Kernel Null Space Methods for Novelty Detection

2013 ◽  
Author(s):  
Paul Bodesheim ◽  
Alexander Freytag ◽  
Erik Rodner ◽  
Michael Kemmler ◽  
Joachim Denzler
Keyword(s):  
Null Space ◽  
Novelty Detection ◽  
Null Space Methods

scholarly journals Prestructuring sparse matrices with dense rows and columns via null space methods

2017 ◽  
Vol 25 (2) ◽  
pp. e2133
Author(s):  
Jason S. Howell
Keyword(s):  
Null Space ◽  
Sparse Matrices ◽  
Null Space Methods

On the Stability of Null-Space Methods for KKT Systems

1997 ◽  
Vol 18 (4) ◽  
pp. 938-958 ◽  
Author(s):  
Roger Fletcher ◽  
Tom Johnson
Keyword(s):  
Null Space ◽  
Kkt Systems ◽  
Null Space Methods ◽  
The Stability

scholarly journals A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block

2022 ◽  
Author(s):  
Jennifer Scott ◽  
Miroslav Tůma
Keyword(s):  
Saddle Point ◽  
Large Scale ◽  
Null Space ◽  
System Matrix ◽  
Practical Applications ◽  
Null Space Methods ◽  
Null Space Approach ◽  
Linear Least Squares Problems ◽  
Saddle Point Matrix ◽  
Space Approach

AbstractNull-space methods have long been used to solve large sparse n × n symmetric saddle point systems of equations in which the (2, 2) block is zero. This paper focuses on the case where the (1, 1) block is ill conditioned or rank deficient and the k × k (2, 2) block is non zero and small (k ≪ n). Additionally, the (2, 1) block may be rank deficient. Such systems arise in a range of practical applications. A novel null-space approach is proposed that transforms the system matrix into a nicer symmetric saddle point matrix of order n that has a non zero (2, 2) block of order at most 2k and, importantly, the (1, 1) block is symmetric positive definite. Success of any null-space approach depends on constructing a suitable null-space basis. We propose methods for wide matrices having far fewer rows than columns with the aim of balancing stability of the transformed saddle point matrix with preserving sparsity in the (1, 1) block. Linear least squares problems that contain a small number of dense rows are an important motivation and are used to illustrate our ideas and to explore their potential for solving large-scale systems.

Data reconciliation and variable classification by null space methods

Measurement ◽  
2010 ◽  
Vol 43 (5) ◽  
pp. 702-707 ◽  
Author(s):  
Christos L. Mitsas
Keyword(s):  
Null Space ◽  
Data Reconciliation ◽  
Null Space Methods

Development of Data Sets for the Validation of Analytical Instrumentation

1994 ◽  
Vol 77 (3) ◽  
pp. 777-781 ◽  
Author(s):  
Stephen L R Ellison ◽  
Maurice G Cox ◽  
Alastatr B Forbes ◽  
Bernard P Butler ◽  
Simon A Hannaby ◽  
...  
Keyword(s):  
Multivariate Regression ◽  
Reference Data ◽  
Dynamic Range ◽  
Null Space ◽  
Data Sets ◽  
Statistical Parameters ◽  
Incorrect Choice ◽  
Wide Range ◽  
Null Space Methods ◽  
Numerical Precision

Abstract Analytical chemistry makes use of a wide range of basic statistical operations, including means; standard deviations; significance tests based on assumed distributions; and linear, polynomial, and multivariate regression. The effects of limited numerical precision, poor choice of algorithm, and extreme dynamic range on these common statistical operations are discussed. The effects of incorrect choice of algorithm on calculations of basic statistical parameters and calibration lines are illustrated by examples. Some approaches to validation of such software are considered. The preparation of reference data sets for testing statistical software is discussed. The use of ‘null space’ methods for producing reference data sets is described, and an example is given. These data sets have well-characterized properties and can be used to test the accuracy of basic statistical procedures. Specific properties that are controlled include the numerical precision required to represent the sets exactly and the analytically correct answers. A further property of some of the data sets under development is the predictability of the deviation from the expected results resulting from poor choice of algorithm.

Incremental Kernel Null Space Discriminant Analysis for Novelty Detection

2017 ◽  
Author(s):  
Juncheng Liu ◽  
Zhouhui Lian ◽  
Yi Wang ◽  
Jianguo Xiao
Keyword(s):  
Discriminant Analysis ◽  
Null Space ◽  
Novelty Detection

On the Representation of a Basis for the Null Space.

1983 ◽  
Author(s):  
P. E. Gill ◽  
W. Murray ◽  
M. A. Saunders ◽  
M. H. Wright
Keyword(s):  
Null Space

scholarly journals Interference Cancellation Based Spectrum Sharing for Massive MIMO Communication Systems

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3584
Author(s):  
Milembolo Miantezila Junior ◽  
Bin Guo ◽  
Chenjie Zhang ◽  
Xuemei Bai
Keyword(s):  
Interference Cancellation ◽  
Communication Systems ◽  
Spectrum Sharing ◽  
Null Space ◽  
Base Station ◽  
Base Stations ◽  
Small Cells ◽  
Data Traffic ◽  
New Approach ◽  
Lte Advanced

Cellular network operators are predicting an increase in space of more than 200 percent to carry the move and tremendous increase of total users in data traffic. The growing of investments in infrastructure such as a large number of small cells, particularly the technologies such as LTE-Advanced and 6G Technology, can assist in mitigating this challenge moderately. In this paper, we suggest a projection study in spectrum sharing of radar multi-input and multi-output, and mobile LTE multi-input multi-output communication systems near m base stations (BS). The radar multi-input multi-output and mobile LTE communication systems split different interference channels. The new approach based on radar projection signal detection has been proposed for free interference disturbance channel with radar multi-input multi-output and mobile LTE multi-input multi-output by using a new proposed interference cancellation algorithm. We chose the channel of interference with the best free channel, and the detected signal of radar was projected to null space. The goal is to remove all interferences from the radar multi-input multi-output and to cancel any disturbance sources from a chosen mobile Communication Base Station. The experimental results showed that the new approach performs very well and can optimize Spectrum Access.

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