Data Exploration and Analysis of Hyperspectral images: Visualization and Symbolic Description
Pai-Hui Hsu
PhD Candidate
Department of Surveying Engineering
National Cheng Kung University
Yi-Hsing Tseng
Associate Professor
No.1, University Road, Tainan 701, TAIWAN
Tel: +886-6-2370876 Fax: +886-6-2375764
Email: p6885101@ccmail.ncku.edu.tw
Republic of China
Abstract:
Some visualization techniques are used to analyzing and exploring the data set of hyperspectral images. The major objectives of data analysis are to summarize and interpret a data set, describing the contents and exposing important features. For dimensionality reduction, visualization can play an important role in illustrating the characteristics of high dimensional data set. Data projection is one of the common visual ways to get the interesting subsets of the original data, and certain properties of the structures can be preserved as faithfully as possible. The difference between different classes can also be interpreted by projecting the class data to special data spaces. Some characteristics and inherent properties of hyperspectral images will emerge from the visualizations for dimension reduction and classifications.
1. Introduction
Imaging spectrometers have been developed to acquire hyperspectral images with several hundreds of spectral bands. For example, the AVIRIS scanners developed by JPL of NASA can provide 224 contiguous spectral channels. Providing such abundant spectral data should increase the abilities in classifying land use/cover types. However, due to the high dimensionality and high correlation between spectral bands, traditional classification approaches do not fit to classify the hyperspectral images. To overcome the problems, one promising approach frequently used by many hyperspectral processing systems is dimensionality reduction. The basic principle of dimensionality reduction should extract the significant features or structures, and eliminate the redundant information. These useful features or structures can take the form of trends, clusters, hypersurfaces, or anomalies and can be used for further applications such as data compression or classifications.
In order to perform the dimensionality reduction effectively, the analyst should fully understand the characteristics of hyperspectral data. Some characteristics of high dimensional space were studied for feature extraction of hyperspectral images (Jimenez and Landgrebe, 1998). One of the apparent characteristic is that high dimensional space is mostly empty. For examples, the volume of a n-dimensional hypercube with edges of length 2r is (2r)
n. The fraction of this volume that is contained between the surface and a smaller hypercube with edges of length 2(r-e) is
Note that lim
nое f
c =1,
"e > 0, implying that most of the volume of a hypercube is concentrated in an outside surface. In other words, in a high-dimensional hypercube region, most of the available space is spread around the surface of the region. The same is true of regions with other hyper-shapes, such as the hypersphere and hyperellipsoid. This property prompts us to reduce the dimensionality of hyperspectral images by projecting the data to a smaller dimensional subspace without losing significant information. The remainder problems are what the clear definition of features is and how to design the algorithms of feature extraction.
