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 assumption is not verified when dealing with spatial data characterized by spatial autocorrelation 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 hyperspectral images. In order to assess the efficiency of our proposed method, we conducted experiments on two remotely sensed images datasets (Indian Pines and Pavia University) 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.

中文翻译：

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空间相关数据的核判别分析

我们提出了一种用于空间相关数据的新型监督分类算法，作为核判别分析的扩展而构建，我们将其命名为空间核判别分析（SKDA）。我们的算法基于空间概率密度函数的内核估计，它集成了第二个内核以考虑数据的空间依赖性。事实上，经典的数据挖掘算法假设数据样本是独立同分布的。然而，当处理以空间自相关现象为特征的空间数据时，这个假设没有得到验证。为了进行准确的分析，有必要利用这一丰富的信息源并捕捉到这一特性。我们已将我们的算法应用于相关领域，其中包括遥感高光谱图像的分类。为了评估我们提出的方法的效率，我们对具有不同特征和场景的两个遥感图像数据集（印度松树和帕维亚大学）进行了实验。实验结果表明，与其他上下文分类方法相比，我们的方法具有竞争力并实现了更高的分类精度。