Application of spectral and spatial indices for specific class identification in Airborne Prism EXperiment (APEX) imaging spectrometer data for improved land cover classification

Hyperspectral remote sensing's ability to capture spectral information of targets in very narrow bandwidths gives rise to many intrinsic applications. However, the major limiting disadvantage to its applicability is its dimensionality, known as the Hughes Phenomenon. Traditional classification and image processing approaches fail to process data along many contiguous bands due to inadequate training samples. Another challenge of successful classification is to deal with the real world scenario of mixed pixels i.e. presence of more than one class within a single pixel. An attempt has been made to deal with the problems of dimensionality and mixed pixels, with an objective to improve the accuracy of class identification. In this paper, we discuss the application of indices to cope with the disadvantage of the dimensionality of the Airborne Prism EXperiment (APEX) hyperspectral Open Science Dataset (OSD) and to improve the classification accuracy using the Possibilistic c–Means (PCM) algorithm. This was used for the formulation of spectral and spatial indices to describe the information in the dataset in a lesser dimensionality. This reduced dimensionality is used for classification, attempting to improve the accuracy of determination of specific classes. Spectral indices are compiled from the spectral signatures of the target and spatial indices have been defined using texture analysis over defined neighbourhoods. The classification of 20 classes of varying spatial distributions was considered in order to evaluate the applicability of spectral and spatial indices in the extraction of specific class information. The classification of the dataset was performed in two stages; spectral and a combination of spectral and spatial indices individually as input for the PCM classifier. In addition to the reduction of entropy, while considering a spectral-spatial indices approach, an overall classification accuracy of 80.50% was achieved, against 65% (spectral indices only) and 59.50% (optimally determined principal component

Optimized kernel minimum noise fraction transformation for hyperspectral image classification

This paper presents an optimized kernel minimum noise fraction transformation (OKMNF) for feature extraction of hyperspectral imagery. The proposed approach is based on the kernel minimum noise fraction (KMNF) transformation, which is a nonlinear dimensionality reduction method. KMNF can map the original data into a higher dimensional feature space and provide a small number of quality features for classification and some other post processing. Noise estimation is an important component in KMNF. It is often estimated based on a strong relationship between adjacent pixels. However, hyperspectral images have limited spatial resolution and usually have a large number of mixed pixels, which make the spatial information less reliable for noise estimation. It is the main reason that KMNF generally shows unstable performance in feature extraction for classification. To overcome this problem, this paper exploits the use of a more accurate noise estimation method to improve KMNF. We propose two new noise estimation methods accurately. Moreover, we also propose a framework to improve noise estimation, where both spectral and spatial de-correlation are exploited. Experimental results, conducted using a variety of hyperspectral images, indicate that the proposed OKMNF is superior to some other related dimensionality reduction methods in most cases. Compared to the conventional KMNF, the proposed OKMNF benefits significant improvements in overall classification accuracy

A new kernel method for hyperspectral image feature extraction

Hyperspectral image provides abundant spectral information for remote discrimination of subtle differences in ground covers. However, the increasing spectral dimensions, as well as the information redundancy, make the analysis and interpretation of hyperspectral images a challenge. Feature extraction is a very important step for hyperspectral image processing. Feature extraction methods aim at reducing the dimension of data, while preserving as much information as possible. Particularly, nonlinear feature extraction methods (e.g. kernel minimum noise fraction (KMNF) transformation) have been reported to benefit many applications of hyperspectral remote sensing, due to their good preservation of high-order structures of the original data. However, conventional KMNF or its extensions have some limitations on noise fraction estimation during the feature extraction, and this leads to poor performances for post-applications. This paper proposes a novel nonlinear feature extraction method for hyperspectral images. Instead of estimating noise fraction by the nearest neighborhood information (within a sliding window), the proposed method explores the use of image segmentation. The approach benefits both noise fraction estimation and information preservation, and enables a significant improvement for classification. Experimental results on two real hyperspectral images demonstrate the efficiency of the proposed method. Compared to conventional KMNF, the improvements of the method on two hyperspectral image classification are 8 and 11%. This nonlinear feature extraction method can be also applied to other disciplines where high-dimensional data analysis is required

Partially integrable systems in multidimensions by a variant of the dressing method. 1

In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially integrable''. Such a construction is achieved using a suitable modification of the classical dressing scheme, consisting in assuming that the kernel of the basic integral operator of the dressing formalism be nontrivial. This new hypothesis leads to the construction of: 1) a linear system of compatible spectral problems for the solution $U(\lambda;x)$ of the integral equation in 3 independent variables each (while the usual dressing method generates spectral problems in 1 or 2 dimensions); 2) a system of nonlinear partial differential equations in $n$ dimensions ($n>3$), possessing a manifold of analytic solutions of dimension ($n-2$), which includes one largely arbitrary relation among the fields. These nonlinear equations can also contain an arbitrary forcing.Comment: 21 page

Dimensionality Reduction for k-Means Clustering and Low Rank Approximation

We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error. Importantly, this class of problems includes $k$-means clustering and unconstrained low rank approximation (i.e. principal component analysis). By reducing data points to just $O(k)$ dimensions, our methods generically accelerate any exact, approximate, or heuristic algorithm for these ubiquitous problems. For $k$-means dimensionality reduction, we provide $(1+\epsilon)$ relative error results for many common sketching techniques, including random row projection, column selection, and approximate SVD. For approximate principal component analysis, we give a simple alternative to known algorithms that has applications in the streaming setting. Additionally, we extend recent work on column-based matrix reconstruction, giving column subsets that not only `cover' a good subspace for \bv{A}, but can be used directly to compute this subspace. Finally, for $k$-means clustering, we show how to achieve a $(9+\epsilon)$ approximation by Johnson-Lindenstrauss projecting data points to just $O(\log k/\epsilon^2)$ dimensions. This gives the first result that leverages the specific structure of $k$-means to achieve dimension independent of input size and sublinear in $k$