An alternative approach to classical correspondence analysis was developed in [3] and involves decomposing the matrix of Pearson contingencies of a contingency table using orthogonal polynomials rather than via singular value decomposition. It is especially useful in analysing contingency tables which are of an ordinal nature. This short paper demonstrates that the confidence circles of Lebart,...

On the process of power system black start after an accident, it can help to optimize the resources allocation and accelerate the recovery process that decomposing the power system into several independent partitions for parallel recovery. On the basis of adequate consideration of fuzziness of black-start zone partitioning, a new algorithm based on fuzzy clustering analysis is presented. Charac...

It is possible for Singular Value Decomposition (SVD) watermark embedding to have a quasi-one-way functionality. While basic SVD embedding has the drawback of being non-reversible, an advanced SVD method which uses a reversible relation only works one-way. When embedding takes place, the decomposing matrix obtained from the original image differs from the one obtained from the embedded image. T...

The hierarchical non-negative matrix factorization (HNMF) is a multilayer generative network for decomposing strictly positive data into strictly positive activations and base vectors in a hierarchical manner. However, the standard hierarchical NMF is not suited for overcomplete representations and does not code efficiently for transformations in the input data. Therefore we extend the standard...

The segment minimization problem consists of finding the smallest set of integer matrices that sum to a given intensity matrix, such that each summand has only one nonzero value, and the non-zeroes in each row are consecutive. This has direct applications in intensity-modulated radiation therapy, an effective form of cancer treatment. We show here that for the case of an 1 × n-matrix, this prob...

In this paper, we consider the connected split rank one Lie group of real type F4 which we denote by F4. We first exhibit F4 as a group of operators on the complexification of A. A. Albert's exceptional simple Jordan algebra. This enables us to explicitly realize the symmetric space F4/Spin(9) as the unit ball in R with boundary S . After decomposing the space of spherical harmonics under the a...

Max-times algebra, sometimes known as subtropical algebra, is a semi-ring over the nonnegative real numbers where the addition operation is the max function and the multiplication is the standard one. Factorizing a nonnegative matrix over the maxtimes algebra, instead of the standard (nonnegative) one, allows us to find structures and regularities that cannot be easily expressed in the standard...

In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the interpolation incrementally and can be used to update the coefficients whenever a nodes is added to or removed from the interpolation. The second algorithm, wh...

A new description of verb valence is proposed. Rather than by full valence frames, verb subcategorization is described by the list of arguments and the matrix of five distinct pairwise argument interactions. This approach is argued to be computationally robust and sufficient although it has been initially motivated only by the need of a reliable test set for machine verb valence learning. Speak...

Transforming a matrix over a field to echelon form, or decomposing the matrix as a product of structured matrices that reveal the rank profile, is a fundamental building block of computational exact linear algebra. This paper surveys the well known variations of such decompositions and transformations that have been proposed in the literature. We present an algorithm to compute the CUP decompos...