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Crossentropy optimization for independent process analysis
, 2006
"... We treat the problem of searching for hidden multidimensional independent autoregressive processes. First, we transform the problem to Independent Subspace Analysis (ISA). Our main contribution concerns ISA. We show that under certain conditions, ISA is equivalent to a combinatorial optimization pr ..."
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Cited by 18 (15 self)
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We treat the problem of searching for hidden multidimensional independent autoregressive processes. First, we transform the problem to Independent Subspace Analysis (ISA). Our main contribution concerns ISA. We show that under certain conditions, ISA is equivalent to a combinatorial optimization problem. For the solution of this optimization we apply the crossentropy method. Numerical simulations indicate that the crossentropy method can provide considerable improvements over other stateoftheart methods.
Towards a general independent subspace analysis
 In: Proc. NIPS
, 2006
"... The increasingly popular independent component analysis (ICA) may only be applied to data following the generative ICA model in order to guarantee algorithmindependent and theoretically valid results. Subspace ICA models generalize the assumption of component independence to independence between gro ..."
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Cited by 13 (2 self)
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The increasingly popular independent component analysis (ICA) may only be applied to data following the generative ICA model in order to guarantee algorithmindependent and theoretically valid results. Subspace ICA models generalize the assumption of component independence to independence between groups of components. They are attractive candidates for dimensionality reduction methods, however are currently limited by the assumption of equal group sizes or less general semiparametric models. By introducing the concept of irreducible independent subspaces or components, we present a generalization to a parameterfree mixture model. Moreover, we relieve the condition of atmostoneGaussian by including previous results on nonGaussian component analysis. After introducing this general model, we discuss joint block diagonalization with unknown block sizes, on which we base a simple extension of JADE to algorithmically perform the subspace analysis. Simulations confirm the feasibility of the algorithm. 1 Independent subspace analysis
Application of Geometric Dependency Analysis to the Separation of Convolved Mixtures
 Independent Component Analysis and Blind Signal Separation: Proceedings of the Fifth International Conference, ICA 2004
, 2004
"... We investigate a generalisation of the structure of frequency domain ICA as applied to the separation of convolved mixtures, and show how a geometric representation of residual dependency can be used both as an aid to visualisation and intuition, and as tool for clustering components into indepe ..."
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Cited by 9 (8 self)
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We investigate a generalisation of the structure of frequency domain ICA as applied to the separation of convolved mixtures, and show how a geometric representation of residual dependency can be used both as an aid to visualisation and intuition, and as tool for clustering components into independent subspaces, thus providing a solution to the source separation problem.
Independent Process Analysis Without a Priori Dimensional Information
"... Abstract. Recently, several algorithms have been proposed for independent subspace analysis where hidden variables are i.i.d. processes. We show that these methods can be extended to certain AR, MA, ARMA and ARIMA tasks. Central to our paper is that we introduce a cascade of algorithms, which aims t ..."
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Cited by 6 (5 self)
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Abstract. Recently, several algorithms have been proposed for independent subspace analysis where hidden variables are i.i.d. processes. We show that these methods can be extended to certain AR, MA, ARMA and ARIMA tasks. Central to our paper is that we introduce a cascade of algorithms, which aims to solve these tasks without previous knowledge about the number and the dimensions of the hidden processes. Our claim is supported by numerical simulations. As an illustrative application where the dimensions of the hidden variables are unknown, we search for subspaces of facial components. 1
Separation theorem for Kindependent subspace analysis with sufficient conditions
, 2006
"... Here, a Separation Theorem about KIndependent Subspace Analysis (K ∈ {R, C} real or complex), a generalization of KIndependent Component Analysis (KICA) is proven. According to the theorem, KISA estimation can be executed in two steps under certain conditions. In the first step, 1dimensional ..."
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Cited by 4 (4 self)
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Here, a Separation Theorem about KIndependent Subspace Analysis (K ∈ {R, C} real or complex), a generalization of KIndependent Component Analysis (KICA) is proven. According to the theorem, KISA estimation can be executed in two steps under certain conditions. In the first step, 1dimensional KICA estimation is executed. In the second step, optimal permutation of the KICA elements is searched for. We present sufficient conditions for the KISA Separation Theorem. Namely, we shall show that (i) spherically symmetric sources (both for real and complex cases), as well as (ii) real 2dimensional sources invariant to 90 ◦ rotation, among others, satisfy the conditions of the theorem.
Separation Theorem for Independent Subspace Analysis with Sufficient Conditions
"... Abstract. Here, a separation theorem about Independent Subspace Analysis (ISA), a generalization of Independent Component Analysis (ICA) is proven. According to the theorem, ISA estimation can be executed in two steps under certain conditions. In the first step, 1dimensional ICA estimation is execu ..."
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Cited by 4 (2 self)
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Abstract. Here, a separation theorem about Independent Subspace Analysis (ISA), a generalization of Independent Component Analysis (ICA) is proven. According to the theorem, ISA estimation can be executed in two steps under certain conditions. In the first step, 1dimensional ICA estimation is executed. In the second step, optimal permutation of the ICA elements is searched for. We present sufficient conditions for the ISA Separation Theorem. Namely, we shall show that (i) elliptically symmetric sources, (ii) 2dimensional sources invariant to 90 ◦ rotation, among others, satisfy the conditions of the theorem. 1
Social network analysis via matrix decompositions: al Qaeda. Available from http://www.cs. queensu.ca/home/skill/alqaeda.pdf
, 2004
"... Social network analysis investigates the structure of human groups using pairwise links among their members. We show how matrix decompositions can be used to extend the standard repertoire of social network and link analysis tools to allow, for example, the inclusion of other information about indiv ..."
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Cited by 3 (0 self)
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Social network analysis investigates the structure of human groups using pairwise links among their members. We show how matrix decompositions can be used to extend the standard repertoire of social network and link analysis tools to allow, for example, the inclusion of other information about individuals, and higherorder information about the relationships among them. We show how these extensions can be applied by analyzing the structure of al Qaeda and its related terrorist organizations. Much of the information about, for example, relative importance of al Qaeda members can be extracted from simple relational information. 1