Search results for "Matrix"
showing 10 items of 3205 documents
Irrelevant Features, Class Separability, and Complexity of Classification Problems
2011
In this paper, analysis of class separability measures is performed in attempt to relate their descriptive abilities to geometrical properties of classification problems in presence of irrelevant features. The study is performed on synthetic and benchmark data with known irrelevant features and other characteristics of interest, such as class boundaries, shapes, margins between classes, and density. The results have shown that some measures are individually informative, while others are less reliable and only can provide complimentary information. Classification problem complexity measurements on selected data sets are made to gain additional insights on the obtained results.
An Scalable matrix computing unit architecture for FPGA and SCUMO user design interface
2019
High dimensional matrix algebra is essential in numerous signal processing and machine learning algorithms. This work describes a scalable square matrix-computing unit designed on the basis of circulant matrices. It optimizes data flow for the computation of any sequence of matrix operations removing the need for data movement for intermediate results, together with the individual matrix operations’ performance in direct or transposed form (the transpose matrix operation only requires a data addressing modification). The allowed matrix operations are: matrix-by-matrix addition, subtraction, dot product and multiplication, matrix-by-vector multiplication, and matrix by scalar multiplication.…
Efficient analysis of cubic junction of rectangular waveguides using admittance-matrix representation
2000
In the paper an efficient and accurate method, based on the multimode-admittance-matrix representation and the theory of cavities, is proposed for the analysis of a six-port ‘cubic’ junction composed of the orthogonal intersection of three rectangular waveguides. Very simple closed-form analytical expressions are explicitly detailed for all matrix elements of this basic key building block. More general waveguide multiport junctions, composed of a central cubic junction with arbitrarily shaped waveguide access ports, are also studied using a segmentation procedure. To validate the theory, numerical results are first discussed for a standard rectangular waveguide six-port cross junction. Fina…
Explicit solutions of Riccati equations appearing in differential games
1990
Abstract In this paper an explicit closed form solution of Riccati differential matrix equations appearing in games theory is given.
Categories, Quantum Computing, and Swarm Robotics: A Case Study
2022
The swarms of robots are examples of artificial collective intelligence, with simple individual autonomous behavior and emerging swarm effect to accomplish even complex tasks. Modeling approaches for robotic swarm development is one of the main challenges in this field of research. Here, we present a robot-instantiated theoretical framework and a quantitative worked-out example. Aiming to build up a general model, we first sketch a diagrammatic classification of swarms relating ideal swarms to existing implementations, inspired by category theory. Then, we propose a matrix representation to relate local and global behaviors in a swarm, with diagonal sub-matrices describing individual featur…
Cholesky decomposition techniques in electronic structure theory
2011
We review recently developed methods to efficiently utilize the Cholesky decomposition technique in electronic structure calculations. The review starts with a brief introduction to the basics of the Cholesky decomposition technique. Subsequently, examples of applications of the technique to ab inito procedures are presented. The technique is demonstrated to be a special type of a resolution-of-identity or density-fitting scheme. This is followed by explicit examples of the Cholesky techniques used in orbital localization, computation of the exchange contribution to the Fock matrix, in MP2, gradient calculations, and so-called method specific Cholesky decomposition. Subsequently, examples o…
Diagnosis of Sensor Faults in PMSM and Drive System Based on Structural Analysis
2021
This paper presents a model-based fault diagnosis method to detect sensor faults in permanent magnet synchronous motor (PMSM) drives based on structural analysis technique. The structural model is built based on the dynamic model of the PMSM in matrix form, including unknown variables, known variables, and faults. The Dulmage-Mendelsohn (DM) decomposition is applied to evaluate the redundancy of the model and obtain redundant testable sub-models. These testable redundant sub-models are used to form residuals to observe the system state, and distinguish between healthy and faulty conditions. This work investigates faults in eleven sensors in a PMSM drive, thus nine structured residuals are d…
Design and calibration of an omni-RGB+D camera
2016
International audience; In this paper, we present the design of a new camera combining both predator-like and prey-like vision features. This setup provides both a spherical RGB-view and a directional depth-view of the environment. The model and calibration of the full setup are described. A few examples will be given to demonstrate the interest and the versatility of such camera for robotics and video surveillance at the oral presentation.
On the Computation of Symmetrized M-Estimators of Scatter
2016
This paper focuses on the computational aspects of symmetrized Mestimators of scatter, i.e. the multivariate M-estimators of scatter computed on the pairwise differences of the data. Such estimators do not require a location estimate, and more importantly, they possess the important block and joint independence properties. These properties are needed, for example, when solving the independent component analysis problem. Classical and recently developed algorithms for computing the M-estimators and the symmetrized M-estimators are discussed. The effect of parallelization is considered as well as new computational approach based on using only a subset of pairwise differences. Efficiencies and…
Geometrical Modeling of Non-Stationary Polarimetric Vehicular Radio Channels
2019
This paper presents a geometry-based statistical model (GBSM) of polarimetric wideband multipath radio channels for vehicle-to-vehicle (V2V) communications. The proposed model captures the effects of depolarization caused by multipath propagation, and it also accounts for the non-stationary characteristics of wideband V2V channels. This is a novel feature, because the existing polarimetric channel models are built on the assumption that the channel is a wide-sense stationary random process. In the modeling framework described in this paper, the channel depolarization function is given by a linear transformation in the form of a simple rotation matrix. This linear transformation is transpare…