The Experts below are selected from a list of 42 Experts worldwide ranked by ideXlab platform
Krzysztof Domino - One of the best experts on this subject based on the ideXlab platform.
-
band selection with higher order multivariate Cumulants for small target detection in hyperspectral images
arXiv: Computer Vision and Pattern Recognition, 2018Co-Authors: Przemyslaw Glomb, Krzysztof Domino, Michal Romaszewski, Michal CholewaAbstract:In the small target detection problem a pattern to be located is on the order of magnitude less numerous than other patterns present in the dataset. This applies both to the case of supervised detection, where the known template is expected to match in just a few areas and unsupervised anomaly detection, as anomalies are rare by definition. This problem is frequently related to the imaging applications, i.e. detection within the scene acquired by a camera. To maximize available data about the scene, hyperspectral cameras are used; at each pixel, they record spectral data in hundreds of narrow bands. The typical feature of hyperspectral imaging is that characteristic properties of target materials are visible in the small number of bands, where light of certain wavelength interacts with characteristic molecules. A target-independent band selection method based on statistical principles is a versatile tool for solving this problem in different practical applications. Combination of a regular background and a rare standing out anomaly will produce a distortion in the joint distribution of hyperspectral pixels. Higher Order Cumulants Tensors are a natural `window' into this distribution, allowing to measure properties and suggest candidate bands for removal. While there have been attempts at producing band selection algorithms based on the 3 rd Cumulant's Tensor i.e. the joint skewness, the literature lacks a systematic analysis of how the order of the Cumulant Tensor used affects effectiveness of band selection in detection applications. In this paper we present an analysis of a general algorithm for band selection based on higher order Cumulants. We discuss its usability related to the observed breaking points in performance, depending both on method order and the desired number of bands. Finally we perform experiments and evaluate these methods in a hyperspectral detection scenario.
-
algorithm for an arbitrary order Cumulant Tensor calculation in a sliding window of data streams
arXiv: Data Structures and Algorithms, 2017Co-Authors: Krzysztof Domino, Piotr GawronAbstract:High order Cumulant Tensors carry information about statistics of non-normally distributed multivariate data. In this work we present a new efficient algorithm for calculation of Cumulants of arbitrary order in a sliding window for data streams. We showed that this algorithms enables speedups of Cumulants updates compared to current algorithms. This algorithm can be used for processing on-line high-frequency multivariate data and can find applications in, e.g., on-line signal filtering and classification of data streams. To present an application of this algorithm, we propose an estimator of non-Gaussianity of a data stream based on the norms of high-order Cumulant Tensors. We show how to detect the transition from Gaussian distributed data to non-Gaussian ones in a~data stream. In order to achieve high implementation efficiency of operations on super-symmetric Tensors, such as Cumulant Tensors, we employ the block structure to store and calculate only one hyper-pyramid part of such Tensors.
-
the use of the multi Cumulant Tensor analysis for the algorithmic optimisation of investment portfolios
Research Papers in Economics, 2016Co-Authors: Krzysztof DominoAbstract:The Cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the Cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2'nd -- 6'th Cumulants of the multidimensional random variable (percentage shares' returns of many companies). Then the algorithm was tested during the recent crash on the Warsaw Stock Exchange. To determine incoming crash and provide enter and exit signal for the investment strategy the Hurst exponent was calculated using the local DFA. It was shown that introduced algorithm is on average better that benchmark and other portfolio determination methods, but only within examination window determined by low values of the Hurst exponent. Remark that the algorithm of is based on Cumulant Tensors up to the 6'th order calculated for a multidimensional random variable, what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.
-
The use of the multi-Cumulant Tensor analysis for the algorithmic search for safe investment portfolios.
arXiv: Portfolio Management, 2016Co-Authors: Krzysztof DominoAbstract:The Cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the Cumulant based algorithm and use it to determine eigenvectors that represent "respectively safe" investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2'nd -- 6'th Cumulants of the multidimensional random variable (percentage shares' returns of many companies). Then the algorithm was examined for daily shares' returns of companies traded on the Warsaw Stock Exchange. It was shown that the algorithm gives the investment portfolios that are on average better than portfolios achieved by other methods, as well as than the proposed benchmark. Remark that the algorithm of is based on Cumulant Tensors up to the 6'th order, what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.
J F Cardoso - One of the best experts on this subject based on the ideXlab platform.
