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Today, vast and unwieldy data collections are regularly being generated and analyzed in hopes of supporting an ever-expanding range of challenging sensing applications. Modern inference schemes usually involve millions of parameters to learn complex real-world tasks, which creates the need for large annotated datasets for training. For several visual learning applications, collecting large amounts of annotated data is either challenging or very expensive; one such domain is medical image analysis. In this thesis, machine learning methods were devised with emphasis on Cancerous Tissue Recognition (CTR) applications. First, a lightweight active constrained clustering scheme was developed for the processing of image data which capitalizes on actively acquired pairwise constraints. The proposed methodology introduces the use of the Silhouette values, conventionally used for measuring clustering performance, in order to rank the degree of information content of the various samples. Second, an active selection framework that operates in tandem with Convolutional Neural Networks (CNNs) was constructed for CTR. In the presence of limited annotations, alternative (or sometimes complementary) venues were explored in an effort to restrain the high expenditure of collecting image annotations required by CNN-based schemes. Third, a Symmetric Positive Definite (SPD) image representation was derived for CTR, termed Covariance Kernel Descriptor (CKD) which consistently outperformed a large collection of popular image descriptors. Even though the CKD successfully describes the tissue architecture for small image regions, its performance decays when implemented on larger slide regions or whole tissue slides due to the larger variability that tissue exhibits at that level, since different types of tissue can be present as the regions grow (healthy, benign disease, malignant disease). Fourth, to leverage the recognition capability of the CKDs to larger slide regions, the Weakly Annotated Image Descriptor (WAID) was devised as the parameters of classifier decision boundaries in a multiple instance learning framework. Fifth, an Information Divergence and Dictionary Learning (IDDL) scheme for SPD matrices was developed for identifying appropriate geometries and similarities for SPD matrices and was successfully tested on a diverse set of recognition problems including activity, object, and texture recognition as well as CTR. Finally, a transition of IDDL to an unsupervised setup was developed, dubbed alpha-beta-KMeans, to address the problem of learning information divergences while clustering SPD matrices in the absence of labeled data.

High Occupancy Toll (HOT) lanes are "oases" of free-flow conditions within congested freeways. Observations support the benefits of HOT and High Occupancy Vehicle (HOV) lanes implementation which in many cases can carry up to half of the people carried on the entire freeway. Developed operational strategies for the HOT lanes aim in controlling the demand so that a high level of service is provided to the users of the facility. A particularly important design feature of HOT lanes is the locations that vehicles can merge in or out; this feature is closely connected to the mobility and safety of the facility. This study paves the way for a systematic methodology that incorporates knowledge obtained from extensive periods of observations to the design of the Optimal Lane Changing Regions (OLCR) on forthcoming facilities. This methodology is applicable to HOT facilities that adopt a conservative design for their access zones by allowing interaction only at areas of high lane changing demand between exit ramps and entrance ramps to the freeway. Existing methodologies are based on engineering judgment or studies that take into consideration limited amount of observations. The proposed methodology was relied on a Monte Carlo sampling framework for revealing the advisory OLCR at various demand levels. Traffic flow is reconstructed for all the General Purpose Lanes (GPLs) of the segment of interest; headway sequences are constructed based on a calibrated Fundamental Diagram investigation for each GPL. A Gap Acceptance model was developed to shape the time increments that vehicles spend on each GPL. The final outcome of this methodology is advisory positions and lengths of merging areas on HOT facilities based on the simulated distance that vehicles travel between the entrance/exit ramp and the HOT lane. Another direction that this study aimed in making a contribution is access restriction on existing facilities in response to future increased demand levels; the goal is to preserve safety and mobility of the HOT facility. A quantity of major importance to the operation of buffer separated shared HOT lanes is the interaction between the HOT lane and its adjacent lane. The proposed methodology uses shockwave activity as surrogate for mobility and safety (shockwave length) to investigate the behavior of existing facilities for future demand levels. Specifically, shockwave length distributions were derived from a Monte Carlo sampling methodology taking advantage of a wave propagation model based on one-dimensional kinematic equations. After the proposed model was successfully tested for its ability to describe shockwave propagation on selected locations at present demand levels, an investigation of wave propagation at artificially increased density levels was conducted. The developed mechanism for achieving the increase in density was based on a scoring system that achieved the desired increase iteratively. Simulated shockwave length distributions were derived and the increased demand levels resulting in a flow breakdown on the HOT facility were identified. The outcome of this methodology can support the decision of engineers to restrict access to locations that reach their operational boundary.