Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel

Segmented Mixture-of-Gaussian Classification for Hyperspectral Image Analysis

Abstract—The same high dimensionality of hyperspectral imagery that facilitates detection of subtle differences in spectral response due to differing chemical composition also hinders the deployment of traditional statistical pattern-classification procedures, particularly when relatively few training samples are available. Traditional approaches to addressing this issue, which typically employ dimensionality reduction based on either projection or feature selection, are at best suboptimal for hyperspectral classification tasks. A divide-and-conquer algorithm is proposed to exploit the high correlation between successive spectral bands and the resulting block-diagonal correlation structure to partition the hyperspectral space into approximately independent subspaces. Subsequently, dimensionality reduction based on a graph-theoretic localitypreserving discriminant analysis is combined with classification driven by Gaussian mixture models independently in each subspace. The locality-preserving discriminant analysis preserves the potentially multimodal statistical structure of the data, which the Gaussian mixture model classifier learns in the reduced-dimensional subspace. Experimental results demonstrate that the proposed system significantly outperforms traditional classification approaches, even when few training samples are employed. Index Terms—Hyperspectral data, information fusion I

Advances in Hyperspectral Image Classification Methods for Vegetation and Agricultural Cropland Studies

Hyperspectral data are becoming more widely available via sensors on airborne and unmanned aerial vehicle (UAV) platforms, as well as proximal platforms. While space-based hyperspectral data continue to be limited in availability, multiple spaceborne Earth-observing missions on traditional platforms are scheduled for launch, and companies are experimenting with small satellites for constellations to observe the Earth, as well as for planetary missions. Land cover mapping via classification is one of the most important applications of hyperspectral remote sensing and will increase in significance as time series of imagery are more readily available. However, while the narrow bands of hyperspectral data provide new opportunities for chemistry-based modeling and mapping, challenges remain. Hyperspectral data are high dimensional, and many bands are highly correlated or irrelevant for a given classification problem. For supervised classification methods, the quantity of training data is typically limited relative to the dimension of the input space. The resulting Hughes phenomenon, often referred to as the curse of dimensionality, increases potential for unstable parameter estimates, overfitting, and poor generalization of classifiers. This is particularly problematic for parametric approaches such as Gaussian maximum likelihoodbased classifiers that have been the backbone of pixel-based multispectral classification methods. This issue has motivated investigation of alternatives, including regularization of the class covariance matrices, ensembles of weak classifiers, development of feature selection and extraction methods, adoption of nonparametric classifiers, and exploration of methods to exploit unlabeled samples via semi-supervised and active learning. Data sets are also quite large, motivating computationally efficient algorithms and implementations. This chapter provides an overview of the recent advances in classification methods for mapping vegetation using hyperspectral data. Three data sets that are used in the hyperspectral classification literature (e.g., Botswana Hyperion satellite data and AVIRIS airborne data over both Kennedy Space Center and Indian Pines) are described in Section 3.2 and used to illustrate methods described in the chapter. An additional high-resolution hyperspectral data set acquired by a SpecTIR sensor on an airborne platform over the Indian Pines area is included to exemplify the use of new deep learning approaches, and a multiplatform example of airborne hyperspectral data is provided to demonstrate transfer learning in hyperspectral image classification. Classical approaches for supervised and unsupervised feature selection and extraction are reviewed in Section 3.3. In particular, nonlinearities exhibited in hyperspectral imagery have motivated development of nonlinear feature extraction methods in manifold learning, which are outlined in Section 3.3.1.4. Spatial context is also important in classification of both natural vegetation with complex textural patterns and large agricultural fields with significant local variability within fields. Approaches to exploit spatial features at both the pixel level (e.g., co-occurrencebased texture and extended morphological attribute profiles [EMAPs]) and integration of segmentation approaches (e.g., HSeg) are discussed in this context in Section 3.3.2. Recently, classification methods that leverage nonparametric methods originating in the machine learning community have grown in popularity. An overview of both widely used and newly emerging approaches, including support vector machines (SVMs), Gaussian mixture models, and deep learning based on convolutional neural networks is provided in Section 3.4. Strategies to exploit unlabeled samples, including active learning and metric learning, which combine feature extraction and augmentation of the pool of training samples in an active learning framework, are outlined in Section 3.5. Integration of image segmentation with classification to accommodate spatial coherence typically observed in vegetation is also explored, including as an integrated active learning system. Exploitation of multisensor strategies for augmenting the pool of training samples is investigated via a transfer learning framework in Section 3.5.1.2. Finally, we look to the future, considering opportunities soon to be provided by new paradigms, as hyperspectral sensing is becoming common at multiple scales from ground-based and airborne autonomous vehicles to manned aircraft and space-based platforms

