Miguel Á. Carreira-Perpiñán

Multiscale conditional random fields for image labeling

We propose an approach to include contextual features for labeling images, in which each pixel is assigned to one of a finite set of labels. The features are incorporated into a probabilistic framework, which combines the outputs of several components. Components differ in the information they encode. Some focus on the image-label mapping, while others focus solely on patterns within the label field. Components also differ in their scale, as some focus on fine-resolution patterns while others on coarser, more global structure. A supervised version of the contrastive divergence algorithm is applied to learn these features from labeled image data. We demonstrate performance on two real-world image databases and compare it to a classifier and a Markov random field.

Gaussian Mean-Shift Is an EM Algorithm

The mean-shift algorithm, based on ideas proposed by Fukunaga and Hosteller, is a hill-climbing algorithm on the density defined by a finite mixture or a kernel density estimate. Mean-shift can be used as a nonparametric clustering method and has attracted recent attention in computer vision applications such as image segmentation or tracking. We show that, when the kernel is Gaussian, mean-shift is an expectation-maximization (EM) algorithm and, when the kernel is non-Gaussian, mean-shift is a generalized EM algorithm. This implies that mean-shift converges from almost any starting point and that, in general, its convergence is of linear order. For Gaussian mean-shift, we show: 1) the rate of linear convergence approaches 0 (superlinear convergence) for very narrow or very wide kernels, but is often close to 1 (thus, extremely slow) for intermediate widths and exactly 1 (sublinear convergence) for widths at which modes merge, 2) the iterates approach the mode along the local principal component of the data points from the inside of the convex hull of the data points, and 3) the convergence domains are nonconvex and can be disconnected and show fractal behavior. We suggest ways of accelerating mean-shift based on the EM interpretation

Mode-finding for mixtures of Gaussian distributions

Gradient-quadratic and fixed-point iteration algorithms and appropriate values for their control parameters are derived for finding all modes of a Gaussian mixture, a problem with applications in clustering and regression. The significance of the modes found is quantified locally by Hessian-based error bars and globally by the entropy as sparseness measure.

Constrained spectral clustering through affinity propagation

Pairwise constraints specify whether or not two samples should be in one cluster. Although it has been successful to incorporate them into traditional clustering methods, such as K-means, little progress has been made in combining them with spectral clustering. The major challenge in designing an effective constrained spectral clustering is a sensible combination of the scarce pairwise constraints with the original affinity matrix. We propose to combine the two sources of affinity by propagating the pairwise constraints information over the original affinity matrix. Our method has a Gaussian process interpretation and results in a closed-form expression for the new affinity matrix. Experiments show it outperforms state-of-the-art constrained clustering methods in getting good clusterings with fewer constraints, and yields good image segmentation with user-specified pairwise constraints.

Fast nonparametric clustering with Gaussian blurring mean-shift

We revisit Gaussian blurring mean-shift (GBMS), a procedure that iteratively sharpens a dataset by moving each data point according to the Gaussian mean-shift algorithm (GMS). (1) We give a criterion to stop the procedure as soon as clustering structure has arisen and show that this reliably produces image segmentations as good as those of GMS but much faster. (2) We prove that GBMS has convergence of cubic order with Gaussian clusters (much faster than GMSs, which is of linear order) and that the local principal component converges last, which explains the powerful clustering and denoising properties of GBMS. (3) We show a connection with spectral clustering that suggests GBMS is much faster. (4) We further accelerate GBMS by interleaving connected-components and blurring steps, achieving 2x--4x speedups without introducing an approximation error. In summary, our accelerated GBMS is a simple, fast, nonparametric algorithm that achieves segmentations of state-of-the-art quality.

Acceleration Strategies for Gaussian Mean-Shift Image Segmentation

Gaussian mean-shift (GMS) is a clustering algorithm that has been shown to produce good image segmentations (where each pixel is represented as a feature vector with spatial and range components). GMS operates by defining a Gaussian kernel density estimate for the data and clustering together points that converge to the same mode under a fixed-point iterative scheme. However, the algorithm is slow, since its complexity is O(kN2), where N is the number of pixels and k the average number of iterations per pixel. We study four acceleration strategies for GMS based on the spatial structure of images and on the fact that GMS is an expectation-maximisation (EM) algorithm: spatial discretisation, spatial neighbourhood, sparse EM and EM-Newton algorithm. We show that the spatial discretisation strategy can accelerate GMS by one to two orders of magnitude while achieving essentially the same segmentation; and that the other strategies attain speedups of less than an order of magnitude.

Practical Identifiability of Finite Mixtures of Multivariate Bernoulli Distributions

The class of finite mixtures of multivariate Bernoulli distributions is known to be nonidentifiable; that is, different values of the mixture parameters can correspond to exactly the same probability distribution. In principle, this would mean that sample estimates using this model would give rise to different interpretations. We give empirical support to the fact that estimation of this class of mixtures can still produce meaningful results in practice, thus lessening the importance of the identifiability problem. We also show that the expectation-maximization algorithm is guaranteed to converge to a proper maximum likelihood estimate, owing to a property of the log-likelihood surface. Experiments with synthetic data sets show that an original generating distribution can be estimated from a sample. Experiments with an electropalatography data set show important structure in the data.

Hashing with binary autoencoders

An attractive approach for fast search in image databases is binary hashing, where each high-dimensional, real-valued image is mapped onto a low-dimensional, binary vector and the search is done in this binary space. Finding the optimal hash function is difficult because it involves binary constraints, and most approaches approximate the optimization by relaxing the constraints and then binarizing the result. Here, we focus on the binary autoencoder model, which seeks to reconstruct an image from the binary code produced by the hash function. We show that the optimization can be simplified with the method of auxiliary coordinates. This reformulates the optimization as alternating two easier steps: one that learns the encoder and decoder separately, and one that optimizes the code for each image. Image retrieval experiments show the resulting hash function outperforms or is competitive with state-of-the-art methods for binary hashing.

On the number of modes of a Gaussian mixture

We consider a problem intimately related to the creation of maxima under Gaussian blurring: the number of modes of a Gaussian mixture in D dimensions. To our knowledge, a general answer to this question is not known. We conjecture that if the components of the mixture have the same covariance matrix (or the same covariance matrix up to a scaling factor), then the number of modes cannot exceed the number of components. We demonstrate that the number of modes can exceed the number of components when the components are allowed to have arbitrary and different covariance matrices. We will review related results from scale-space theory, statistics and machine learning, including a proof of the conjecture in 1D. We present a convergent, EM-like algorithm for mode finding and compare results of searching for all modes starting from the centers of the mixture components with a brute-force search. We also discuss applications to data reconstruction and clustering.

Occupancy Modeling and Prediction for Building Energy Management

Heating, cooling and ventilation accounts for 35% energy usage in the United States. Currently, most modern buildings still condition rooms assuming maximum occupancy rather than actual usage. As a result, rooms are often over-conditioned needlessly. Thus, in order to achieve efficient conditioning, we require knowledge of occupancy. This article shows how real time occupancy data from a wireless sensor network can be used to create occupancy models, which in turn can be integrated into building conditioning system for usage-based demand control conditioning strategies. Using strategies based on sensor network occupancy model predictions, we show that it is possible to achieve 42% annual energy savings while still maintaining American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) comfort standards.