An Intrusion Detection Model Based on Non-Negative Matrix Factorization

In this paper ,we discus a wide class of loss functions for non-negative matrix factorization (NMF) and derive flexible and improved NMF algorithms based alpha-divergences for error measures, which generalize or combine several different criteria in order to extract intrusion signal.

ON THE UNIVERSAL CLUSTERING UNDER A BROAD CLASS OF LOSS FUNCTIONS

Determination of the number of significant clusters in the sample represents a very important problem. It is expected that the outcome of clustering under a broad class of loss functions will be more stable if the correct number of clusters is used. In order to illustrate the model of universal clustering we consider 1) family of power loss functions in probabilistic space; 2) family of exponential loss functions in Euclidean space. The proposed model is general, and proved to be effective in application to the synthetic datasets.

On the discrepancy principle and generalised maximum likelihood for regularisation

Let fnλ be the regularised solution of a general, linear operator equation, K f0 = g, from discrete, noisy data yi = g(xi ) + εi, i = 1, …, n, where εi are uncorrelated random errors with variance σ2. In this paper, we consider the two well–known methods – the discrepancy principle and generalised maximum likelihood (GML), for choosing the crucial regularisation parameter λ. We investigate the asymptotic properties as n → ∞ of the “expected” estimates λD and λM corresponding to these two methods respectively. It is shown that if f0 is sufficiently smooth, then λD is weakly asymptotically optimal (ao) with respect to the risk and an L2 norm on the output error. However, λD oversmooths for all sufficiently large n and also for all sufficiently small σ2. If f0 is not too smooth relative to the regularisation space W, then λD can also be weakly ao with respect to a whole class of loss functions involving stronger norms on the input error. For the GML method, we show that if f0 is smooth relative to W (for example f0 ∈ Wθ, 2, θ > m, if W = Wm, 2), then λM is asymptotically sub-optimal and undersmoothing with respect to all of the loss functions above.

SENSOR‐ARRAY PROCESSING WITH CHANNEL‐RECURSIVE BAYES TECHNIQUES

Arrays of seismometers, hydrophones, and electromagnetic receivers have several signal processing problems in common. This paper is concerned primarily with source location and secondarily with signal extraction. The basic problem can be described as follows: A transient signal from an event is detected in the outputs of the sensor array. We determine the location of the source from the temporal positions of the signal in the array outputs. Further, if the signal is unknown, we estimate it. The approach taken here differs from previous investigations in three ways: (i) a Bayes estimation approach is used, (ii) the estimates are evaluated recursively with respect to channels, and (iii) a time‐domain approach is used, as opposed to a frequency‐domain approach. The proposed estimation technique is optimum with respect to a large class of loss functions, since it is based on the expectation of the posterior distribution. Recursive evaluation of the posterior expectation has several advantages. At each step we have the optimum estimate of the unknown parameters and the corresponding covariance matrix. A channel selection rule and stopping rule are defined in terms of the covariance matrix. Further, having an optimum estimate at each step permits simplification of the processing; e.g., the search interval may be limited to the most probable region of the parameter space. Such techniques significantly decrease the processing time and increase the rate of convergence. Equations are developed for the known‐signal case with planar and spherical wavefronts, and results are presented from a computer simulation. Subsequently, equations for the unknown‐signal case are presented with simulation results.