A New Approach to Detection of Changes in Multidimensional Patterns

A New Approach to Detection of Changes in Multidimensional Patterns - Part II

In the paper we develop an algorithm based on the Parzen kernel estimate for detection of sudden changes in 3-dimensional shapes which happen along the edge curves. Such problems commonly arise in various areas of computer vision, e.g., in edge detection, bioinformatics and processing of satellite imagery. In many engineering problems abrupt change detection may help in fault protection e.g. the jump detection in functions describing the static and dynamic properties of the objects in mechanical systems. We developed an algorithm for detecting abrupt changes which is nonparametric in nature and utilizes Parzen regression estimates of multivariate functions and their derivatives. In tests we apply this method, particularly but not exclusively, to the functions of two variables.

Learning Novelty Detection Outside a Class of Random Curves with Application to COVID-19 Growth

Let a class of proper curves is specified by positive examples only. We aim to propose a learning novelty detection algorithm that decides whether a new curve is outside this class or not. In opposite to the majority of the literature, two sources of a curve variability are present, namely, the one inherent to curves from the proper class and observations errors’. Therefore, firstly a decision function is trained on historical data, and then, descriptors of each curve to be classified are learned from noisy observations.When the intrinsic variability is Gaussian, a decision threshold can be established from T 2 Hotelling distribution and tuned to more general cases. Expansion coefficients in a selected orthogonal series are taken as descriptors and an algorithm for their learning is proposed that follows nonparametric curve fitting approaches. Its fast version is derived for descriptors that are based on the cosine series. Additionally, the asymptotic normality of learned descriptors and the bound for the probability of their large deviations are proved. The influence of this bound on the decision threshold is also discussed.The proposed approach covers curves described as functional data projected onto a finite-dimensional subspace of a Hilbert space as well a shape sensitive description of curves, known as square-root velocity (SRV). It was tested both on synthetic data and on real-life observations of the COVID-19 growth curves.

Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions—Computational Aspects

We consider a rather general problem of nonparametric estimation of an uncountable set of probability density functions (p.d.f.’s) of the form: f ( x ; r ) , where r is a non-random real variable and ranges from R 1 to R 2 . We put emphasis on the algorithmic aspects of this problem, since they are crucial for exploratory analysis of big data that are needed for the estimation. A specialized learning algorithm, based on the 2D FFT, is proposed and tested on observations that allow for estimate p.d.f.’s of a jet engine temperatures as a function of its rotation speed. We also derive theoretical results concerning the convergence of the estimation procedure that contains hints on selecting parameters of the estimation algorithm.