Hyperspectral remote sensing image classification based on tighter random projection with minimal intra-class variance algorithm
Introduction
Hyperspectral remote sensing image classification is the process of dividing hyperspectral remote sensing image into a set of adjacent homogeneous regions and determining their specific classes [1]. Because of the consecutive and extensive spectral bands, hyperspectral remote sensing image classification needs to face many problems, such as the curse of dimensionality [2], serious time-consuming [3] and computational cost [4]. At the same time, the variance within the same class is large in hyperspectral remote sensing image, which easily results in the small class separability [5], [6]. To solve these problems, dimensionality reduction that guarantees the large class separability is the basic and key technology for hyperspectral remote sensing image classification. Therefore, it is very necessary to reduce the dimension of the hyperspectral remote sensing image first, and then the classification operation is performed on the low dimensional image [7].
It is difficult to find out a few dimensions that are actually necessary for hyperspectral remote sensing image classification. The main algorithms currently used in dimensionality reduction include Principal Component Analysis (PCA) [8], Independent Component Analysis (ICA) [9], Linear Discriminant Analysis (LDA) [10], Locally Linear Embedding (LLE) [11], and Random Projection (RP) [12]. Specifically, PCA can reduce the image to any dimension, while it takes a lot of time to calculate the covariance matrix [13]. ICA can be used for parallel computing, which can greatly reduce the time of calculation. However, when the number of features is larger than the dimension of original data, this algorithm will be difficult in optimize. That is, it will face the problem of long training time [14]. For LDA, although prior knowledge of classes can be used, it still has the phenomenon of over fitting [15]. LLE has relatively small computational complexity, but the algorithm is sensitive to the selection of nearest neighbor samples. Namely, the number of nearest neighbor has great influence on the final result of dimensionality reductions [16]. RP, an emergent dimensionality reduction technology, has been used in many fields, such as biology [17], environmental monitoring [18], pattern recognition [19], and disaster monitoring [20]. Due to its computational tractability compared to other algorithms, RP is a valuable algorithm for dimensionality reduction of hyperspectral remote sensing image, which provides a feasible mapping of the Johnson-Lindenstrauss (JL) lemma [21]. However, because the relationship between the original dimension and the number of spectral pixels is exponential [22], RP can only be applied to a small size hyperspectral remote sensing image. Moreover, due to the highly randomness of the traditional RP, different low dimensional images will be produced by different RP matrices during the projection process, which may result in different classification results [23], [24].
Due to the importance and difficulty of classification problems, many researchers have been attracted to do research in this area, and many classification algorithms for dimensionality reduction have been proposed. It can be divided into supervised classification algorithm [25] and unsupervised classification algorithm [26] according to the condition of prior information. The representative supervised classification algorithms include Minimum Distance (MD) [27], Convolution Neural Network (CNN) [28], and Support Vector Machine (SVM) [29]. Su et al. [30] proposed a land parcel extraction algorithm based on training data and MD classifier, which combines PCA for extracting the first principal component of the original satellite image, MD for pre-classification, and watershed algorithm for subdividing. Be careful that the result of each step determines whether the algorithm can ultimately achieve the ideal extraction result. Li et al. [31] proposed a new Hyperspectral image Reconstruction with deep CNN (HRCNN) algorithm based on feature enhancement.The algorithm combines the CNN algorithm for image reconstruction and the Extreme Learning Machine (ELM) for classification. When there is a big difference between the test set and the training set, even if the parameters are adjusted, it is difficult to improve the adaptability of the CNN model. Porta et al. [32] studied a hyperspectral image classification algorithm based on Compressed Sensing (CS) [33], which utilizes CS with the Restricted Isometry Property (RIP) for compressing the image and SVM algorithm for classification. The difference between CS and RP is that CS limits the length of data points before and after compressing, while RP controls the distance between data points before and after projecting. So, RP is more conducive to the identification of similarity. The typical unsupervised classification algorithms include K-means clustering algorithm [34] and Fuzzy C-Means (FCM) clustering algorithm [35]. Among them, cluster ensemble algorithms based on RP and fuzzy or probabilistic clustering algorithms are the most interesting. Numerous models have been proposed to this end [36], [37]. The idea behind these algorithms is that RP is proceeded to generate multiple projection results in a low dimensional space. Then, each projection result is clustered by the fuzzy or probabilistic clustering algorithm to create the membership matrix. Finally, all membership matrices are integrated to generate the final clustering result by various ways. Popescu et al. [38] proposed a Random Projection Fuzzy C-Means algorithm (RPFCM) for big data clustering, which concatenates all membership matrices to generate the concatenated matrix. Then the similarity matrix is defined by calculating the product of the concatenated matrix. When applied to large-scale image, the algorithm is time-consuming and needs more storage places for placing the similarity matrix. Therefore, the image size will be greatly limited for ordinary software. To avoid the product operation, Ye et al. [39] studied a FCM clustering algorithm with RP to extract the feature, which is the spectral clustering on all membership matrices. It is more effective, robust and suitable for a wider range of geometric data sets. When the original dimension is not large enough, the number of spectral pixels will be greatly constrained to achieve the purpose of dimensionality reduction. To reduce time, Rathore et al. [40] proposed a novel Cumulative Agreement Fuzzy C-Means algorithm (CAFCM), which uses the cluster validity indices to sort all membership matrices and accumulates aggregates to obtain the final clustering result. However, this algorithm cannot get an ideal result for bad projection results. Besides, because the relationship between the number of spectral pixels and the original dimension in the traditional RP algorithm is positively correlated, the image size is greatly restricted for hyperspectral remote sensing image with a low original dimension.
