Bounding Embeddings of VC Classes into Maximum Classes

One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinality for their VC dimension. The most promising approach to positively resolving the conjecture is by embedding general VC classes into maximum classes without super-linear increase to their VC dimensions, as such embeddings would extend the known compression schemes to all VC classes. We show that maximum classes can be characterised by a local-connectivity property of the graph obtained by viewing the class as a cubical complex. This geometric characterisation of maximum VC classes is applied to prove a negative embedding result which demonstrates VC-d classes that cannot be embedded in any maximum class of VC dimension lower than 2d. On the other hand, we show that every VC-d class C embeds in a VC-(d+D) maximum class where D is the deficiency of C, i.e., the difference between the cardinalities of a maximum VC-d class and of C. For VC-2 classes in binary n-cubes for 4 <= n <= 6, we give best possible results on embedding into maximum classes. For some special classes of Boolean functions, relationships with maximum classes are investigated. Finally we give a general recursive procedure for embedding VC-d classes into VC-(d+k) maximum classes for smallest k.Comment: 22 pages, 2 figure

Automatic age progression and estimation from faces

Recently, automatic age progression has gained popularity due to its numerous applications. Among these is the frequent search for missing people, in the UK alone up to 300,000 people are reported missing every year. Although many algorithms have been proposed, most of the methods are affected by image noise, illumination variations, and facial expressions. Furthermore, most of the algorithms use a pattern caricaturing approach which infers ages by manipulating the target image and a template face formed by averaging faces at the intended age. To this end, this thesis investigates the problem with a view to tackling the most prominent issues associated with the existing algorithms. Initially using active appearance models (AAM), facial features are extracted and mapped to people’s ages, afterward a formula is derived which allows the convenient generation of age progressed images irrespective of whether the intended age exists in the training database or not. In order to handle image noise as well as varying facial expressions, a nonlinear appearance model called kernel appearance model (KAM) is derived. To illustrate the real application of automatic age progression, both AAM and KAM based algorithms are then used to synthesise faces of two popular long missing British and Irish kids; Ben Needham and Mary Boyle. However, both statistical techniques exhibit image rendering artefacts such as low-resolution output and the generation of inconsistent skin tone. To circumvent this problem, a hybrid texture enhancement pipeline is developed. To further ensure that the progressed images preserve people’s identities while at the same time attaining the intended age, rigorous human and machine based tests are conducted; part of this tests resulted to the development of a robust age estimation algorithm. Eventually, the results of the rigorous assessment reveal that the hybrid technique is able to handle all existing problems of age progression with minimal error.National Information Technology Development Agency of Nigeria (NITDA

Data mining methodologies for supporting engineers during system identification

Data alone are worth almost nothing. While data collection is increasing exponentially worldwide, a clear distinction between retrieving data and obtaining knowledge has to be made. Data are retrieved while measuring phenomena or gathering facts. Knowledge refers to data patterns and trends that are useful for decision making. Data interpretation creates a challenge that is particularly present in system identification, where thousands of models may explain a given set of measurements. Manually interpreting such data is not reliable. One solution is to use data mining. This thesis thus proposes an integration of techniques from data mining, a field of research where the aim is to find knowledge from data, into an existing multiple-model system identification methodology. It is shown that, within a framework for decision support, data mining techniques constitute a valuable tool for engineers performing system identification. For example, clustering techniques group similar models together in order to guide subsequent decisions since they might indicate possible states of a structure. A main issue concerns the number of clusters, which, usually, is unknown. For determining the correct number of clusters in data and estimating the quality of a clustering algorithm, a score function is proposed. The score function is a reliable index for estimating the number of clusters in a given data set, thus increasing understanding of results. Furthermore, useful information for engineers who perform system identification is achieved through the use of feature selection techniques. They allow selection of relevant parameters that explain candidate models. The core algorithm is a feature selection strategy based on global search. In addition to providing information about the candidate model space, data mining is found to be a valuable tool for supporting decisions related to subsequent sensor placement. When integrated into a methodology for iterative sensor placement, clustering is found to provide useful support through providing a rational basis for decisions related to subsequent sensor placement on existing structures. Greedy and global search strategies should be selected according to the context. Experiments show that whereas global search is more efficient for initial sensor placement, a greedy strategy is more suitable for iterative sensor placement

A compression approach to support vector model selection

In this paper we investigate connections between statistical learning theory and data compression on the basis of support vector machine (SVM) model selection. Inspired by several generalization bounds we construct ``compression coefficients'' for SVMs, which measure the amount by which the training labels can be compressed by some classification hypothesis. The main idea is to relate the coding precision of this hypothesis to the width of the margin of the SVM. The compression coefficients connect well known quantities such as the radius-margin ratio R^2/rho^2, the eigenvalues of the kernel matrix and the number of support vectors. To test whether they are useful in practice we ran model selection experiments on several real world datasets. As a result we found that compression coefficients can fairly accurately predict the parameters for which the test error is minimized

A compression approach to support vector model selection

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