In this paper, we develop some results based on Relational model (Klimova, et al. 2012) which permits a decomposition of logarithm of expected cell frequencies under a log-linear type model. These results imply plain answers to several questions in the context of analyzing of contingency tables. Moreover, determination of design matrix and hypothesis-induced matrix of the model will be discusse...

Non – negative matrix factorization (NMF) was generally used to obtain representation of data using non – negativity constraints. It lead to parts – based (or) region based representation in the vector space because they allow only additive combinations of original data. NMF has been applied so far in image and text data analysis, audio signal separation, signal separation in bio-medical applic...

Low rank matrix approximations have many applications in different domains. In system theory it has been used in model reduction schemes, in system identification with outputerror models and in static errors-in-variables problems, for instance. The approximations are mostly performed using the singular value decomposition. This is optimal for all unitarily invariant matrix norms, such as the Fr...

In this work an efficient algorithm to perform a block decomposition for large dense rectangular matrices with entries in 2 is presented. Matrices are stored as column blocks of row major matrices in order to facilitate rows operation and matrix multiplications with block of columns. One of the major bottlenecks of matrix decomposition is the pivoting involving both rows and column exchanges. S...

Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have applications in a variety of numerical problems including system identification, latent variable graphical modeling, and principal components analysis. We study conditi...

Matrix Decomposition methods are applied to a wide range of tasks, such as data denoising, dimensionality reduction, co-clustering and community detection. However, in the presence of boolean inputs, common methods either do not scale or do not provide a boolean reconstruction, which results in high reconstruction error and low interpretability of the decomposition. We propose a novel step deco...

General 3×3 linear or 4×4 homogenous matrices can be formed by composing primitive matrices for translation, rotation, scale, shear, and perspective. Current 3-D computer graphics systems manipulate and interpolate parametric forms of these primitives to generate scenes and motion. For this and other reasons, decomposing a composite matrix in a meaningful way has been a longstanding challenge. ...

Matrix decomposition, when the rating matrix has missing values, is recognized as an outstanding technique for recommendation system. In order to approximate user-item rating matrix, we construct loss function and append regularization constraint to prevent overfitting. Thus, the solution of matrix decomposition becomes an optimization problem. Alternating least squares (ALS) and stochastic gra...