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1

A comparative study for outlier detection methods in high dimensional text data

Park Cheong Hee

Journal of Artificial Intelligence and Soft Computing Research

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2023

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Vol. 13, No. 1

5--17

EN

Outlier detection aims to find a data sample that is significantly different from other data samples. Various outlier detection methods have been proposed and have been shown to be able to detect anomalies in many practical problems. However, in high dimensional data, conventional outlier detection methods often behave unexpectedly due to a phenomenon called the curse of dimensionality. In this paper, we compare and analyze outlier detection performance in various experimental settings, focusing on text data with dimensions typically in the tens of thousands. Experimental setups were simulated to compare the performance of outlier detection methods in unsupervised versus semisupervised mode and uni-modal versus multi-modal data distributions. The performance of outlier detection methods based on dimension reduction is compared, and a discussion on using k-NN distance in high dimensional data is also provided. Analysis through experimental comparison in various environments can provide insights into the application of outlier detection methods in high dimensional data.

2

On Projection Based Operators in lp Space for Exact Similarity Search

Wichert A., Moreira C.

Fundamenta Informaticae

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2015

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Vol. 136, nr 4

461--474

EN

We investigate exact indexing for high dimensional lp norms based on the 1-Lipschitz property and projection operators. The orthogonal projection that satisfies the 1-Lipschitz property for the lp norm is described. The adaptive projection defined by the first principal component is introduced.

3

Multivariate function approximation using sparse grids and High Dimensional Model Representation – a comparison

Baran M.

Czasopismo Techniczne. Nauki Podstawowe

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2014

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R. 111, z. 3-NP

97--107

EN

In many areas of science and technology, there is a need for effective procedures for approximating multivariate functions. Sparse grids and cut-HDMR (High Dimensional Model Representation) are two alternative approaches to such multivariate approximations. It is therefore interesting to compare these two methods. Numerical experiments performed in this study indicate that the sparse grid approximation is more accurate than the cut-HDMR approximation that uses a comparable number of known values of the approximated function unless the approximated function can be expressed as a sum of high order polynomials of one or two variables.

PL

W wielu obszarach nauki i technologii potrzebne są efektywne metody aproksymacji funkcji wielu zmiennych. Sieci rzadkie i cut-HDMR (High Dimensional Model Representation) są dwoma alternatywnymi podejściami do aproksymacji funkcji wielu zmiennych. Interesujące jest zatem porównanie tych dwóch metod. Eksperymenty numeryczne przeprowadzone w ramach niniejszych badań wskazują, że aproksymacja sieciami rzadkimi jest bardziej dokładna niż aproksymacja cut-HDMR wykorzystująca porównywalną liczbę znanych o ile aproksymowana funkcja nie może być wyrażona jako suma wielomianów wysokiego stopnia jednej lub dwóch zmiennych.

4

Indexing Schemes for Similarity Search: an Illustrated Paradigm

Pestov V., Stojmirović A.

Fundamenta Informaticae

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2006

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Vol. 70, nr 4

367-385

EN

We suggest a variation of the Hellerstein-Koutsoupias-Papadimitriou indexability model for datasets equipped with a similarity measure, with the aim of better understanding the structure of indexing schemes for similarity-based search and the geometry of similarity workloads. This in particular provides a unified approach to a great variety of schemes used to index into metric spaces and facilitates their transfer to more general similarity measures such as quasi-metrics. We discuss links between performance of indexing schemes and high-dimensional geometry. The concepts and results are illustrated on a very large concrete dataset of peptide fragments equipped with a biologically significant similarity measure.

5

The corridor method: a dynamic programming inspired metaheuristic

Sniedovich M., Viß S.

Control and Cybernetics

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2006

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Vol. 35, no 3

551-578

EN

This paper presents a dynamic programming inspired metaheuristic called Corridor Method. It can be classified as a method-based iterated local search in that it deploys method-based neighborhoods. By this we mean that the search for a new candidate solution is carried out by a fully-fledged optimization method and generates a global optimal solution over the neighborhood. The neighborhoods are thus constructed to be suitable domains for the fully-fledged optimization method used. Typically, these neighborhoods are obtained by the imposition of exogenous constraints on the decision space of the target problem and therefore must be compatible with the optimization method used to search these neighborhoods. This is in sharp contrast to traditional metaheuristics where neighborhoods are move-based, that is, they are generated by subjecting the candidate solution to small changes called moves. While conceptually this method-based paradigm applies to any optimization method, in practice it is best suited to support optimization methods such as dynamic programming, where it is easy to control the size of a problem, hence the complexity of algorithms, by means of exogenous constraints. The essential features of the Corridor Method are illustrated by a number of examples, including the traveling salesman problem, where exponentially large neighborhoods are searched by a linear time/space dynamic programming algorithm.

6

Dynamic Programming: an overview

Sniedovich M.

Control and Cybernetics

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2006

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Vol. 35, no 3

513-533

EN

Dynamic programing is one of the major problem-solving methodologies in a number of disciplines such as operations research and computer science. It is also a very important and powerful tool of thought. But not all is well on the dynamic programming front. There is definitely lack of commercial software support and the situation in the classroom is not as good as it should be. In this paper we take a bird's view of dynamic programming so as to identify ways to make it more accessible to students, academics and practitioners alike.