Depending on the node ordering, an adjacency matrix can highlight distinct characteristics of a graph. Deriving a "proper" node ordering is thus a critical step in visualizing a graph as an adjacency matrix. Users often try multiple matrix reorderings using different methods until they find one that meets the analysis goal. However, this trial-and-error approach is laborious and disorganized, which is especially challenging for novices. This paper presents a technique that enables users to effortlessly find a matrix reordering they want. Specifically, we design a generative model that learns a latent space of diverse matrix reorderings of the given graph. We also construct an intuitive user interface from the learned latent space by creating a map of various matrix reorderings. We demonstrate our approach through quantitative and qualitative evaluations of the generated reorderings and learned latent spaces. The results show that our model is capable of learning a latent space of diverse matrix reorderings. Most existing research in this area generally focused on developing algorithms that can compute "better" matrix reorderings for particular circumstances. This paper introduces a fundamentally new approach to matrix visualization of a graph, where a machine learning model learns to generate diverse matrix reorderings of a graph.

Analyzing air pollution data is challenging as there are various analysis focuses from different aspects: feature (what), space (where), and time (when). As in most geospatial analysis problems, besides high-dimensional features, the temporal and spatial dependencies of air pollution induce the complexity of performing analysis. Machine learning methods, such as dimensionality reduction, can extract and summarize important information of the data to lift the burden of understanding such a complicated environment. In this paper, we present a methodology that utilizes multiple machine learning methods to uniformly explore these aspects. With this methodology, we develop a visual analytic system that supports a flexible analysis workflow, allowing domain experts to freely explore different aspects based on their analysis needs. We demonstrate the capability of our system and analysis workflow supporting a variety of analysis tasks with multiple use cases.

Motivation: Heatmap is a popular visualization technique in biology and related fields. In this study, we extend heatmaps within the framework of matrix visualization (MV) by incorporating a covariate adjustment process through the estimation of conditional correlations. MV can explore the embedded information structure of high-dimensional large-scale datasets effectively without dimension reduction. The benefit of the proposed covariate-adjusted heatmap is in the exploration of conditional association structures among the subjects or variables that cannot be done with conventional MV. Results: For adjustment of a discrete covariate, the conditional correlation is estimated by the within and between analysis. This procedure decomposes a correlation matrix into the within- and between-component matrices. The contribution of the covariate effects can then be assessed through the relative structure of the between-component to the original correlation matrix while the within-component acts as a residual. When a covariate is of continuous nature, the conditional correlation is equivalent to the partial correlation under the assumption of a joint normal distribution. A test is then employed to identify the variable pairs which possess the most significant differences at varying levels of correlation before and after a covariate adjustment. In addition, a z-score significance map is constructed to visualize these results. A simulation and three biological datasets are employed to illustrate the power and versatility of our proposed method. Availability and implementation: GAP is available to readers and is free to non-commercial applications. The installation instructions, the user's manual, and the detailed tutorials can be found at http://gap.stat.sinica.edu.tw/Software/GAP. Supplementary information: Supplementary Data are available at Bioinformatics online.

BACKGROUND: Genome-wide single-nucleotide polymorphism (SNP) arrays containing hundreds of thousands of SNPs from the human genome have proven useful for studying important human genome questions. Data quality of SNP arrays plays a key role in the accuracy and precision of downstream data analyses. However, good indices for assessing data quality of SNP arrays have not yet been developed. RESULTS: We developed new quality indices to measure the quality of SNP arrays and/or DNA samples and investigated their statistical properties. The indices quantify a departure of estimated individual-level allele frequencies (AFs) from expected frequencies via standardized distances. The proposed quality indices followed lognormal distributions in several large genomic studies that we empirically evaluated. AF reference data and quality index reference data for different SNP array platforms were established based on samples from various reference populations. Furthermore, a confidence interval method based on the underlying empirical distributions of quality indices was developed to identify poor-quality SNP arrays and/or DNA samples. Analyses of authentic biological data and simulated data show that this new method is sensitive and specific for the detection of poor-quality SNP arrays and/or DNA samples. CONCLUSIONS: This study introduces new quality indices, establishes references for AFs and quality indices, and develops a detection method for poor-quality SNP arrays and/or DNA samples. We have developed a new computer program that utilizes these methods called SNP Array Quality Control (SAQC). SAQC software is written in R and R-GUI and was developed as a user-friendly tool for the visualization and evaluation of data quality of genome-wide SNP arrays. The program is available online (http://www.stat.sinica.edu.tw/hsinchou/genetics/quality/SAQC.htm).

