Abstract
Principal Component Analysis (PCA) is a method based on statistics and linear algebra techniques, used in hyperspectral satellite imagery for data dimensionality reduction required in order to speed up and increase the performance of subsequent hyperspectral image processing algorithms. This paper introduces the PCA approximation method based on a geometric construction approach (gaPCA) method, an alternative algorithm for computing the principal components based on a geometrical constructed approximation of the standard PCA and presents its application to remote sensing hyperspectral images. gaPCA has the potential of yielding better land classification results by preserving a higher degree of information related to the smaller objects of the scene (or to the rare spectral objects) than the standard PCA, being focused not on maximizing the variance of the data, but the range. The paper validates gaPCA on four distinct datasets and performs comparative evaluations and metrics with the standard PCA method. A comparative land classification benchmark of gaPCA and the standard PCA using statistical-based tools is also described. The results show gaPCA is an effective dimensionality-reduction tool, with performance similar to, and in several cases, even higher than standard PCA on specific image classification tasks. gaPCA was shown to be more suitable for hyperspectral images with small structures or objects that need to be detected or where preponderantly spectral classes or spectrally similar classes are present.
Highlights
The ongoing advances in the field of remotely sensed data opens up new opportunities while raising challenges regarding their processing and analysis [1]
Fostered by the continuous innovation efforts in the field of Earth Observation, this paper proposes a novel principal component analysis (PCA) approximation method based on a geometric construction approach for hyperspectral remote sensing data analysis, with a specific focus on land classification
In order to validate the hypothesis that gaPCA yields better classification results due to its enhanced ability to retain information in its principal components compared to the canonical PCA, we used a well-known image quality metric, namely the Gray level co-occurrence matrix (GLCM) textural analysis to assess the amount of information in each method’s principal components
Summary
The ongoing advances in the field of remotely sensed data opens up new opportunities while raising challenges regarding their processing and analysis [1]. The availability of hyperspectral images widens the spectrum of information (providing detailed characteristics of objects), and the complexity associated with huge data sets [2]. A unique task in hyperspectral image analysis is represented by the efforts to manage the high data volume, either by selecting a subset of the available bands or by applying data reduction techniques [3]. Being a dimensionality reduction technique, principal component analysis (PCA) is credited as a preprocessing technique in remote sensing for different purposes [4]. Given that in the case of hyperspectral images, neighboring bands provide usually the same information, the original data is transformed using PCA with the goal to remove the redundancy and decorrelate the bands [3]
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