A kernel discriminant analysis for spatially dependent data
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A kernel discriminant analysis for spatially dependent data Soumia Boumeddane1 · Leila Hamdad1 · Hamid Haddadou1 · Sophie Dabo‑Niang2
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We propose a novel supervised classification algorithm for spatially dependent data, built as an extension of kernel discriminant analysis, that we named Spatial Kernel Discriminant Analysis (SKDA). Our algorithm is based on a kernel estimate of the spatial probability density function, which integrates a second kernel to take into account spatial dependency of data. In fact, classical data mining algorithms assume that data samples are independent and identically distributed. However, this assump‑ tion is not verified when dealing with spatial data characterized by spatial autocorre‑ lation phenomenon. To make an accurate analysis, it is necessary to exploit this rich source of information and to capture this property. We have applied our algorithm to a relevant domain, which consist of the classification of remotely sensed hyperspec‑ tral images. In order to assess the efficiency of our proposed method, we conducted experiments on two remotely sensed images datasets (Indian Pines and Pavia Uni‑ versity) with different characteristics and scenarios. The experimental results show that our method is competitive and achieves higher classification accuracy compared to other contextual classification methods. Keywords Kernel density estimation · Kernel discriminant analysis · Spatial autocorrelation · Supervised classification · Hyperspectral images
* Soumia Boumeddane [email protected] Leila Hamdad [email protected] Hamid Haddadou [email protected] Sophie Dabo‑Niang sophie.dabo@univ‑lille.fr 1
Laboratoire de la Communication dans les Systèmes Informatiques, Ecole nationale Supérieure d’Informatique, BP 68M, 16309 Oued‑Smar, Algiers, Algeria
2
Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé, 59000 Lille, France
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Vol.:(0123456789)
Distributed and Parallel Databases
1 Introduction Data collected in many fields such as ecology, image analysis, epidemiology and environmental science, have a spatial component that refers to a geographi‑ cal position. Analyzing and discovering interesting patterns from such data is a challenging task due to spatial dependency. This characteristic is defined as the tendency of near observations to be more similar than distant observations in space [9]. In geography, it is justified by Tobler’s first law, according to which: “Everything is related to everything else, but near things are more related than distant things” [26], which means that the more objects are close to each other, the higher is the correlation between them. For example, measurements taken in neighboring sites are more likely to be similar then those of distant locations, nat‑ ural phenomena vary gradually over space (e.g., temperature values and weather) and objects of similar characteristics tend to be clustered (e.g., population with similar socio-economic characteristics and preferen
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