, which builds an auxiliary index based on an offline constructed nearest neighbor table to avoid large rh . This auxiliary index can be easily combined with all the traditional hashing methods. Extensive experimental results over various real large-scale datasets demonstrate the superiority of the proposed approach.

Similarity measure learning in closed-form solution for image classification

Adopting a measure is essential in many multimedia applications. Recently, distance learning is becoming an active research problem. In fact, the distance is the natural measure for dissimilarity. Generally, a pairwise relationship between two objects in learning tasks includes two aspects: similarity and dissimilarity. The similarity measure provides different information for pairwise relationships. However, similarity learning has been paid less attention in learning problems. In this work, firstly, we propose a general framework for similarity measure learning (SML). Additionally, we define a generalized type of correlation as a similarity measure. By a set of parameters, generalized correlation provides flexibility for learning tasks. Based on this similarity measure, we present a specific algorithm under the SML framework, called correlation similarity measure learning (CSML), to learn a parameterized similarity measure over input space. A nonlinear extension version of CSML, kernel CSML, is also proposed. Particularly, we give a closed-form solution avoiding iterative search for a local optimal solution in the high-dimensional space as the previous work did. Finally, classification experiments have been performed on face databases and a handwritten digits database to demonstrate the efficiency and reliability of CSML and KCSML.

Clustering of High Throughput Gene Expression Data

High throughput biological data need to be processed, analyzed, and interpreted to address problems in life sciences. Bioinformatics, computational biology, and systems biology deal with biological problems using computational methods. Clustering is one of the methods used to gain insight into biological processes, particularly at the genomics level. Clearly, clustering can be used in many areas of biological data analysis. However, this paper presents a review of the current clustering algorithms designed especially for analyzing gene expression data. It is also intended to introduce one of the main problems in bioinformatics - clustering gene expression data - to the operations research community.