A Fractional Programming Framework for Support Vector Machine-type Formulations

We develop a theoretical framework for relating various formulations of regularization problems through fractional programming. We focus on problems with objective functions of the type L + λ · P , where the parameter λ lacks intuitive interpretation. We observe that fractional programming is an elegant approach to obtain bounds on the range of the parameter, and then generalize this approach to show that different forms can be obtained from a common fractional program. Furthermore, we apply the proposed framework in two concrete settings; we consider support vector machines (SVMs), where the framework clarifies the relation between various existing soft-margin dual forms for classification, and the SVM+ algorithm (Vapnik and Vashist, 2009), where we use this methodology to derive a new dual formulation, and obtain bounds on the cost parameter

Data mining based learning algorithms for semi-supervised object identification and tracking

Sensor exploitation (SE) is the crucial step in surveillance applications such as airport security and search and rescue operations. It allows localization and identification of movement in urban settings and can significantly boost knowledge gathering, interpretation and action. Data mining techniques offer the promise of precise and accurate knowledge acquisition techniques in high-dimensional data domains (and diminishing the “curse of dimensionality” prevalent in such datasets), coupled by algorithmic design in feature extraction, discriminative ranking, feature fusion and supervised learning (classification). Consequently, data mining techniques and algorithms can be used to refine and process captured data and to detect, recognize, classify, and track objects with predictable high degrees of specificity and sensitivity. Automatic object detection and tracking algorithms face several obstacles, such as large and incomplete datasets, ill-defined regions of interest (ROIs), variable scalability, lack of compactness, angular regions, partial occlusions, environmental variables, and unknown potential object classes, which work against their ability to achieve accurate real-time results. Methods must produce fast and accurate results by streamlining image processing, data compression and reduction, feature extraction, classification, and tracking algorithms. Data mining techniques can sufficiently address these challenges by implementing efficient and accurate dimensionality reduction with feature extraction to refine incomplete (ill-partitioning) data-space and addressing challenges related to object classification, intra-class variability, and inter-class dependencies. A series of methods have been developed to combat many of the challenges for the purpose of creating a sensor exploitation and tracking framework for real time image sensor inputs. The framework has been broken down into a series of sub-routines, which work in both series and parallel to accomplish tasks such as image pre-processing, data reduction, segmentation, object detection, tracking, and classification. These methods can be implemented either independently or together to form a synergistic solution to object detection and tracking. The main contributions to the SE field include novel feature extraction methods for highly discriminative object detection, classification, and tracking. Also, a new supervised classification scheme is presented for detecting objects in urban environments. This scheme incorporates both novel features and non-maximal suppression to reduce false alarms, which can be abundant in cluttered environments such as cities. Lastly, a performance evaluation of Graphical Processing Unit (GPU) implementations of the subtask algorithms is presented, which provides insight into speed-up gains throughout the SE framework to improve design for real time applications. The overall framework provides a comprehensive SE system, which can be tailored for integration into a layered sensing scheme to provide the war fighter with automated assistance and support. As more sensor technology and integration continues to advance, this SE framework can provide faster and more accurate decision support for both intelligence and civilian applications

Topological shape optimization of multifunctional tissue engineering scaffolds with level set method

© 2016, Springer-Verlag Berlin Heidelberg. A tissue engineering scaffold provides a proper environment to support physiological loads, and enhance cell migration and delivery for re-modeling of regenerating tissue. Hence, in the design of scaffolds, it is required to control the scaffold architecture with mechanical and mass transport properties simultaneously. In this paper, a level set-based topology optimization method will be developed to systematically generate three dimensional (3D) microstructures for tissue engineering scaffolds, with the prescribed properties for mechanical stiffness, fluid porosity and permeability. To create the internal architecture for scaffolds with desired properties, the numerical homogenization method will be used to evaluate the effective properties of the microstructure for building the periodic composite media, and a parametric level set method will be introduced to find the optimized shape and topology of the microstructure. Several numerical examples are used to demonstrate the effectiveness of the proposed method in achieving scaffolds with desired multifunctional properties, within the numerically estimated cross-property bounds between the effective bulk modulus and permeability under different porosities