-
super symmetric decomposition of the fourth order Cumulant Tensor blind identification of more sources than sensors
International Conference on Acoustics Speech and Signal Processing, 1991Co-Authors: J F CardosoAbstract:Ideas for higher-order array processing are introduced, focusing on fourth-order Cumulant statistics. They are expressed in an index-free formalism allowing the exploitation of all their symmetry properties. It is shown that, when dealing with 4-index quantities, symmetries are related to rank properties. The rich symmetry structure yields a class of identification algorithms. An algebraic technique for blind identification is included, and a few others are briefly indicated. >
M Kawanabe - One of the best experts on this subject based on the ideXlab platform.
-
linear dimension reduction based on the fourth order Cumulant Tensor
International Conference on Artificial Neural Networks, 2005Co-Authors: M KawanabeAbstract:In high dimensional data analysis, finding non-Gaussian components is an important preprocessing step for efficient information processing. By modifying the contrast function of JADE algorithm for Independent Component Analysis, we propose a new linear dimension reduction method to identify the non-Gaussian subspace based on the fourth-order Cumulant Tensor. A numerical study demonstrates the validity of our method and its usefulness for extracting sub-Gaussian structures.
Joos Vandewalle - One of the best experts on this subject based on the ideXlab platform.
-
independent component analysis and simultaneous third order Tensor diagonalization
IEEE Transactions on Signal Processing, 2001Co-Authors: L De Lathauwer, B De Moor, Joos VandewalleAbstract:Comon's (1994) well-known scheme for independent component analysis (ICA) is based on the maximal diagonalization, in a least-squares sense, of a higher-order Cumulant Tensor. In a previous paper, we proved that for fourth-order Cumulants, the computation of an elementary Jacobi rotation is equivalent to the computation of the best rank-1 approximation of a fourth-order Tensor. In this paper, we show that for third-order Tensors, the computation of an elementary Jacobi rotation is again equivalent to a best rank-1 approximation; however, here, it is a matrix that has to be approximated. This favorable computational load makes it attractive to do "something third-order-like" for fourth-order Cumulant Tensors as well. We show that simultaneous optimal diagonalization of "third-order Tensor slices" of the fourth-order Cumulant is a suitable strategy. This "simultaneous third-order Tensor diagonalization" approach (STOTD) is similar in spirit to the efficient JADE-algorithm.
L De Lathauwer - One of the best experts on this subject based on the ideXlab platform.
-
Independent Component Analysis and (Simultaneous)
2008Co-Authors: Third-order Tensor Diagonalization, L De Lathauwer, B De Moor, Senior MemberAbstract:Abstract—Comon’s well-known scheme for independent component analysis (ICA) is based on the maximal diagonalization, in a least-squares sense, of a higher-order Cumulant Tensor. In a previous papr, we proved that for fourth-order Cumulants, the computation of an elementary Jacobi rotation is equivalent to the computation of the best rank-1 approximation of a fourth-order Tensor. In this paper, we show that for third-order Tensors, the computation of an elementary Jacobi-rotation is again equivalent to a best rank-1 approximation; however, here, it is a matrix that has to be approximated. This favorable computational load makes it attractive to do “something third-order-like ” for fourth-order Cumulant Tensors as well. We show that simultaneous optimal diagonalization of “third-order Tensor slices ” of the fourth-order Cumulant is a suitable strategy. This “simultaneous third-order Tensor diagonalization” approach (STOTD) is similar in spirit to the efficient JADE-algorithm. Index Terms—Eigenvalue decomposition, higher order statistics, independent component analysis, multilinear algebra, principal component analysis. I
-
independent component analysis and simultaneous third order Tensor diagonalization
IEEE Transactions on Signal Processing, 2001Co-Authors: L De Lathauwer, B De Moor, Joos VandewalleAbstract:Comon's (1994) well-known scheme for independent component analysis (ICA) is based on the maximal diagonalization, in a least-squares sense, of a higher-order Cumulant Tensor. In a previous paper, we proved that for fourth-order Cumulants, the computation of an elementary Jacobi rotation is equivalent to the computation of the best rank-1 approximation of a fourth-order Tensor. In this paper, we show that for third-order Tensors, the computation of an elementary Jacobi rotation is again equivalent to a best rank-1 approximation; however, here, it is a matrix that has to be approximated. This favorable computational load makes it attractive to do "something third-order-like" for fourth-order Cumulant Tensors as well. We show that simultaneous optimal diagonalization of "third-order Tensor slices" of the fourth-order Cumulant is a suitable strategy. This "simultaneous third-order Tensor diagonalization" approach (STOTD) is similar in spirit to the efficient JADE-algorithm.
