To find out how the representations of structured visual objects depend on the co-occurrence statistics of their constituents, we exposed subjects to a set of composite images with tight control exerted over (1) the conditional probabilities of the constituent fragments, and (2) the value of Barlow's criterion of "suspicious coincidence" (the ratio of joint probability to the product of marginals). We then compared the part verification response times for various probe/target combinations before and after the exposure. For composite probes, the speedup was much larger for targets that contained pairs of fragments perfectly predictive of each other, compared to those that did not. This effect was modulated by the significance of their co-occurrence as estimated by Barlow's criterion. For lone-fragment probes, the speedup in all conditions was generally lower than for composites. These results shed light on the brain's strategies for unsupervised acquisition of structural information in vision.

To find out how the representations of structured visual objects depend on the co-occurrence statistics of their constituents, we exposed subjects to a set of composite images with tight control exerted over (1) the conditional probabilitiesof the constituent fragments, and (2) the value of Barlow's criterion of "suspicious coincidence" (the ratio of joint probability to the product of marginals). We then compared the part verification response timesfor various probe/target combinations before and after the exposure. For composite probes, the speedup was much larger for targets thatcontained pairs of fragments perfectly predictive of each other, compared to those that did not. This effect was modulated by the significance oftheir co-occurrence as estimated by Barlow's criterion. For lone-fragment probes, the speedup in all conditions was generally lower than for composites. These results shed light on the brain's strategies for unsupervised acquisition of structural information in vision.

This paper presents an unsupervised learning algorithm that can derive the probabilistic dependence structure of parts of an object (a moving human bodyin our examples) automatically from unlabeled data. The distinguished partof this work is that it is based on unlabeled data, i.e., the training features include both useful foreground parts and background clutter and the correspondence between the parts and detected features are unknown. We use decomposable triangulated graphs to depict the probabilistic independence of parts, but the unsupervised technique is not limited to this type of graph. In the new approach, labeling of the data (part assignments) is taken as hidden variables and the EM algorithm isapplied. A greedy algorithm is developed to select parts and to search for the optimal structure based on the differential entropy of these variables. The success of our algorithm is demonstrated by applying it to generate models of human motion automatically from unlabeled real image sequences.

In many discrimination problems a large amount of data is available but only a few of them are labeled. This provides a strong motivation to improve or develop methods for semi-supervised learning. In this paper, boosting is generalized to this task within the optimization framework of MarginBoost . We extend the margin definition to unlabeled data and develop the gradient descent algorithm that corresponds to the resulting margin cost function. This meta-learning scheme can be applied to any base classifier able to benefit from unlabeled data. We propose here to apply it to mixture models trained with an Expectation-Maximization algorithm. Promising results are presented on benchmarks with different rates of labeled data.

Unsupervised Learning: Foundations of Neural Computation is a collection of 21 papers published in the journal Neural Computation in the 10-year period since its founding in 1989 by Terrence Sejnowski. Neural Computation has become the leading journal of its kind. The editors of the book are Geoffrey Hinton and Terrence Sejnowski, two pioneers in neural networks. The selected papers include some of the most influential titles of late, for example, "What Is the Goal of Sensory Coding" by David Field and "An Information-Maximization Approach to Blind Separation and Blind Deconvolution" by Anthony Bell and Terrence Sejnowski. The edited volume provides a sample of important works on unsupervised learning, which cut across the fields of

For example, it is trivial to record hours of heartbeats from hundreds of patients. However, it is expensive to hire cardiologists to label each of the recorded beats. One response to the expense of class labels is to squeeze the most information possible out of each labeled example. Regularization and cross-validation both have this goal. A second response is to start with a small set of labeled examples and request labels of only those currently unlabeled examples that are expected to provide a significant improvement in the behavior of the classifier (Lewis & Catlett, 1994; Freund et al., 1993). A third response is to tap into a largely ignored potential source of information; namely, unlabeled examples. This response is supported by the theoretical work of Castelli and Cover (1995) which suggests that unlabeled examples have value in learning classification problems.

For example, it is trivial to record hours of heartbeats from hundreds of patients. However, it is expensive to hire cardiologists to label each of the recorded beats. One response to the expense of class labels is to squeeze the most information possible out of each labeled example. Regularization and cross-validation both have this goal. A second response is to start with a small set of labeled examples and request labels of only those currently unlabeled examples that are expected to provide a significant improvement in the behavior of the classifier (Lewis & Catlett, 1994; Freund et al., 1993). A third response is to tap into a largely ignored potential source of information; namely, unlabeled examples. This response is supported by the theoretical work of Castelli and Cover (1995) which suggests that unlabeled examples have value in learning classification problems.

This paper presents a formulation for unsupervised learning of clusters reflecting multiple causal structure in binary data. Unlike the standard mixture model, a multiple cause model accounts for observed data by combining assertions from many hidden causes, each of which can pertain to varying degree to any subset of the observable dimensions. A crucial issue is the mixing-function for combining beliefs from different cluster-centers in order to generate data reconstructions whose errors are minimized both during recognition and learning. We demonstrate a weakness inherent to the popular weighted sum followed by sigmoid squashing, and offer an alternative form of the nonlinearity. Results are presented demonstrating the algorithm's ability successfully to discover coherent multiple causal representat.ions of noisy test data and in images of printed characters. 1 Introduction The objective of unsupervised learning is to identify patterns or features reflecting underlying regularities in data. Single-cause techniques, including the k-means algorithm and the standard mixture-model (Duda and Hart, 1973), represent clusters of data points sharing similar patterns of Is and Os under the assumption that each data point belongs to, or was generated by, one and only one cluster-center; output activity is constrained to sum to 1. In contrast, a multiple-cause model permits more than one cluster-center to become fully active in accounting for an observed data vector.

We represent objects with n-dimensional pattern vectors and consider piecewise-linear classifiers consisting of a collection of (labeled) codebook vectors in the space of the input patterns (See Figure 1). The classification boundaries are gi ven by the voronoi tessellation of the codebook vectors. Patterns are said to belong to the class (given by the label) of the codebook vector to which they are closest.

We represent objects with n-dimensional pattern vectors and consider piecewise-linear classifiers consisting of a collection of (labeled) codebook vectors in the space of the input patterns (See Figure 1). The classification boundaries are gi ven by the voronoi tessellation of the codebook vectors. Patterns are said to belong to the class (given by the label) of the codebook vector to which they are closest.