Many Data Mining tasks deal with data which are presented in high dimensional spaces, and the ‘curse of dimensionality’ phenomena is often an obstacle to the use of many methods for solving these tasks. To avoid these phenomena, various Representation learning algorithms are used as a first key step in solutions of these tasks to transform the original high-dimensional data into their lower-dimensional representations so that as much information about the original data required for the considered Data Mining task is preserved as possible. The above Representation learning problems are formulated as various Dimensionality Reduction problems (Sample Embedding, Data Manifold embedding, Manifold Learning and newly proposed Tangent Bundle Manifold Learning) which are motivated by various Data Mining tasks. A new geometrically motivated algorithm that solves the Tangent Bundle Manifold Learning and gives new solutions for all the considered Dimensionality Reduction problems is presented.
This paper addresses the problem of prediction with expert advice for outcomes in a geodesic space with non-positive curvature in the sense of Alexandrov. Via geometric considerations, and in particular the notion of barycenters, we extend to this setting the definition and analysis of the classical exponentially weighted average forecaster. We also adapt the principle of online to batch conversion to this setting. We shortly discuss the application of these results in the context of aggregation and for the problem of barycenter estimation.
This book constitutes the refereed proceedings of the 6th IAPR TC3 International Workshop on Artificial Neural Networks in Pattern Recognition, ANNPR 2014, held in Montreal, QC, Canada, in October 2014. The 24 revised full papers presented were carefully reviewed and selected from 37 submissions for inclusion in this volume. They cover a large range of topics in the field of learning algorithms and architectures and discussing the latest research, results, and ideas in these areas.
Objects have a variety of different features that can be represented as probability distributions. Recent findings show that in addition to mean and variance, the visual system can also encode the shape of feature distributions for features like color or orientation. In an odd-one-out search task we investigated observers' ability to encode two feature distributions simultaneously. Our stimuli were defined by two distinct features (color and orientation) while only one was relevant to the search task. We investigated whether the irrelevant feature distribution influences learning of the task-relevant distribution and whether observers also encode the irrelevant distribution. Although considerable learning of feature distributions occurred, especially for color, our results also suggest that adding a second irrelevant feature distribution negatively affected the encoding of the relevant one and that little learning of the irrelevant distribution occurred. There was also an asymmetry between the two different features: Searching for the oddly oriented target was more difficult than searching for the oddly colored target, which was reflected in worse learning of the color distribution. Overall, the results demonstrate that it is possible to encode information about two feature distributions simultaneously but also reveal considerable limits to this encoding.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.