Learning with Multiple Similarities

The notion of similarities between data points is central to many classification and clustering algorithms. We often encounter situations when there are more than one set of pairwise similarity graphs between objects, either arising from different measures of similarity between objects or from a single similarity measure defined on multiple data representations, or a combination of these. Such examples can be found in various applications in computer vision, natural language processing and computational biology. Combining information from these multiple sources is often beneficial in learning meaningful concepts from data. This dissertation proposes novel methods to effectively fuse information from these multiple similarity graphs, targeted towards two fundamental tasks in machine learning - classification and clustering. In particular, I propose two models for learning spectral embedding from multiple similarity graphs using ideas from co-training and co-regularization. Further, I propose a novel approach to the problem of multiple kernel learning (MKL), converting it to a more familiar problem of binary classification in a transformed space. The proposed MKL approach learns a ``good'' linear combination of base kernels by optimizing a quality criterion that is justified both empirically and theoretically. The ideas of the proposed MKL method are also extended to learning nonlinear combinations of kernels, in particular, polynomial kernel combination and more general nonlinear kernel combination using random forests

Motion-capture-based hand gesture recognition for computing and control

This dissertation focuses on the study and development of algorithms that enable the analysis and recognition of hand gestures in a motion capture environment. Central to this work is the study of unlabeled point sets in a more abstract sense. Evaluations of proposed methods focus on examining their generalization to users not encountered during system training. In an initial exploratory study, we compare various classification algorithms based upon multiple interpretations and feature transformations of point sets, including those based upon aggregate features (e.g. mean) and a pseudo-rasterization of the capture space. We find aggregate feature classifiers to be balanced across multiple users but relatively limited in maximum achievable accuracy. Certain classifiers based upon the pseudo-rasterization performed best among tested classification algorithms. We follow this study with targeted examinations of certain subproblems. For the first subproblem, we introduce the a fortiori expectation-maximization (AFEM) algorithm for computing the parameters of a distribution from which unlabeled, correlated point sets are presumed to be generated. Each unlabeled point is assumed to correspond to a target with independent probability of appearance but correlated positions. We propose replacing the expectation phase of the algorithm with a Kalman filter modified within a Bayesian framework to account for the unknown point labels which manifest as uncertain measurement matrices. We also propose a mechanism to reorder the measurements in order to improve parameter estimates. In addition, we use a state-of-the-art Markov chain Monte Carlo sampler to efficiently sample measurement matrices. In the process, we indirectly propose a constrained k-means clustering algorithm. Simulations verify the utility of AFEM against a traditional expectation-maximization algorithm in a variety of scenarios. In the second subproblem, we consider the application of positive definite kernels and the earth mover\u27s distance (END) to our work. Positive definite kernels are an important tool in machine learning that enable efficient solutions to otherwise difficult or intractable problems by implicitly linearizing the problem geometry. We develop a set-theoretic interpretation of ENID and propose earth mover\u27s intersection (EMI). a positive definite analog to ENID. We offer proof of EMD\u27s negative definiteness and provide necessary and sufficient conditions for ENID to be conditionally negative definite, including approximations that guarantee negative definiteness. In particular, we show that ENID is related to various min-like kernels. We also present a positive definite preserving transformation that can be applied to any kernel and can be used to derive positive definite EMD-based kernels, and we show that the Jaccard index is simply the result of this transformation applied to set intersection. Finally, we evaluate kernels based on EMI and the proposed transformation versus ENID in various computer vision tasks and show that END is generally inferior even with indefinite kernel techniques. Finally, we apply deep learning to our problem. We propose neural network architectures for hand posture and gesture recognition from unlabeled marker sets in a coordinate system local to the hand. As a means of ensuring data integrity, we also propose an extended Kalman filter for tracking the rigid pattern of markers on which the local coordinate system is based. We consider fixed- and variable-size architectures including convolutional and recurrent neural networks that accept unlabeled marker input. We also consider a data-driven approach to labeling markers with a neural network and a collection of Kalman filters. Experimental evaluations with posture and gesture datasets show promising results for the proposed architectures with unlabeled markers, which outperform the alternative data-driven labeling method

Relative Comparison Kernel Learning with Auxiliary Kernels

In this work we consider the problem of learning a positive semidefinite kernel matrix from relative comparisons of the form: "object A is more similar to object B than it is to C", where comparisons are given by humans. Existing solutions to this problem assume many comparisons are provided to learn a high quality kernel. However, this can be considered unrealistic for many real-world tasks since relative assessments require human input, which is often costly or difficult to obtain. Because of this, only a limited number of these comparisons may be provided. In this work, we explore methods for aiding the process of learning a kernel with the help of auxiliary kernels built from more easily extractable information regarding the relationships among objects. We propose a new kernel learning approach in which the target kernel is defined as a conic combination of auxiliary kernels and a kernel whose elements are learned directly. We formulate a convex optimization to solve for this target kernel that adds only minor overhead to methods that use no auxiliary information. Empirical results show that in the presence of few training relative comparisons, our method can learn kernels that generalize to more out-of-sample comparisons than methods that do not utilize auxiliary information, as well as similar methods that learn metrics over objects

A review on distance based time series classification

Time series classification is an increasing research topic due to the vast amount of time series data that is being created over a wide variety of fields. The particularity of the data makes it a challenging task and different approaches have been taken, including the distance based approach. 1-NN has been a widely used method within distance based time series classification due to its simplicity but still good performance. However, its supremacy may be attributed to being able to use specific distances for time series within the classification process and not to the classifier itself. With the aim of exploiting these distances within more complex classifiers, new approaches have arisen in the past few years that are competitive or which outperform the 1-NN based approaches. In some cases, these new methods use the distance measure to transform the series into feature vectors, bridging the gap between time series and traditional classifiers. In other cases, the distances are employed to obtain a time series kernel and enable the use of kernel methods for time series classification. One of the main challenges is that a kernel function must be positive semi-definite, a matter that is also addressed within this review. The presented review includes a taxonomy of all those methods that aim to classify time series using a distance based approach, as well as a discussion of the strengths and weaknesses of each method.TIN2016-78365-