A continuous analogue of the tensor-train decomposition

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents functions using a tensor-train ansatz by replacing the three-dimensional TT cores with univariate matrix-valued functions. The main contribution of this paper is a framework to compute the FT that employs adaptive approximations of univariate fibers, and that is not tied to any tensorized discretization. The algorithm can be coupled with any univariate linear or nonlinear approximation procedure. We demonstrate that this approach can generate multivariate function approximations that are several orders of magnitude more accurate, for the same cost, than those based on the conventional approach of compressing the coefficient tensor of a tensor-product basis. Our approach is in the spirit of other continuous computation packages such as Chebfun, and yields an algorithm which requires the computation of "continuous" matrix factorizations such as the LU and QR decompositions of vector-valued functions. To support these developments, we describe continuous versions of an approximate maximum-volume cross approximation algorithm and of a rounding algorithm that re-approximates an FT by one of lower ranks. We demonstrate that our technique improves accuracy and robustness, compared to TT and quantics-TT approaches with fixed parameterizations, of high-dimensional integration, differentiation, and approximation of functions with local features such as discontinuities and other nonlinearities

Rough sets theory for travel demand analysis in Malaysia

This study integrates the rough sets theory into tourism demand analysis. Originated from the area of Artificial Intelligence, the rough sets theory was introduced to disclose important structures and to classify objects. The Rough Sets methodology provides definitions and methods for finding which attributes separates one class or classification from another. Based on this theory can propose a formal framework for the automated transformation of data into knowledge. This makes the rough sets approach a useful classification and pattern recognition technique. This study introduces a new rough sets approach for deriving rules from information table of tourist in Malaysia. The induced rules were able to forecast change in demand with certain accuracy

Joint Image Reconstruction and Segmentation Using the Potts Model

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from $7$ angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data

Stumping along a Summary for Exploration & Exploitation Challenge 2011

International audienceThe Pascal Exploration & Exploitation challenge 2011 seeks to evaluate algorithms for the online website content selection problem. This article presents the solution we used to achieve second place in this challenge and some side-experiments we performed. The methods we evaluated are all structured in three layers. The rst layer provides an online summary of the data stream for continuous and nominal data. Continuous data are handled using an online quantile summary. Nominal data are summarized with a hash-based counting structure. With these techniques, we managed to build an accurate stream summary with a small memory footprint. The second layer uses the summary to build predictors. We exploited several kinds of trees from simple decision stumps to deep multivariate ones. For the last layer, we explored several combination strategies: online bagging, exponential weighting, linear ranker, and simple averaging

Discretization of Continuous Attributes

7 pagesIn the data mining field, many learning methods -like association rules, Bayesian networks, induction rules (Grzymala-Busse & Stefanowski, 2001)- can handle only discrete attributes. Therefore, before the machine learning process, it is necessary to re-encode each continuous attribute in a discrete attribute constituted by a set of intervals, for example the age attribute can be transformed in two discrete values representing two intervals: less than 18 (a minor) and 18 and more (of age). This process, known as discretization, is an essential task of the data preprocessing, not only because some learning methods do not handle continuous attributes, but also for other important reasons: the data transformed in a set of intervals are more cognitively relevant for a human interpretation (Liu, Hussain, Tan & Dash, 2002); the computation process goes faster with a reduced level of data, particularly when some attributes are suppressed from the representation space of the learning problem if it is impossible to find a relevant cut (Mittal & Cheong, 2002); the discretization can provide non-linear relations -e.g., the infants and the elderly people are more sensitive to illness

Inverse Optimal Planning for Air Traffic Control

We envision a system that concisely describes the rules of air traffic control, assists human operators and supports dense autonomous air traffic around commercial airports. We develop a method to learn the rules of air traffic control from real data as a cost function via maximum entropy inverse reinforcement learning. This cost function is used as a penalty for a search-based motion planning method that discretizes both the control and the state space. We illustrate the methodology by showing that our approach can learn to imitate the airport arrival routes and separation rules of dense commercial air traffic. The resulting trajectories are shown to be safe, feasible, and efficient

Multivariate discretization of continuous valued attributes.

The area of Knowledge discovery and data mining is growing rapidly. Feature Discretization is a crucial issue in Knowledge Discovery in Databases (KDD), or Data Mining because most data sets used in real world applications have features with continuously values. Discretization is performed as a preprocessing step of the data mining to make data mining techniques useful for these data sets. This thesis addresses discretization issue by proposing a multivariate discretization (MVD) algorithm. It begins withal number of common discretization algorithms like Equal width discretization, Equal frequency discretization, Naïve; Entropy based discretization, Chi square discretization, and orthogonal hyper planes. After that comparing the results achieved by the multivariate discretization (MVD) algorithm with the accuracy results of other algorithms. This thesis is divided into six chapters, covering a few common discretization algorithms and tests these algorithms on a real world datasets which varying in size and complexity, and shows how data visualization techniques will be effective in determining the degree of complexity of the given data set. We have examined the multivariate discretization (MVD) algorithm with the same data sets. After that we have classified discrete data using artificial neural network single layer perceptron and multilayer perceptron with back propagation algorithm. We have trained the Classifier using the training data set, and tested its accuracy using the testing data set. Our experiments lead to better accuracy results with some data sets and low accuracy results with other data sets, and this is subject ot the degree of data complexity then we have compared the accuracy results of multivariate discretization (MVD) algorithm with the results achieved by other discretization algorithms. We have found that multivariate discretization (MVD) algorithm produces good accuracy results in comparing with the other discretization algorithm