Set-based similarity learning in subspace for agricultural remote sensing classification
Introduction
Distinguishing the crops on the ground is an important application of agricultural remote sensing. Hyper-spectral information of kinds of crops is recorded by sampling hundreds or even thousands of bands of continuous spectra, which contains rich discriminant information on classifying crops. Because of the discriminant information, different crops could be classified by measuring the similarity between their spectral lines. Though agricultural remote sensing classification is possible by directly using spectral information, it is more efficient and effective to modify the spectral information for classification.
It is prevalent to learn discriminant information of spectral lines via subspace learning [1], [2], [3], [4] in the field of hyper-spectral image classification [5]. The discriminant information of original spectral lines is extracted by representing the original spectral lines in a low-dimensional space explicitly or implicitly [6]. For example, general subspace learning based methods include the linear discriminant analysis [7], [8] and nonparametric weighted feature extraction [9].
Based on these subspace based methods, more efficient and effective methods are also proposed for dealing with the specific problems of agricultural remote sensing classification. For instants, regularized linear discriminant analysis [10] and refined Fisher׳s linear discriminant analysis [8] are introduced into for releasing the interference of the scarcity of labeled spectral lines. Taking advantages of unlabeled spectral lines, manifold subspace learning methods [11], [12] and graph-based semi-supervised learning methods are also employed. The core of these methods is to design an appropriate similarity measure in a low-dimensional subspace to boost the separability of training samples.
Similarity measure is the paraphrase of the labeled information of training spectral lines. For example, the samples are similar if they share same label index, but not vice versa. Unfortunately, the similarity induced by label indices may be inconsistent with the similarity induced by a similarity measure defined in the spectral feature space. So learning a suitable similarity measure is a hot topic in the field of designing classification algorithms. Especially, the process of learning similarity in a spectral feature space is mostly a part of many nearest-neighbor-based classification algorithms. For example, nearest-neighbor-based nonparametric feature extraction method [13] emphasizes the importance of refining the similarity measure, and the similarity of matrix-based features is employed in [14].
The relation between classification and similarity learning motivates us to consider the problem of agricultural remote sensing classification via learning an appropriate similarity measure. By using nearest-based classifiers as medias, learning a classifier is equivalent to learning a similarity measure which is represented by a low-rank and positive-definite matrix. It should be noticed that the size of training set gets much huger when a problem of classification turns into a problem of learning similarity measure. For example, given n labeled training samples for classification, labeled training samples for learning similarity measure could be generated by pairing the samples for classification.
Motivated by the success of set–set distance learning [15], [16], spectrum-set similarity measure is introduced in this paper for responding to the challenges of large scale problem of treating a classification as learning similarity. Different from traditional similarity learning algorithms such as [17], [18], [19], spectrum-set similarity measure defines the similarity between training subsets. Because training subsets replace training points, the size of training set will be dramatically reduced, which could improve the efficiency of learning similarity measure.
The main contribution of this paper is treating agricultural remote sensing classification as a set-based similarity learning which is helpful in balancing the effectiveness of classification and the efficiency of learning similarity measure.
The rest of this paper is organized as follows. The results about main algorithm are reported in Section 2. Experimental results have shown in Section 3. The paper is ended with a conclusion in Section 4.
Section snippets
Point-based model
In this subsection, a point-based model is introduced for unveiling the core idea of classification via learning similarity measure. Let be a training set containing n training samples where is a spectral feature space and is the label indices space. For a test sample , the label of x could be estimated by comparing the similarity between training and test spectral features. Specifically, the estimated label corresponding to x is defined by
Hyperspectral data set
In the following experiments, the hyperspectral data sets of Salinas and Indian Pine which are obtained by the National Aeronautics and Space Administrations AVIRIS sensor are employed for testing the performance of all compared algorithms.
In the scene of Salinas, there are 16 classes of objects which include vegetables, bare soils, and vineyard fields. Among the hyperspectral data set of Salinas, each spectral line is recorded by 224 spectral bands, and 512×217 pixels are covered all of the
Conclusion and future work
In this paper, agriculture sensing classification is treated as a similarity measure learning because of the relation between the similarity learning and the nearest neighbor based classification strategy. By pairing the training samples, binary training set for classification transforms into a triple training set for similarity learning. Noticing the increasing on the size of triple training set, set-based similarity measure is introduced into by generating traditional point-based similarity
Acknowledgement
This work is supported by the National Natural Science Foundation of China (Grant nos. 41001345 and 61105051), the Excellent Talent of Beijing (2011D002020000001), the National Ministry of Science and Technology “Twelfth Five-Year” Technology Support Program (2012BAD15B01), and the Science and Technology Plan Project of Yunnan Province (Grant no. 2014FB148).
Xinrong Li received the Ph.D degree from Peking University, Peking, China, in 2007, and the M.S degree from China Agricultural University, Beijing, China, in 2000. She is currently a Research Associate with the Institute of Plant Nutrition and Natural Resources, Beijing Academy of Agriculture and Forestry Sciences, Beijing, China. Her main research topics include agricultural remote sensing and environmental models.
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Xinrong Li received the Ph.D degree from Peking University, Peking, China, in 2007, and the M.S degree from China Agricultural University, Beijing, China, in 2000. She is currently a Research Associate with the Institute of Plant Nutrition and Natural Resources, Beijing Academy of Agriculture and Forestry Sciences, Beijing, China. Her main research topics include agricultural remote sensing and environmental models.
Yi Tang received the B.S., the M.S. and Ph.D. degrees in mathematics from Hubei University, Wuhan, China, in 2001, 2006, and 2010 respectively. He is currently with the Department of Mathematics and Computer Science, Yunnan Minzu University, Kunming, China. His research interests include machine learning, statistical learning theory and pattern recognition.