The two-thirds power law, an empirical law stating an inverse nonlinear relationship between the tangential hand speed and the curvature of its trajectory during curved motion, is widely acknowledged to be an invariant ofupper-limb movement. It has also been shown to exist in eyemotion, locomotionand was even demonstrated in motion perception and prediction. This ubiquity has fostered various attempts to uncover the origins of this empirical relationship. In these it was generally attributed eitherto smoothness in hand-or joint-space or to the result of mechanisms that damp noise inherent in the motor system to produce the smooth trajectories evident in healthy human motion. We show here that white Gaussian noise also obeys this power-law. Analysis ofsignal and noise combinations shows that trajectories that were synthetically created not to comply with the power-law are transformed to power-law compliant ones after combination with low levels of noise. Furthermore, there exist colored noise types that drive non-power-law trajectories to power-law compliance and are not affected by smoothing. These results suggest caution when running experiments aimed at verifying thepower-law or assuming its underlying existence without proper analysis of the noise. Our results could also suggest that the power-law might be derived not from smoothness or smoothness-inducing mechanisms operatingon the noise inherent in our motor system but rather from the correlated noise which is inherent in this motor system.

Theories of visual attention commonly posit that early parallel processes extract conspicuous featuressuch as color contrast and motion from the visual field. These features are then combined into a saliency map, and attention is directed to the most salient regions first. Top-down attentional control is achieved by modulating the contribution of different feature types to the saliency map. A key source of data concerning attentional control comes from behavioral studies in which the effect of recent experience is examined asindividuals repeatedly perform a perceptual discrimination task (e.g., "what shape is the odd-colored object?"). The robust finding is that repetition of features of recent trials (e.g., target color) facilitates performance. We view this facilitation as an adaptation to the statistical structure of the environment. We propose a probabilistic model of the environment that is updated after each trial. Under the assumption that attentional control operates so as to make performance more efficient for more likely environmental states, we obtain parsimonious explanations for data from four different experiments. Further, our model provides a rational explanation for why the influence of past experience on attentional control is short lived.

To investigate how top-down (TD) and bottom-up (BU) information is weighted in the guidance of human search behavior, we manipulated the proportions of BU and TD components in a saliency-based model. The model is biologically plausible and implements an artificial retina and a neuronal population code. The BU component is based on featurecontrast. TheTD component is defined by a feature-template match to a stored target representation. We compared the model's behavior at different mixturesof TD and BU components to the eye movement behavior of human observers performing the identical search task. We found that a purely TD model provides a much closer match to human behavior than any mixture model using BU information. Only when biological constraints areremoved (e.g., eliminating the retina) did a BU/TD mixture model begin to approximate human behavior.

We present a series of theoretical arguments supporting the claim that a large class of modern learning algorithms that rely solely on the smoothness prior-with similarity between examples expressed with a local kernel - are sensitive to the curse of dimensionality, or more precisely to the variability of the target. Our discussion covers supervised, semisupervised andunsupervised learning algorithms. These algorithms are found to be local in the sense that crucial properties of the learned function atx depend mostly on the neighbors of x in the training set. This makes them sensitive to the curse of dimensionality, well studied for classical nonparametric statistical learning. We show in the case of the Gaussian kernel that when the function to be learned has many variations, these algorithms require a number of training examples proportional to the number of variations, which could be large even though there may exist shortdescriptions of the target function, i.e. their Kolmogorov complexity maybe low. This suggests that there exist non-local learning algorithms that at least have the potential to learn about such structured but apparently complex functions (because locally they have many variations), whilenot using very specific prior domain knowledge.

Motivated by the problem of learning to detect and recognize objects with minimal supervision, we develop a hierarchical probabilistic model for the spatial structure of visual scenes. In contrast with most existing models, our approach explicitly captures uncertainty in the number of object instances depicted in a given image. Our scene model is based on the transformed Dirichlet process (TDP), a novel extension of the hierarchical DPin which a set of stochastically transformed mixture components are shared between multiple groups of data. For visual scenes, mixture components describe the spatial structure of visual features in an object-centered coordinate frame, while transformations model the object positionsin a particular image. Learning and inference in the TDP, which has many potential applications beyond computer vision, is based on an empirically effective Gibbs sampler. Applied to a dataset of partially labeledstreet scenes, we show that the TDP's inclusion of spatial structure improves detection performance, flexibly exploiting partially labeled training images.

It is well-known that everything that is learnable in the difficult online setting, where an arbitrary sequences of examples must be labeled one at a time, is also learnable in the batch setting, where examples are drawn independently from a distribution. We show a result in the opposite direction. Wegive an efficient conversion algorithm from batch to online that is transductive: it uses future unlabeled data. This demonstrates the equivalence between what is properly and efficiently learnable in a batch model and a transductive online model.

Standard statistical models of language fail to capture one of the most striking properties of natural languages: the power-law distribution in the frequencies of word tokens. We present a framework for developing statistical models that generically produce power-laws, augmenting standard generativemodels with an adaptor that produces the appropriate pattern of token frequencies. We show that taking a particular stochastic process - the Pitman-Yor process - as an adaptor justifies the appearance of type frequencies in formal analyses of natural language, and improves the performance of a model for unsupervised learning of morphology.

Spectral clustering enjoys its success in both data clustering and semisupervised learning.But, most spectral clustering algorithms cannot handle multi-class clustering problems directly. Additional strategies are needed to extend spectral clustering algorithms to multi-class clustering problems.Furthermore, most spectral clustering algorithms employ hard cluster membership, which is likely to be trapped by the local optimum. Inthis paper, we present a new spectral clustering algorithm, named "Soft Cut". It improves the normalized cut algorithm by introducing softmembership, and can be efficiently computed using a bound optimization algorithm. Our experiments with a variety of datasets have shown the promising performance of the proposed clustering algorithm.

We present a simple and scalable algorithm for large-margin estimation of structured models, including an important Class of Markov networks and combinatorial models.

An analog focal-plane processor having a 128 128 photodiode array has been developed for directional edge filtering. It can perform 4 4-pixel kernel convolution for entire pixels only with 256 steps of simple analog processing.Newly developed cyclic line access and row-parallel processing scheme in conjunction with the "only-nearest-neighbor interconnects" architecturehas enabled a very simple implementation. A proof-of-conceptchip was fabricated in a 0.35-m 2-poly 3-metal CMOS technology and the edge filtering at a rate of 200 frames/sec.