Analysis and inference for networks in bio-informatics and other applications

Abstract

Networks are useful models in science and engineering with many applications such as bio-informatics. An important problem is network analysis where one aims to estimate the relations among the quantities from measurements, from which further inference can be carried out. For example, by analyzing the gene interactions from gene microarray or other data may help to improve our understanding of biological processes and more importantly underlying mechanism leading to various diseases. Images or videos can also be viewed as a network with strong local and inter frame correlation. With the advancement of modern information collection techniques, a large amount of quantitative measurements can be collected, which present great challenges to network analysis and inference due to the significantly increased numbers of variables for describing the relationships. Consequently, the associated complexity and dimensionality grow dramatically. Moreover, in group-based or longitudinal-based studies, multiple networks and dynamic networks are encountered, which further complicate the network analysis problem. Validation is also a critical issue in gene microarray data analysis due to the absence of ground truth. This thesis addresses these challenges by proposing several novel extensions to existing network analysis, inference techniques and focuses on practical applications in bio-informatics and target tracking in ultrasound videos. First, a new inter-network analysis method is proposed for identifying the difference in the network connections among different classes of data or different time points in time-series data. The proposed approach first identifies a set of “class specific features” and then the connections between these features and other remaining features. In particular, we propose a novel consensus gene selection criterion for partial least square (PLS) regression, which is able to identify more comprehensive but essential features by randomly partitioning of the training data of assessing their relative importance through the rank statistic. Through regressing these genes with the remaining genes for each class, “class specific subnetwork analysis” is performed. As the entire network may contain thousands of genes and millions of connections, an efficient parallel implementation based on the graphic processing unit (GPU) is also proposed to reduce the computational time. Second, a systematic method is proposed for analyzing large-scale time-course gene microarray data. The proposed approach first identifies putative genes and their interactions from time-course gene microarray data. Then, these identified genes and interactions are used for discovering new findings. In particular, we proposed a novel enrichment method, which is able to validate the statistical significance of the putative interactions by comparing these interactions with existing knowledge of interactions summarized in related databases. In this way, although no ground truth is available, the statistical validation results can still quantify the statistical significance of identified networks. Finally, a new target tracking algorithm for ultrasound videos is proposed. In particular, a novel position and intensity transformation is proposed to establish the correspondence between pixels in two frames. The usefulness of this proposed is verified by tracking Central Tendon of Rectus Femoris (CT-RF) in ultrasound videos. Experimental results on 20 subjects show that the proposed algorithm can better adapt to the intensity and shape variation in the image sequences and offers better tracking performance than conventional methods.