Clustering is a popular problem with many applications. We consider the k-means problem in the situation where the data is too large to be stored in main memory and must be accessed sequentially, such as from a disk, and where we must use as little memory as possible. Our algorithm is based on recent theoretical results, with significant improvements to make it practical. Our approach greatly simplifies arecently developed algorithm, both in design and in analysis, and eliminates large constant factors in the approximation guarantee, the memory requirements, and the running time. We then incorporate approximate nearest neighbor search to compute k-means in o(nk) (where n is the number of data points; note that computing thecost, given a solution, takes 8(nk) time). We show that our algorithm compares favorably to existing algorithms - both theoretically and experimentally, thus providing state-of-the-art performance in both theory and practice.

Most state-of-the-art techniques for multi-class image segmentation and labeling use conditional random fields defined over pixels or image regions. While regionlevel modelsoften feature dense pairwise connectivity, pixel-level models are considerably largerand have only permitted sparse graph structures. In this paper, we consider fully connected CRF models defined on the complete set of pixels in an image. The resulting graphs have billions of edges, making traditional inference algorithms impractical. Our main contribution is a highly efficient approximate inference algorithm for fully connected CRF models in which the pairwise edge potentials are defined by a linear combination of Gaussian kernels. Our experiments demonstratethat dense connectivity at the pixel level substantially improves segmentation and labeling accuracy.

In this work we use Branch-and-Bound (BB) to efficiently detect objects with deformable part models. Instead of evaluating the classifier score exhaustively over image locations and scales, we use BB to focus on promising image locations. The core problem is to compute bounds that accommodate part deformations; for this we adapt the Dual Trees data structure to our problem. We evaluate our approach using Mixture-of-Deformable Part Models. We obtain exactly the same results but are 10-20 times faster on average. We also develop a multiple-object detection variation of the system, where hypotheses for 20 categories are inserted in a common priority queue. For the problem of finding the strongest category in an image this results in up to a 100-fold speedup.

The difficulty in inverse reinforcement learning (IRL) arises in choosing the best reward function since there are typically an infinite number of reward functions that yield the given behaviour data as optimal. Using a Bayesian framework, we address this challenge by using the maximum a posteriori (MAP) estimation for the reward function, and show that most of the previous IRL algorithms can be modeled into our framework. We also present a gradient method for the MAP estimation based on the (sub)differentiability of the posterior distribution. We show the effectiveness of our approach by comparing the performance of the proposed method to those of the previous algorithms.

How do people determine which elements of a set are most representative of that set? We extend an existing Bayesian measure of representativeness, which indicates the representativeness of a sample from a distribution, to define a measure of the representativeness of an item to a set. We show that this measure is formally related to a machine learning method known as Bayesian Sets. Building on this connection, we derive an analytic expression for the representativeness of objects described by a sparse vector of binary features. We then apply this measure to a large database of images, using it to determine which images are the most representative members of different sets. Comparing the resulting predictions to human judgments of representativeness provides a test of this measure with naturalistic stimuli, and illustrates how databases that are more commonly used in computer vision and machine learning can be used to evaluate psychological theories.

We investigate a discriminatively trained model of person-object interactions for recognizing common human actions in still images. We build on the locally order-less spatial pyramid bag-of-features model, which was shown to perform extremely well on a range of object, scene and human action recognition tasks. We introduce three principal contributions. First, we replace the standard quantized local HOG/SIFT features with stronger discriminatively trained body part and object detectors. Second, we introduce new person-object interaction features based on spatial co-occurrences of individual body parts and objects. Third, we address the combinatorial problem of a large number of possible interaction pairs and propose a discriminative selection procedure using a linear support vector machine (SVM) with a sparsity inducing regularizer. Learning of action-specific body part and object interactions bypasses the difficult problem of estimating the complete human body pose configuration. Benefits of the proposed model are shown on human action recognition in consumer photographs, outperforming the strong bag-of-features baseline.

We propose a novel generative model that is able to reason jointly about the 3D scene layout as well as the 3D location and orientation of objects in the scene. In particular, we infer the scene topology, geometry as well as traffic activities from a short video sequence acquired with a single camera mounted on a moving car. Our generative model takes advantage of dynamic information in the form of vehicle tracklets as well as static information coming from semantic labels and geometry (i.e., vanishing points). Experiments show that our approach outperforms a discriminative baseline based on multiple kernel learning (MKL) which has access to the same image information. Furthermore, as we reason about objects in 3D, we are able to significantly increase the performance of state-of-the-art object detectors in their ability to estimate object orientation.

Many machine learning and signal processing problems can be formulated as linearly constrained convex programs, which could be efficiently solved by the alternating direction method (ADM). However, usually the subproblems in ADM are easily solvable only when the linear mappings in the constraints are identities. To address this issue, we propose a linearized ADM (LADM) method by linearizing the quadratic penalty term and adding a proximal term when solving the subproblems. For fast convergence, we also allow the penalty to change adaptively according a novel update rule. We prove the global convergence of LADM with adaptive penalty (LADMAP). As an example, we apply LADMAP to solve low-rank representation (LRR), which is an important subspace clustering technique yet suffers from high computation cost. By combining LADMAP with a skinny SVD representation technique, we are able to reduce the complexity $O(n^3)$ of the original ADM based method to $O(rn^2)$, where $r$ and $n$ are the rank and size of the representation matrix, respectively, hence making LRR possible for large scale applications. Numerical experiments verify that for LRR our LADMAP based methods are much faster than state-of-the-art algorithms.

Compositional models provide an elegant formalism for representing the visual appearance of highly variable objects. While such models are appealing from a theoretical point of view, it has been difficult to demonstrate that they lead to performance advantages on challenging datasets. Here we develop a grammar model for person detection and show that it outperforms previous high-performance systems on the PASCAL benchmark. Our model represents people using a hierarchy of deformable parts, variable structure and an explicit model of occlusion for partially visible objects. To train the model, we introduce a new discriminative framework for learning structured prediction models from weakly-labeled data.

We present an asymptotic analysis of Viterbi Training (VT) and contrast it with a more conventional Maximum Likelihood (ML) approach to parameter estimation in Hidden Markov Models. While ML estimator works by (locally) maximizing the likelihood of the observed data, VT seeks to maximize the probability of the most likely hidden state sequence. We develop an analytical framework based on a generating function formalism and illustrate it on an exactly solvable model of HMM with one unambiguous symbol. For this particular model the ML objective function is continuously degenerate. VT objective, in contrast, is shown to have only finite degeneracy. Furthermore, VT converges faster and results in sparser (simpler) models, thus realizing an automatic Occam's razor for HMM learning. For more general scenario VT can be worse compared to ML but still capable of correctly recovering most of the parameters.