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In this paper, we propose a window-based mechanism visualization approach as an alternative way to measure the seriousness of the difference among data-insights extracted from a composite biodata point. The approach is based on two components: undirected graph and Mosaab-metric space. The significant application of this approach is to visualize the segmented genome of a virus. We use Influenza and Ebola viruses as examples to demonstrate the robustness of this approach and to conduct comparisons. This approach can provide researchers with deep insights about information structures extracted from a segmented genome as a composite biodata point, and consequently, to capture the segmented genetic variations and diversity (variants) in composite data points.

In this paper, we propose a novel approach to analyze and visualize genetic variation of a segmented genome of a virus in feature spaces embedded in IRp and/or higher feature spaces embedded in IRp′ ∋ p′ > p. The segmented genome of a virus is considered as a heterogeneous sequence-set with different mutation rates. In this approach, the dispersion maps of a virus are computed in a decentralized manner using an arbitrary set of substrings of specific length (e.g. 2-grams). The new approach is considered as new decentralized alignment-free visualization tool. The new decentralized alignment-free visualization tool, shows effectiveness in capturing and analyzing genetic variation that causes the genetic biodiversity of the segmented gnome of a virus. The new alignment-free visualization tool is expected to be a useful tool in biomedical sector, specifically with a network of mobile laboratories.

Our goal in this dissertation is to solve the sequence-set proximity problem (SSPP) under the homology-free assumption, which is defined as the problem of measuring the closeness between any two sets of biosequences, where there is no prior knowledge of homology within each sequence-set or between sequence-sets (homology is defined as a property of two or more sequences that share a common ancestor). It is a generalization of the sequence proximity problem. These sets of bio-sequences are the subject matter of several applications, such as unsupervised classification (clustering), supervised classification, and observing the changes that may take place over time in a biological phenomenon. Measuring the distance between two sets of sequences can be achieved using a distance measure at the sequence-set level. Discriminating sets of sequences based on their biological variation using a mathematical distance measure defined at the sequence-set level is a complicated task, and the question is: Can we observe the biological variation in sets of sequences, and employ it for the discrimination process between them? In this dissertation we propose distance measure(s)/metric(s) defined in terms of the variance-covariance structure to capture the biological variation, as an alternative structure to solve the sequence-set proximity problem under the homology-free assumption, where this assumption prevents the effective use of all the existing homology-based alignment measures and homology-based alignment-free measures. The variance-covariance structure has several appealing properties that make it useful in describing biological variation. The proposed measures/metric are matrix inverse operation-free, and thus they can work with singular variance-covariance matrices, and are computationally simpler than the existing variance-covariance-based distance measures (or models). We build a number of algorithms upon the proposed distance measure(s)/metric(s), to perform a variety of tasks at the sequence-set level, such as: searching, unsupervised classification, supervised classification, variability detection, and visualization, all without relying on any assumptions of homology. The datasets under investigation are sequence-based datasets. Thus, there is a need for feature extraction algorithms (i.e. adapters), to map bio-sequences from the data space ( D ) to the feature space ( F : 'p'), in order to enable the proposed algorithms to work with real-valued patterns. In this context, we propose (i) a new mechanism for the 'n'-grams technique, to extract features from these sets of biosequences. The new mechanism has the capability to map the changes in these sequences over the time (i.e. sequence time, where a sequence is a one dimensional time series), to the feature space, and (ii) a new approach for defining a new feature vector, where the features are defined as the distances between successive recurrences of a set of words of length 'n.' We perform a number of experiments using real datasets, and our algorithms show robustness in performing the required tasks.