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2017年计算机视觉矩阵和张量因子分解方法研讨会（Workshop on Matrix and Tensor Factorization Methods in Computer Vision）
2017年 计算机视觉矩阵和张量因子分解方法 研讨会
2017/9/21
Matrix and tensor factorizations have a long history in machine learning. Being able to recover latent factors in the data and flexible enough to accommodate a large set of constraints and regularizat...
This note is related to Theorem 1 of the ICA-BSS Conference’paper “AR Processes and Sources can be Reconstructed from Degenerate Mixtures” [1]. Here we study further the uniqueness of the decompositio...
When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts?
Non-Negative Matrix Factorization Parts
2015/8/21
We interpret non-negative matrix factorization geometrically, as the
problem of finding a simplicial cone which contains a cloud of data
points and which is contained in the positive orthant.
Grouping tasks and data display items via the non-negative matrix factorization
Grouping tasks non-negative matrix factorization
2015/8/21
Analyzing work functions and the IO variables they
need is an important component of designing and evaluating
complex systems. We develop a biclustering method for jointly
grouping work functions a...
FIR filter design via spectral factorization and convex optimization
Finite impulse response filter filter coefficient variables spectral decomposition linear and nonlinear convex programming
2015/8/11
We consider the design of finite impulse response (FIR) filters subject to upper and lower bounds on the frequency response magnitude. The associated optimization problems, with the filter coefficient...
BUTTERFLY FACTORIZATION
data-sparse matrix butterfly algorithm randomized algorithm matrix factorization operator compression Fourier integral operators special functions
2015/7/14
The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if eit...
Hierarchical Interpolative Factorization for Elliptic Operators:Integral Equations
Hierarchical Interpolative Factorization Elliptic Operators Integral Equations
2015/7/14
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions.This factorization takes the form of an...
Hierarchical Interpolative Factorization for Elliptic Operators:Differential Equations
Hierarchical Interpolative Factorization Elliptic Operators Differential Equations
2015/7/14
This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an a...
Factorization of the Cyclotomic Polynomials Q2^(n+1)(x)
Algebra cyclotomic polynomial order of an integer Factorization theorem
2011/9/25
In this paper we study the factorization of the polynomials 1+x^(2^n)over a field K, which have the same form as the Fermat numbers . As we notice that 1+x^(2^n) is equal to the 2^(n+1)th cyclotomic p...
Factorization of the Cyclotomic Polynomials Qp^(n+1)(x)
Algebra cyclotomic polynomial order of an integer Factorization theorem
2011/9/25
In this paper we study the factorization of the p^(n+1)th cyclotomic polynomials Qp^(n+1)(x) over a field K for prime p>2 and integer n>=0. Our methodology to solve the problem is due to some conclusi...
Canonical Factorization of cyclotomic polynomials
algebra finite fields order of an integer cyclotomic polynomials factorization
2011/9/25
In this article, we studied the order of an integer q modulo integer m, and then studied the factorization of the mth cyclotomic polynomial over a field K. We discussed the order of q modulo m by the ...
Cyclotomic Polynomials and Factorization Theorems
algebra finite fields order of an integer cyclotomic polynomials factorization theorem
2011/9/24
Let Qm(x) be the mth cyclotomic polynomial over finite field Fq. The factorization of Qm(x^t) and f(x^t) over Fq are discussed, where t is an positive integer larger than one and f(x) is any irreducib...
Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization
nonnegative matrix factorization algorithms multiplicative updates hierarchical alternating least squares
2011/9/21
Abstract: Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational ...
Factorization of linear and nonlinear differential operators: necessary and sufficient conditions
Linear differential equations nonlinear differential equations factorization
2011/9/20
Abstract: An algebraic approach for factorizing nonlinear partial differential equations (PDEs) and systems of PDEs is provided.
In the particular case of second order linear and nonlinear PDEs and ...
Tangle sums and factorization of A-polynomials
Tangle sums factorization of A-polynomials Geometric Topology
2011/9/5
Abstract: We show that there exist infinitely many examples of pairs of knots, K_1 and K_2, that have no epimorphism $\pi_1(S^3\setminus K_1) \to \pi_1(S^3\setminus K_2)$ preserving peripheral structu...