Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

Video Categorization Using Semantics and Semiotics

There is a great need to automatically segment, categorize, and annotate video data, and to develop efficient tools for browsing and searching. We believe that the categorization of videos can be achieved by exploring the concepts and meanings of the videos. This task requires bridging the gap between low-level content and high-level concepts (or semantics). Once a relationship is established between the low-level computable features of the video and its semantics, the user would be able to navigate through videos through the use of concepts and ideas (for example, a user could extract only those scenes in an action film that actually contain fights) rat her than sequentially browsing the whole video. However, this relationship must follow the norms of human perception and abide by the rules that are most often followed by the creators (directors) of these videos. These rules are called film grammar in video production literature. Like any natural language, this grammar has several dialects, but it has been acknowledged to be universal. Therefore, the knowledge of film grammar can be exploited effectively for the understanding of films. To interpret an idea using the grammar, we need to first understand the symbols, as in natural languages, and second, understand the rules of combination of these symbols to represent concepts. In order to develop algorithms that exploit this film grammar, it is necessary to relate the symbols of the grammar to computable video features. In this dissertation, we have identified a set of computable features of videos and have developed methods to estimate them. A computable feature of audio-visual data is defined as any statistic of available data that can be automatically extracted using image/signal processing and computer vision techniques. These features are global in nature and are extracted using whole images, therefore, they do not require any object detection, tracking and classification. These features include video shots, shot length, shot motion content, color distribution, key-lighting, and audio energy. We use these features and exploit the knowledge of ubiquitous film grammar to solve three related problems: segmentation and categorization of talk and game shows; classification of movie genres based on the previews; and segmentation and representation of full-length Hollywood movies and sitcoms. We have developed a method for organizing videos of talk and game shows by automatically separating the program segments from the commercials and then classifying each shot as the host\u27s or guest\u27s shot. In our approach, we rely primarily on information contained in shot transitions and utilize the inherent difference in the scene structure (grammar) of commercials and talk shows. A data structure called a shot connectivity graph is constructed, which links shots over time using temporal proximity and color similarity constraints. Analysis of the shot connectivity graph helps us to separate commercials from program segments. This is done by first detecting stories, and then assigning a weight to each story based on its likelihood of being a commercial or a program segment. We further analyze stories to distinguish shots of the hosts from those of the guests. We have performed extensive experiments on eight full-length talk shows (e.g. Larry King Live, Meet the Press, News Night) and game shows (Who Wants To Be A Millionaire), and have obtained excellent classification with 96% recall and 99% precision. http://www.cs.ucf.edu/~vision/projects/LarryKing/LarryKing.html Secondly, we have developed a novel method for genre classification of films using film previews. In our approach, we classify previews into four broad categories: comedies, action, dramas or horror films. Computable video features are combined in a framework with cinematic principles to provide a mapping to these four high-level semantic classes. We have developed two methods for genre classification; (a) a hierarchical method and (b) an unsupervised classification met hod. In the hierarchical method, we first classify movies into action and non-action categories based on the average shot length and motion content in the previews. Next, non-action movies are sub-classified into comedy, horror or drama categories by examining their lighting key. Finally, action movies are ranked on the basis of number of explosions/gunfire events. In the unsupervised method for classifying movies, a mean shift classifier is used to discover the structure of the mapping between the computable features and each film genre. We have conducted extensive experiments on over a hundred film previews and demonstrated that low-level features can be efficiently utilized for movie classification. We achieved about 87% successful classification. http://www.cs.ucf.edu/-vision/projects/movieClassification/movieClmsification.html Finally, we have addressed the problem of detecting scene boundaries in full-length feature movies. We have developed two novel approaches to automatically find scenes in the videos. Our first approach is a two-pass algorithm. In the first pass, shots are clustered by computing backward shot coherence; a shot color similarity measure that detects potential scene boundaries (PSBs) in the videos. In the second pass we compute scene dynamics for each scene as a function of shot length and the motion content in the potential scenes. In this pass, a scene-merging criterion is used to remove weak PSBs in order to reduce over-segmentation. In our second approach, we cluster shots into scenes by transforming this task into a graph-partitioning problem. This is achieved by constructing a weighted undirected graph called a shot similarity graph (SSG), where each node represents a shot and the edges between the shots are weighted by their similarities (color and motion). The SSG is then split into sub-graphs by applying the normalized cut technique for graph partitioning. The partitions obtained represent individual scenes in the video. We further extend the framework to automatically detect the best representative key frames of identified scenes. With this approach, we are able to obtain a compact representation of huge videos in a small number of key frames. We have performed experiments on five Hollywood films (Terminator II, Top Gun, Gone In 60 Seconds, Golden Eye, and A Beautiful Mind) and one TV sitcom (Seinfeld) that demonstrate the effectiveness of our approach. We achieved about 80% recall and 63% precision in our experiments. http://www.cs.ucf.edu/~vision/projects/sceneSeg/sceneSeg.htm

An Evolutionary Algorithm to Generate Ellipsoid Detectors for Negative Selection

Negative selection is a process from the biological immune system that can be applied to two-class (self and nonself) classification problems. Negative selection uses only one class (self) for training, which results in detectors for the other class (nonself). This paradigm is especially useful for problems in which only one class is available for training, such as network intrusion detection. Previous work has investigated hyper-rectangles and hyper-spheres as geometric detectors. This work proposes ellipsoids as geometric detectors. First, the author establishes a mathematical model for ellipsoids. He develops an algorithm to generate ellipsoids by training on only one class of data. Ellipsoid mutation operators, an objective function, and a convergence technique are described for the evolutionary algorithm that generates ellipsoid detectors. Testing on several data sets validates this approach by showing that the algorithm generates good ellipsoid detectors. Against artificial data sets, the detectors generated by the algorithm match more than 90% of nonself data with no false alarms. Against a subset of data from the 1999 DARPA MIT intrusion detection data, the ellipsoids generated by the algorithm detected approximately 98% of nonself (intrusions) with an approximate 0% false alarm rate

決定木・回帰木のための多変量判別ルール発見アルゴリズム

広島大学(Hiroshima University)博士(工学)Engineeringdoctora

Iowa Core: Mathematics, December 2012

Iowa Core Mathematics includes recommendations for curriculum, instruction, and assessment, as well as standards for mathematical content and mathematical practices