BACKGROUND: The hierarchical clustering tree (HCT) with a dendrogram 1 and the singular value decomposition (SVD) with a dimension-reduced representative map 2 are popular methods for two-way sorting the gene-by-array matrix map employed in gene expression profiling. While HCT dendrograms tend to optimize local coherent clustering patterns, SVD leading eigenvectors usually identify better global grouping and transitional structures. RESULTS: This study proposes a flipping mechanism for a conventional agglomerative HCT using a rank-two ellipse (R2E, an improved SVD algorithm for sorting purpose) seriation by Chen 3 as an external reference. While HCTs always produce permutations with good local behaviour, the rank-two ellipse seriation gives the best global grouping patterns and smooth transitional trends. The resulting algorithm automatically integrates the desirable properties of each method so that users have access to a clustering and visualization environment for gene expression profiles that preserves coherent local clusters and identifies global grouping trends. CONCLUSION: We demonstrate, through four examples, that the proposed method not only possesses better numerical and statistical properties, it also provides more meaningful biomedical insights than other sorting algorithms. We suggest that sorted proximity matrices for genes and arrays, in addition to the gene-by-array expression matrix, can greatly aid in the search for comprehensive understanding of gene expression structures. Software for the proposed methods can be obtained at http://gap.stat.sinica.edu.tw/Software/GAP.

BACKGROUND: Survival time is an important clinical trait for many disease studies. Previous works have shown certain relationship between patients' gene expression profiles and survival time. However, due to the censoring effects of survival time and the high dimensionality of gene expression data, effective and unbiased selection of a gene expression signature to predict survival probabilities requires further study. METHOD: We propose a method for an integrated study of survival time and gene expression. This method can be summarized as a two-step procedure: in the first step, a moderate number of genes are pre-selected using correlation or liquid association (LA). Imputation and transformation methods are employed for the correlation/LA calculation. In the second step, the dimension of the predictors is further reduced using the modified sliced inverse regression for censored data (censorSIR). RESULTS: The new method is tested via both simulated and real data. For the real data application, we employed a set of 295 breast cancer patients and found a linear combination of 22 gene expression profiles that are significantly correlated with patients' survival rate. CONCLUSION: By an appropriate combination of feature selection and dimension reduction, we find a method of identifying gene expression signatures which is effective for survival prediction.

BACKGROUND: A microarray study may select different differentially expressed gene sets because of different selection criteria. For example, the fold-change and p-value are two commonly known criteria to select differentially expressed genes under two experimental conditions. These two selection criteria often result in incompatible selected gene sets. Also, in a two-factor, say, treatment by time experiment, the investigator may be interested in one gene list that responds to both treatment and time effects. RESULTS: We propose three layer ranking algorithms, point-admissible, line-admissible (convex), and Pareto, to provide a preference gene list from multiple gene lists generated by different ranking criteria. Using the public colon data as an example, the layer ranking algorithms are applied to the three univariate ranking criteria, fold-change, p-value, and frequency of selections by the SVM-RFE classifier. A simulation experiment shows that for experiments with small or moderate sample sizes (less than 20 per group) and detecting a 4-fold change or less, the two-dimensional (p-value and fold-change) convex layer ranking selects differentially expressed genes with generally lower FDR and higher power than the standard p-value ranking. Three applications are presented. The first application illustrates a use of the layer rankings to potentially improve predictive accuracy. The second application illustrates an application to a two-factor experiment involving two dose levels and two time points. The layer rankings are applied to selecting differentially expressed genes relating to the dose and time effects. In the third application, the layer rankings are applied to a benchmark data set consisting of three dilution concentrations to provide a ranking system from a long list of differentially expressed genes generated from the three dilution concentrations. CONCLUSION: The layer ranking algorithms are useful to help investigators in selecting the most promising genes from multiple gene lists generated by different filter, normalization, or analysis methods for various objectives.

BACKGROUND: Most virus detection methods are geared towards the detection of specific single viruses or just a few known targets, and lack the capability to uncover the novel viruses that cause emerging viral infections. To address this issue, we developed a computational method that identifies the conserved viral sequences at the genus level for all viral genomes available in GenBank, and established a virus probe library. The virus probes are used not only to identify known viruses but also for discerning the genera of emerging or uncharacterized ones. RESULTS: Using the microarray approach, the identity of the virus in a test sample is determined by the signals of both genus and species-specific probes. The genera of emerging and uncharacterized viruses are determined based on hybridization of the viral sequences to the conserved probes for the existing viral genera. A detection and classification procedure to determine the identity of a virus directly from detection signals results in the rapid identification of the virus. CONCLUSION: We have demonstrated the validity and feasibility of the above strategy with a small number of viral samples. The probe design algorithm can be applied to any publicly available viral sequence database. The strategy of using separate genus and species probe sets enables the use of a straightforward virus identity calculation directly based on the hybridization signals. Our virus identification strategy has great potential in the diagnosis of viral infections. The virus genus and specific probe database and the associated summary tables are available at http://genestamp.sinica.edu.tw/virus/index.htm.