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In the context of computer experiments, metamodels are largely used to represent the output of computer codes. Among these models, Gaussian process regression (kriging) is very efficient see e.g Snelson (Flexible and efficient Gaussian process models for machine learning. ProQuest LLC, Ann Arbor, MI. Thesis (Ph.D.)–University of London, University College London, London, 2008). In high dimension that is with a large number of input variables, but with few observations, the estimation of the parameters with a classical anisotropic kriging can be completely inaccurate. Because there are equal numbers of ranges and input variables the optimization space becomes too large compared to available information. One way to overcome this drawback is to use an isotropic kernel that only depends on one parameter. However this model is too restrictive. The aim of this paper is twofold. Our first objective is to propose a smooth kernel with as few parameters as warranted. We introduce a kernel which is a tensor product of few isotropic kernels built on well-chosen subgroup of variables. The main difficulty is to find the number and the composition of the groups. Our second objective is to propose algorithmic strategies to overcome this difficulty. Four forward strategies are proposed. They all start with the simplest isotropic kernel and stop when the best model according to BIC criterion is found. They all show very good accuracy results on simulation test cases. But one of them is more efficient. Tested on a real data set, our kernel shows very good prediction results. [ABSTRACT FROM AUTHOR]

The global k-means algorithm is an incremental approach to clustering that dynamically adds one cluster center at a time through a deterministic global search procedure from suitable initial positions, and employs k-means to minimize the sum of the intra-cluster variances. However the global k-means algorithm sometimes results singleton clusters and the initial positions sometimes are bad, after a bad initialization, poor local optimal can be easily obtained by k-means algorithm. In this paper, we modified the global k-means algorithm to eliminate the singleton clusters at first, and then we apply MinMax k-means clustering error method to global k-means algorithm to overcome the effect of bad initialization, proposed the global Minmax k-means algorithm. The proposed clustering method is tested on some popular data sets and compared to the k-means algorithm, the global k-means algorithm and the MinMax k-means algorithm. The experiment results show our proposed algorithm outperforms other algorithms mentioned in the paper. [ABSTRACT FROM AUTHOR]

Dimensionality reduction techniques such as principal component analysis and factor analysis are used to discover a linear mapping between high-dimensional data samples and points in a lower-dimensional subspace. Previously, Frey and Jojic introduced transformation-invariant component analysis (TCA) to learn a linear mapping, invariant to a set of known form of global transformations. However, parameter estimation in that model using the previously-proposed expectation maximization (EM) algorithm required scalar operations in the order of N 2 where N is the dimensionality of each training example. This is prohibitive for many applications of interest such as modeling mid-to large-size images, where, for instance, N may be as high as 786432 (512×512 RGB image). In this paper, we present an efficient algorithm that reduces the computational requirements to order of Nlog N. With this speedup, we show the effectiveness of transformation-invariant component analysis in various applications including tracking, learning video textures, clustering, object recognition and object detection in images. Software for TCA can be downloaded from . [ABSTRACT FROM AUTHOR]

The nature of map generalization may be non-uniform along the length of an individual line, requiring the application of methods that adapt to the local geometry and the geographical context. Geographical databases need to be enriched in terms of shape description structures (geometrical knowledge), knowledge of appropriate order of operations and of appropriate algorithms (procedural knowledge). Stored knowledge should take account of semantic and morphological characteristics, and of cartographic constraints. This paper proposes and discusses three experiments on knowledge acquisition using unsupervised and supervised learning techniques. In order to exploit geometrical shape knowledge, classifications were computed according to a set of morphological measures using unsupervised learning. Choice of appropriate operations was determined by the results of a test with IGN cartographers considering line characteristics. These results were given to a supervised learning algorithm, along with corresponding computed measures in order to discover rules. The approach and the resulting rules are presented and discussed. Tests have also been conducted on the tuning of parameter values, applying a Gaussian smoothing tolerance value to a set of lines using the supervised learning algorithm. The values obtained by means of the learning algorithm have been compared with interactive choices of an expert. Results are promising with a prediction rate higher than 80% having been obtained. [ABSTRACT FROM AUTHOR]