Orthogonality-Constrained CNMF-Based Noise Reduction with Reduced Degradation of Biological Sound

The number of deaths due to cardiovascular and respiratory diseases is increasing annually. Cardiovascular diseases with high mortality rates, such as strokes, are frequently caused by atrial fibrillation without subjective symptoms. Chronic obstructive pulmonary disease is another condition in which early detection is difficult owing to the slow progression of the disease. Hence, a device that enables the early diagnosis of both diseases is necessary. In our previous study, a sensor for monitoring biological sounds such as vascular and respiratory sounds was developed and a noise reduction method based on semi-supervised convolutive non-negative matrix factorization (SCNMF) was proposed for the noisy environments of users. However, SCNMF attenuated part of the biological sound in addition to the noise. Therefore, this paper proposes a novel noise reduction method that achieves less distortion by imposing orthogonality constraints on the SCNMF. The effectiveness of the proposed method was verified experimentally using the biological sounds of 21 subjects. The experimental results showed an average improvement of 1.4 dB in the signal-to-noise ratio and 2.1 dB in the signal-to-distortion ratio over the conventional method. These results demonstrate the capability of the proposed approach to measure biological sounds even in noisy environments.

Iterative multilinear optimization for planar model fitting under geometric constraints

Planes are the core geometric models present everywhere in the three-dimensional real world. There are many examples of manual constructions based on planar patches: facades, corridors, packages, boxes, etc. In these constructions, planar patches must satisfy orthogonal constraints by design (e.g. walls with a ceiling and floor). The hypothesis is that by exploiting orthogonality constraints when possible in the scene, we can perform a reconstruction from a set of points captured by 3D cameras with high accuracy and a low response time. We introduce a method that can iteratively fit a planar model in the presence of noise according to three main steps: a clustering-based unsupervised step that builds pre-clusters from the set of (noisy) points; a linear regression-based supervised step that optimizes a set of planes from the clusters; a reassignment step that challenges the members of the current clusters in a way that minimizes the residuals of the linear predictors. The main contribution is that the method can simultaneously fit different planes in a point cloud providing a good accuracy/speed trade-off even in the presence of noise and outliers, with a smaller processing time compared with previous methods. An extensive experimental study on synthetic data is conducted to compare our method with the most current and representative methods. The quantitative results provide indisputable evidence that our method can generate very accurate models faster than baseline methods. Moreover, two case studies for reconstructing planar-based objects using a Kinect sensor are presented to provide qualitative evidence of the efficiency of our method in real applications.

A New Algorithm for Computing Disjoint Orthogonal Components in the Parallel Factor Analysis Model with Simulations and Applications to Real-World Data

In this paper, we extend the use of disjoint orthogonal components to three-way table analysis with the parallel factor analysis model. Traditional methods, such as scaling, orthogonality constraints, non-negativity constraints, and sparse techniques, do not guarantee that interpretable loading matrices are obtained in this model. We propose a novel heuristic algorithm that allows simple structure loading matrices to be obtained by calculating disjoint orthogonal components. This algorithm is also an alternative approach for solving the well-known degeneracy problem. We carry out computational experiments by utilizing simulated and real-world data to illustrate the benefits of the proposed algorithm.

Effective Algorithms for Solving Trace Minimization Problem in Multivariate Statistics

This paper develops two novel and fast Riemannian second-order approaches for solving a class of matrix trace minimization problems with orthogonality constraints, which is widely applied in multivariate statistical analysis. The existing majorization method is guaranteed to converge but its convergence rate is at best linear. A hybrid Riemannian Newton-type algorithm with both global and quadratic convergence is proposed firstly. A Riemannian trust-region method based on the proposed Newton method is further provided. Some numerical tests and application to the least squares fitting of the DEDICOM model and the orthonormal INDSCAL model are given to demonstrate the efficiency of the proposed methods. Comparisons with some latest Riemannian gradient-type methods and some existing Riemannian second-order algorithms in the MATLAB toolbox Manopt are also presented.