We extend the mixtures of Gaussians (MOG) model to the projected mixture of Gaussians (PMOG) model. In the PMOG model, we assume that q dimensional input data points z_i are projected by a q dimensional vector w into 1-D variables u_i. The projected variables u_i are assumed to follow a 1-D MOG model. In the PMOG model, we maximize the likelihood of observing u_i to find both the model parameters for the 1-D MOG as well as the projection vector w. First, we derive an EM algorithm for estimating the PMOG model. Next, we show how the PMOG model can be applied to the problem of blind source separation (BSS). In contrast to conventional BSS where an objective function based on an approximation to differential entropy is minimized, PMOG based BSS simply minimizes the differential entropy of projected sources by fitting a flexible MOG model in the projected 1-D space while simultaneously optimizing the projection vector w. The advantage of PMOG over conventional BSS algorithms is the more flexible fitting of non-Gaussian source densities without assuming near-Gaussianity (as in conventional BSS) and still retaining computational feasibility.

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing image acquisition in magnetic resonance scanners, can be addressed by querying the SLM posterior covariance, unrelated to the density's mode. We propose a scalable algorithmic framework, with which SLM posteriors over full, high-resolution images can be approximated for the first time, solving a variational optimization problem which is convex iff posterior mode finding is convex. These methods successfully drive the optimization of sampling trajectories for real-world magnetic resonance imaging through Bayesian experimental design, which has not been attempted before. Our methodology provides new insight into similarities and differences between sparse reconstruction and approximate Bayesian inference, and has important implications for compressive sensing of real-world images.

Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many signal and image processing tasks. It is now well understood that the choice of the sparsity regularization term is critical in the success of such models. Based on a codelength minimization interpretation of sparse coding, and using tools from universal coding theory, we propose a framework for designing sparsity regularization terms which have theoretical and practical advantages when compared to the more standard l0 or l1 ones. The presentation of the framework and theoretical foundations is complemented with examples that show its practical advantages in image denoising, zooming and classification.

As increasing amounts of sensitive personal information is aggregated into data repositories, it has become important to develop mechanisms for processing the data without revealing information about individual data instances. The differential privacy model provides a framework for the development and theoretical analysis of such mechanisms. In this paper, we propose an algorithm for learning a discriminatively trained multi-class Gaussian classifier that satisfies differential privacy using a large margin loss function with a perturbed regularization term. We present a theoretical upper bound on the excess risk of the classifier introduced by the perturbation.

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.

We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen's self-organizing maps, a class of artificial neural networks. On several examples we show advantages of using non-linear objects for data approximation in comparison to the linear ones. We propose four numerical criteria for comparing linear and non-linear mappings of datasets into the spaces of lower dimension. The examples are taken from comparative political science, from analysis of high-throughput data in molecular biology, from analysis of dynamical systems.

Human vision is often guided by instinctual commonsense such as proportions and contours. In this paper, we explore how to use the proportion as the key knowledge for designing a privacy algorithm that detects human private parts in a 3D scan dataset. The Analogia Graph is introduced to study the proportion of structures. It is a graph-based representation of the proportion knowledge. The intrinsic human proportions are applied to reduce the search space by an order of magnitude. A feature shape template is constructed to match the model data points using Radial Basis Functions in a non-linear regression and the relative measurements of the height and area factors. The method is tested on 100 datasets from CAESAR database. Two surface rendering methods are studied for data privacy: blurring and transparency. It is found that test subjects normally prefer to have the most possible privacy in both rendering methods. However, the subjects adjusted their privacy measurement to a certain degree as they were informed the context of security.

The work presented in this paper is part of a multidisciplinary team collaborating in the deployment of an autonomous oceanographic probe with the task of exploring marine regions and take phytoplankton samples for their subsequent analysis in a laboratory. We will describe an autonomous system that, from sensor data, is able to characterize phytoplankton structures. Because the system has to work inboard, a main goal of our approach is to dramatically reduce the dimensionality of the problem. Specifically, our development uses two AI techniques, namely Particle Swarm Optimization and Case-Based Reasoning. We report results of experiments performed with simulated environments.

Non-invasive identity inference in the home environment is a very challenging problem. A practical solution to the problem could have far reaching implications in many industries, such as home entertainment. In this work, we consider the problem of identity inference using a TV remote control. In particular, we address two challenges that have so far prevented the work of Chang et al. (2009) from being applied in a home entertainment system. First, we show how to learn the patterns of TV remote controls incrementally and online. Second, we generalize our results to partially labeled data. To achieve our goal, we use state-of-the-art methods for max-margin learning and online convex programming. Our solution is efficient, runs in real time, and comes with theoretical guarantees. It performs well in practice and we demonstrate this on 4 datasets of 2 to 4 people.

Human core body temperature (Tcore) is an important measure of thermal state, e.g., hypo-or hyperthermia, but is difficult to measure using noninvasive wearable sensors. We estimated parameters for a discrete KF model from data collected during several Military training events and from distance runners (n 38). Model performance was evaluated in 25 physically-active subjects who participated in various laboratory and field studies involving exercise of 2-to-8 h duration at ambient temperatures of 20 to 40 C. Overall, the KF model's estimate of Tcore had a root mean square error of 0.30 0.13 ºC from the observed Tcore, and was within 0.5 ºC over 85% of the time. The benefit of the KF approach is that it requires only one input while current state of the art models typically require multiple inputs including individual anthropometrics, metabolic rate, clothing characteristics, and environmental conditions. This state estimation problem in computational physiology illustrates the potential for collaboration between the artificial intelligence and ambulatory physiological monitoring communities. Figure 1: U.S. National Guard Civil Support Team (CST) member engaged in a chemical biological training event.