Discriminative learning is challenging when examples are sets of features, and the sets vary in cardinality and lack any sort of meaningful ordering. Kernel-based classification methods can learn complex decision boundaries, but a kernel over unordered set inputs must somehow solve for correspondences – generally a computationally expensive task that becomes impractical for large set sizes. We present a new fast kernel function which maps unordered feature sets to multi-resolution histograms and computes a weighted histogram intersection in this space. This “pyramid match ” computation is linear in the number of features, and it implicitly finds correspondences based on the finest resolution histogram cell where a matched pair first appears. Since the kernel does not penalize the presence of extra features, it is robust to clutter. We show the kernel function is positive-definite, making it valid for use in learning algorithms whose optimal solutions are guaranteed only for Mercer kernels. We demonstrate our algorithm on object recognition tasks and show it to be accurate and dramatically faster than current approaches. 1.

Abstract. The PASCAL Visual Object Classes Challenge ran from February to March 2005. The goal of the challenge was to recognize objects from a number of visual object classes in realistic scenes (i.e. not pre-segmented objects). Four object classes were selected: motorbikes, bicycles, cars and people. Twelve teams entered the challenge. In this chapter we provide details of the datasets, algorithms used by the teams, evaluation criteria, and results achieved. 1

The advantages of discriminative learning algorithms and kernel machines are combined with generative modeling using a novel kernel between distributions. In the probability product kernel, data points in the input space are mapped to distributions over the sample space and a general inner product is then evaluated as the integral of the product of pairs of distributions. The kernel is straightforward to evaluate for all exponential family models such as multinomials and Gaussians and yields interesting nonlinear kernels. Furthermore, the kernel is computable in closed form for latent distributions such as mixture models, hidden Markov models and linear dynamical systems. For intractable models, such as switching linear dynamical systems, structured mean-field approximations can be brought to bear on the kernel evaluation. For general distributions, even if an analytic expression for the kernel is not feasible, we show a straightforward sampling method to evaluate it. Thus, the kernel permits discriminative learning methods, including support vector machines, to exploit the properties, metrics and invariances of the generative models we infer from each datum. Experiments are shown using multinomial models for text, hidden Markov models for biological data sets and linear dynamical systems for time series data.

In numerous domains it is useful to represent a single example by the set of the local features or parts that comprise it. However, this representation poses a challenge to many conventional machine learning techniques, since sets may vary in cardinality and elements lack a meaningful ordering. Kernel methods can learn complex functions, but a kernel over unordered set inputs must somehow solve for correspondences—generally a computationally expensive task that becomes impractical for large set sizes. We present a new fast kernel function called the pyramid match that measures partial match similarity in time linear in the number of features. The pyramid match maps unordered feature sets to multi-resolution histograms and computes a weighted histogram intersection in order to find implicit correspondences based on the finest resolution histogram cell where a matched pair first appears. We show the pyramid match yields a Mercer kernel, and we prove bounds on its error relative to the optimal partial matching cost. We demonstrate our algorithm on both classification and regression tasks, including object recognition, 3-D human pose inference, and time of publication estimation for documents, and we show that the proposed method is accurate and significantly more efficient than current approaches.

Abstract — Finding appropriate stable grasps for a hand (either robotic or human) on an arbitrary object has proved to be a challenging and difficult problem. The space of grasping parameters coupled with the degrees-of-freedom and geometry of the object to be grasped creates a high-dimensional, non- smooth manifold. Traditional search methods applied to this manifold are typically not powerful enough to find appropriate stable grasping solutions, let alone optimal grasps. We address this issue in this paper, which attempts to find optimal grasps of objects using a grasping simulator. Our unique approach to the problem involves a combination of numerical methods to recover parts of the grasp quality surface with any robotic hand, and contemporary machine learning methods to interpolate that surface, in order to find the optimal grasp. I.

A new class of kernels for object recognition based on local image feature representations are introduced in this paper. Formal proofs are given to show that these kernels satisfy the Mercer condition. In addition, multiple types of local features and semilocal constraints are incorporated. Experimental results of SVM classifiers coupled with the proposed kernels are reported on recognition tasks with the COIL-100 database and compared with existing methods. The proposed kernels achieved competitive performance and were robust to changes in object configurations and image degradations.

“If we knew what it was we were doing, it would not be called research, would it?”

Abstract. In this paper, we propose to combine an efficient image representation based on local descriptors with a Support Vector Machine classifier in order to perform object categorization. For this purpose, we apply kernels defined on sets of vectors. After testing different combinations of kernel / local descriptors, we have been able to identify a very performant one. 1

We introduce a new class of kernels between distributions. These induce a kernel on the input...

We develop a framework for the automatic discovery of query classes for query-class-dependent search models in multimodal retrieval. The framework automatically discovers useful query classes by clustering queries in a training set according to the performance of various unimodal search methods, yielding classes of queries which have similar fusion strategies for the combination of unimodal components for multimodal search. We further combine these performance features with the semantic features of the queries during clustering in order to make discovered classes meaningful. The inclusion of the semantic space also makes it possible to choose the correct class for new, unseen queries, which have unknown performance space features. We evaluate the system against the TRECVID 2004 automatic video search task and find that the automatically discovered query classes give an improvement of 18% in MAP over hand-defined query classes used in previous works. We also find that some hand-defined query classes, such as “Named Person ” and “Sports ” do, indeed, have similarities in search method performance and are useful for query-class-dependent multimodal search, while other hand-defined classes, such as “Named Object” and “General Object ” do not have consistent search method performance and should be split apart or replaced with other classes. The proposed framework is general and can be applied to any new domain without expert domain knowledge.