Results 1 - 10 of 786

Reachability Problems in Quaternion Matrix and Rotation Semigroups

by Paul Bell, Igor Potapov
"... Abstract. We examine computational problems on quaternion matrix and rotation semigroups. It is shown that in the ultimate case of quaternion matrices, in which multiplication is still associative, most of the decision problems for matrix semigroups are undecidable in dimension two. The geometric in ..."
Abstract - Cited by 5 (2 self) - Add to MetaCart
Abstract. We examine computational problems on quaternion matrix and rotation semigroups. It is shown that in the ultimate case of quaternion matrices, in which multiplication is still associative, most of the decision problems for matrix semigroups are undecidable in dimension two. The geometric

Reachability problems in low-dimensional iterative maps

by Oleksiy Kurganskyy, Igor Potapov, O Sancho Caparrini
"... Abstract. In this paper we analyse the dynamics of one-dimensional piecewise maps (PAMs). We show that one-dimensional PAMs are equivalent to pseudo-billiard or so called “strange billiard ” systems. We also show that the more general class of rational functions leads to undecidability of reachabili ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
of reachability problem for one-dimensional piecewise maps with a finite number of intervals.

Fast maximum margin matrix factorization for collaborative prediction

by Jason D. M. Rennie, Nathan Srebro - In Proceedings of the 22nd International Conference on Machine Learning (ICML , 2005
"... Maximum Margin Matrix Factorization (MMMF) was recently suggested (Srebro et al., 2005) as a convex, infinite dimensional alternative to low-rank approximations and standard factor models. MMMF can be formulated as a semi-definite programming (SDP) and learned using standard SDP solvers. However, cu ..."
Abstract - Cited by 248 (6 self) - Add to MetaCart
Maximum Margin Matrix Factorization (MMMF) was recently suggested (Srebro et al., 2005) as a convex, infinite dimensional alternative to low-rank approximations and standard factor models. MMMF can be formulated as a semi-definite programming (SDP) and learned using standard SDP solvers. However

From Post Systems to the Reachability Problems for Matrix Semigroups and Multicounter Automata

by Igor Potapov - Developments in Language Theory, LNCS 3340 , 2004
"... Abstract. The main result of this paper is the reduction of PCP(n) to the vector reachability problem for a matrix semigroup generated by n 4 \Theta 4 integral matrices. It follows that the vector reachability problem is undecidable for a semigroup generated by 7 integral matrices of dimension 4. Th ..."
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Abstract. The main result of this paper is the reduction of PCP(n) to the vector reachability problem for a matrix semigroup generated by n 4 \Theta 4 integral matrices. It follows that the vector reachability problem is undecidable for a semigroup generated by 7 integral matrices of dimension 4

Sparse subspace clustering

by Ehsan Elhamifar, René Vidal - In CVPR , 2009
"... We propose a method based on sparse representation (SR) to cluster data drawn from multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all oth ..."
Abstract - Cited by 241 (14 self) - Add to MetaCart
We propose a method based on sparse representation (SR) to cluster data drawn from multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all

On the Computational Complexity of Matrix Semigroup Problems

by Paul C. Bell, Igor Potapov
"... Abstract. Most computational problems for matrix semigroups and groups are inherently difficult to solve and even undecidable starting from dimension three. The questions about the decidability and complexity of problems for two-dimensional matrix semigroups remain open and are directly linked with ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
Abstract. Most computational problems for matrix semigroups and groups are inherently difficult to solve and even undecidable starting from dimension three. The questions about the decidability and complexity of problems for two-dimensional matrix semigroups remain open and are directly linked

Low-Dimensional Models for PCA and Regression Low-Dimensional Models for PCA and Regression

by Christian Ladapo Omidiran , Christian Ladapo Omidiran , Professor Laurent El Ghaoui , Co-Chair Professor Martin Wainwright
"... This thesis examines two separate statistical problems for which low-dimensional models are effective. In the first part of this thesis, we examine the Robust Principal Components Analysis (RPCA) problem: given a matrix X that is the sum of a low-rank matrix L * and a sparse noise matrix S * , reco ..."
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This thesis examines two separate statistical problems for which low-dimensional models are effective. In the first part of this thesis, we examine the Robust Principal Components Analysis (RPCA) problem: given a matrix X that is the sum of a low-rank matrix L * and a sparse noise matrix

Membership and Reachability Problems for Row-monomial Transformations

by Alexei Lisitsa, Igor Potapov
"... Abstract. In this paper we study the membership and vector reachability problems for labelled transition systems with row-monomial transformations. We show the decidability of these problems for row-monomial martix semigroups over rationals and extend these results to the wider class of matrix semig ..."
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Abstract. In this paper we study the membership and vector reachability problems for labelled transition systems with row-monomial transformations. We show the decidability of these problems for row-monomial martix semigroups over rationals and extend these results to the wider class of matrix

c ○ World Scientific Publishing Company REACHABILITY PROBLEMS IN LOW-DIMENSIONAL ITERATIVE MAPS

by Oleksiy Kurganskyy, Igor Potapov, Fernando Sancho Caparrini
"... In this paper we analyze the dynamics of one-dimensional piecewise maps (PAMs). We show that one-dimensional PAMs are equivalent to pseudo-billiard or so called “strange billiard ” systems. We also show that the more general class of rational functions leads to undecidability of reachability problem ..."
Abstract - Add to MetaCart
In this paper we analyze the dynamics of one-dimensional piecewise maps (PAMs). We show that one-dimensional PAMs are equivalent to pseudo-billiard or so called “strange billiard ” systems. We also show that the more general class of rational functions leads to undecidability of reachability

Reachability Of Fuzzy Matrix Period

by Martin Gavalec, Günter Rote , 1997
"... The computational complexity of the matrix period reachability (MPR) problem in a fuzzy algebra B is studied. Given an n n matrix A with elements in B, the problem is to decide whether there is an n-vector x such that the sequence of matrix powers A; A²; A³ ; : : : has the same period length as the ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
The computational complexity of the matrix period reachability (MPR) problem in a fuzzy algebra B is studied. Given an n n matrix A with elements in B, the problem is to decide whether there is an n-vector x such that the sequence of matrix powers A; A²; A³ ; : : : has the same period length
Results 1 - 10 of 786