To solve the problem of image size, this paper proposes a novel Tighter Random Projection (TRP) with Minimal Intra-class Variance (TRP-MIV) algorithm for dimensionality reduction of hyperspectral remote sensing image. That is a different version of RP with tighter boundary and wider image size. Meanwhile, TRP-MIV algorithm is proposed to select the TRP-MIV matrix with the help of samples based on the idea of maximizing the class separability. After reducing the dimensions of samples and testing images, MD classifier is devised to classify by measuring similarity between low dimensional testing images and each class feature center of low dimensional samples. Experimental results show that the proposed dimensionality reduction algorithm can be applied to a larger image size and maintain greater class separability, which can effectively improve the subsequent accuracy of hyperspectral remote sensing image classification. This paper is organized in following. The traditional RP algorithm and the proposed algorithm are provided in Sections 2 and 3, respectively. In Section 4, the experimental results and discussion are outlined. Section 5 introduces conclusions.
Section snippets
Traditional random projection
Hyperspectral remote sensing images have the capacity of detecting more detailed and accurate earth surface information. However, due to its high spectral resolution, it is necessary for hyperspectral remote sensing image classification to reduce the original dimension. As a dimensionality reduction algorithm, RP will effectively maintain pair wise distances based on JL lemma, which has attracted a growing number of attentions of researchers. What surprised us is that RP is easier to work and
The proposed algorithm
The traditional RP algorithm has main problem in the application of hyperspectral remote sensing image dimensionality reduction. For dimensionality reduction of hyperspectral remote sensing image, the maximum amount of data, that is, the maximum number of vectors is determined by the original dimension according to Eq. (4). This means that the image size is limited by the number of the original dimension. Take into account this problem, a new TRP-MIV scheme is proposed in this paper.
Experimental results and discussion
To validate the feasibility and effectiveness of the proposed algorithm, classification experiments in real hyperspectral remote sensing images were performed on a PC with Intel (R) Core (TM) i5-4460, 3.20GHz and 8GB memory using MATLAB R2016a. The experimental images are captured from the Indian Pines scene in North-western Indiana of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) sensor with the wavelength range from 0.4 × 106 to 2.5 × 106 meters, the Pavia Centre scene in
Conclusions
RP, which aims to reduce the number of bands by linear projection of the original data using random projection matrix, has been a disciplinary field attracting a lot of researchers over the recent years. In this stage, a systematic review and summary on existing RP algorithms can promote the further development of the research area. Motivated by such, our work focuses on the following points. (1) A significant improvement on Gaussian dimensional bounds for RP is proposed with detailed proved.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by Department of Science and Technology of Liaoning Province of China (LJ2019JL001). The authors would like to thank Prof. P. Gamba for providing the ROSIS Pavia data, Prof. D. Landgrebe for making the AVIRIS Indian Pines hyperspectral data set, and Dr. L. Johnson and Dr. J. A. Gualtieri for providing the AVIRIS Salinas data set used in our experiments.
Zhao Quanhua received her M.Sc. degree in 2004 and Ph.D. degree in 2009 both from Liaoning Technical University. Now she is a professor and doctoral supervisor in Liaoning Technical University. Her main research interests include modeling and analysis of remote sensing image, and application of random geometry.
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Zhao Quanhua received her M.Sc. degree in 2004 and Ph.D. degree in 2009 both from Liaoning Technical University. Now she is a professor and doctoral supervisor in Liaoning Technical University. Her main research interests include modeling and analysis of remote sensing image, and application of random geometry.
Jia Shuhan is a Ph.D. student in Liaoning Technical University now. Her main research interests are the identification and extraction of remote sensing image information.
Li Yu received his Ph.D. degree in 2010 from University of Waterloo. Now, he is a professor and doctoral supervisor in Liaoning Technical University. His main research interests are remote sensing data processing theory and basic application research, including spatial statistics, random geometry, fuzzy mathematics, object geometry and feature extraction.