Dominant sets are a new graph-theoretic concept that has proven to be relevant in pairwise data clustering problems, such as image segmentation. They generalize the notion of a maximal clique to edgeweighted graphs and have intriguing, nontrivial connections to continuous quadratic optimization and spectral-based grouping. We address the problem of grouping out-of-sample examples after the clustering process has taken place. This may serve either to drastically reduce the computational burden associated to the processing of very large data sets, or to efficiently deal with dynamic situations whereby data sets need to be updated continually. We show that the very notion of a dominant set offers a simple and efficient way of doing this. Numerical experiments on various grouping problems show the effectiveness of the approach.

Choice-based conjoint analysis builds models of consumer preferences over products with answers gathered in questionnaires. Our main goal is to bring tools from the machine learning community to solve this problem more efficiently. Thus, we propose two algorithms to quickly and accurately estimate consumer preferences.

In this paper we propose a probabilistic model for online document clustering. We use nonparametric Dirichlet process prior to model the growing number of clusters, and use a prior of general English language model as the base distribution to handle the generation of novel clusters. Furthermore, cluster uncertainty is modeled with a Bayesian Dirichletmultinomial distribution. We use empirical Bayes method to estimate hyperparameters based on a historical dataset. Our probabilistic model is applied to the novelty detection task in Topic Detection and Tracking (TDT) and compared with existing approaches in the literature.

Such a complexity is significant even for moderate size problems and is prohibitive for large datasets. We present an approximation technique based on the improved fast Gauss transform to reduce the computation to O(N). We also give an error bound for the approximation, and provide experimental results on the UCI datasets.

We give a fast rejection scheme that is based on image segments and demonstrate it on the canonical example of face detection. However, instead of focusing on the detection step we focus on the rejection step and show that our method is simple and fast to be learned, thus making it an excellent pre-processing step to accelerate standard machine learning classifiers, such as neural-networks, Bayes classifiers or SVM. We decompose a collection of face images into regions of pixels with similar behavior over the image set. The relationships between the mean and variance of image segments are used to form a cascade of rejectors that can reject over 99.8% of image patches, thus only a small fraction of the image patches must be passed to a full-scale classifier. Moreover, the training time for our method is much less than an hour, on a standard PC.

Most existing tracking algorithms construct a representation of a target object prior to the tracking task starts, and utilize invariant features to handle appearance variation of the target caused by lighting, pose, and view angle change. In this paper, we present an efficient and effective online algorithm that incrementally learns and adapts a low dimensional eigenspace representation to reflect appearance changes of the target, thereby facilitating the tracking task. Furthermore, our incremental method correctly updates the sample mean and the eigenbasis, whereas existing incremental subspace update methods ignore the fact the sample mean varies over time. The tracking problem is formulated as a state inference problem within a Markov Chain Monte Carlo framework and a particle filter is incorporated for propagating sample distributions over time. Numerous experiments demonstrate the effectiveness of the proposed tracking algorithm in indoor and outdoor environments where the target objects undergo large pose and lighting changes.

We claim and present arguments to the effect that a large class of manifold learning algorithms that are essentially local and can be framed as kernel learning algorithms will suffer from the curse of dimensionality, at the dimension of the true underlying manifold. This observation suggests to explore non-local manifold learning algorithms which attempt to discover shared structure in the tangent planes at different positions. A criterion for such an algorithm is proposed and experiments estimating a tangent plane prediction function are presented, showing its advantages with respect to local manifold learning algorithms: it is able to generalize very far from training data (on learning handwritten character image rotations), where a local nonparametric method fails.

During the last ten years there has been growing interest in the development of Brain Computer Interfaces (BCIs). The field has mainly been driven by the needs of completely paralyzed patients to communicate. With a few exceptions, most human BCIs are based on extracranial electroencephalography (EEG). However, reported bit rates are still low. One reason for this is the low signal-to-noise ratio of the EEG [16]. We are currently investigating if BCIs based on electrocorticography (ECoG) are a viable alternative. In this paper we present the method and examples of intracranial EEG recordings of three epilepsy patients with electrode grids placed on the motor cortex. The patients were asked to repeatedly imagine movements of two kinds, e.g., tongue or finger movements. We analyze the classifiability of the data using Support Vector Machines (SVMs) [18, 21] and Recursive Channel Elimination (RCE) [11].

Embedding algorithms search for low dimensional structure in complex data, but most algorithms only handle objects of a single type for which pairwise distances are specified. This paper describes a method for embedding objects of different types, such as images and text, into a single common Euclidean space based on their co-occurrence statistics. The joint distributions are modeled as exponentials of Euclidean distances in the low-dimensional embedding space, which links the problem to convex optimization over positive semidefinite matrices.

Visual action recognition is an important problem in computer vision. In this paper, we propose a new method to probabilistically model and recognize actions of articulated objects, such as hand or body gestures, in image sequences. Our method consists of three levels of representation. At the low level, we first extract a feature vector invariant to scale and in-plane rotation by using the Fourier transform of a circular spatial histogram. Then, spectral partitioning [20] is utilized to obtain an initial clustering; this clustering is then refined using a temporal smoothness constraint. Gaussian mixture model (GMM) based clustering and density estimation in the subspace of linear discriminant analysis (LDA) are then applied to thousands of image feature vectors to obtain an intermediate level representation. Finally, at the high level we build a temporal multiresolution histogram model for each action by aggregating the clustering weights of sampled images belonging to that action. We discuss how this high level representation can be extended to achieve temporal scaling invariance and to include Bigram or Multi-gram transition information. Both image clustering and action recognition/segmentation results are given to show the validity of our three tiered representation.