Graph-based Data Modeling and Analysis for Data Fusion in Remote Sensing

Hyperspectral imaging provides the capability of increased sensitivity and discrimination over traditional imaging methods by combining standard digital imaging with spectroscopic methods. For each individual pixel in a hyperspectral image (HSI), a continuous spectrum is sampled as the spectral reflectance/radiance signature to facilitate identification of ground cover and surface material. The abundant spectrum knowledge allows all available information from the data to be mined. The superior qualities within hyperspectral imaging allow wide applications such as mineral exploration, agriculture monitoring, and ecological surveillance, etc. The processing of massive high-dimensional HSI datasets is a challenge since many data processing techniques have a computational complexity that grows exponentially with the dimension. Besides, a HSI dataset may contain a limited number of degrees of freedom due to the high correlations between data points and among the spectra. On the other hand, merely taking advantage of the sampled spectrum of individual HSI data point may produce inaccurate results due to the mixed nature of raw HSI data, such as mixed pixels, optical interferences and etc. Fusion strategies are widely adopted in data processing to achieve better performance, especially in the field of classification and clustering. There are mainly three types of fusion strategies, namely low-level data fusion, intermediate-level feature fusion, and high-level decision fusion. Low-level data fusion combines multi-source data that is expected to be complementary or cooperative. Intermediate-level feature fusion aims at selection and combination of features to remove redundant information. Decision level fusion exploits a set of classifiers to provide more accurate results. The fusion strategies have wide applications including HSI data processing. With the fast development of multiple remote sensing modalities, e.g. Very High Resolution (VHR) optical sensors, LiDAR, etc., fusion of multi-source data can in principal produce more detailed information than each single source. On the other hand, besides the abundant spectral information contained in HSI data, features such as texture and shape may be employed to represent data points from a spatial perspective. Furthermore, feature fusion also includes the strategy of removing redundant and noisy features in the dataset. One of the major problems in machine learning and pattern recognition is to develop appropriate representations for complex nonlinear data. In HSI processing, a particular data point is usually described as a vector with coordinates corresponding to the intensities measured in the spectral bands. This vector representation permits the application of linear and nonlinear transformations with linear algebra to find an alternative representation of the data. More generally, HSI is multi-dimensional in nature and the vector representation may lose the contextual correlations. Tensor representation provides a more sophisticated modeling technique and a higher-order generalization to linear subspace analysis. In graph theory, data points can be generalized as nodes with connectivities measured from the proximity of a local neighborhood. The graph-based framework efficiently characterizes the relationships among the data and allows for convenient mathematical manipulation in many applications, such as data clustering, feature extraction, feature selection and data alignment. In this thesis, graph-based approaches applied in the field of multi-source feature and data fusion in remote sensing area are explored. We will mainly investigate the fusion of spatial, spectral and LiDAR information with linear and multilinear algebra under graph-based framework for data clustering and classification problems

Bidirectional-Convolutional LSTM Based Spectral-Spatial Feature Learning for Hyperspectral Image Classification

This paper proposes a novel deep learning framework named bidirectional-convolutional long short term memory (Bi-CLSTM) network to automatically learn the spectral-spatial feature from hyperspectral images (HSIs). In the network, the issue of spectral feature extraction is considered as a sequence learning problem, and a recurrent connection operator across the spectral domain is used to address it. Meanwhile, inspired from the widely used convolutional neural network (CNN), a convolution operator across the spatial domain is incorporated into the network to extract the spatial feature. Besides, to sufficiently capture the spectral information, a bidirectional recurrent connection is proposed. In the classification phase, the learned features are concatenated into a vector and fed to a softmax classifier via a fully-connected operator. To validate the effectiveness of the proposed Bi-CLSTM framework, we compare it with several state-of-the-art methods, including the CNN framework, on three widely used HSIs. The obtained results show that Bi-CLSTM can improve the classification performance as compared to other methods

Hyperspectral Imaging for Landmine Detection

This PhD thesis aims at investigating the possibility to detect landmines using hyperspectral imaging. Using this technology, we are able to acquire at each pixel of the image spectral data in hundreds of wavelengths. So, at each pixel we obtain a reflectance spectrum that is used as fingerprint to identify the materials in each pixel, and mainly in our project help us to detect the presence of landmines. The proposed process works as follows: a preconfigured drone (hexarotor or octorotor) will carry the hyperspectral camera. This programmed drone is responsible of flying over the contaminated area in order to take images from a safe distance. Various image processing techniques will be used to treat the image in order to isolate the landmine from the surrounding. Once the presence of a mine or explosives is suspected, an alarm signal is sent to the base station giving information about the type of the mine, its location and the clear path that could be taken by the mine removal team in order to disarm the mine. This technology has advantages over the actually used techniques: • It is safer because it limits the need of humans in the searching process and gives the opportunity to the demining team to detect the mines while they are in a safe region. • It is faster. A larger area could be cleared in a single day by comparison with demining techniques • This technique can be used to detect at the same time objects other than mines such oil or minerals. First, a presentation of the problem of landmines that is expanding worldwide referring to some statistics from the UN organizations is provided. In addition, a brief presentation of different types of landmines is shown. Unfortunately, new landmines are well camouflaged and are mainly made of plastic in order to make their detection using metal detectors harder. A summary of all landmine detection techniques is shown to give an idea about the advantages and disadvantages of each technique. In this work, we give an overview of different projects that worked on the detection of landmines using hyperspectral imaging. We will show the main results achieved in this field and future work to be done in order to make this technology effective. Moreover, we worked on different target detection algorithms in order to achieve high probability of detection with low false alarm rate. We tested different statistical and linear unmixing based methods. In addition, we introduced the use of radial basis function neural networks in order to detect landmines at subpixel level. A comparative study between different detection methods will be shown in the thesis. A study of the effect of dimensionality reduction using principal component analysis prior to classification is also provided. The study shows the dependency between the two steps (feature extraction and target detection). The selection of target detection algorithm will define if feature extraction in previous phase is necessary. A field experiment has been done in order to study how the spectral signature of landmine will change depending on the environment in which the mine is planted. For this, we acquired the spectral signature of 6 types of landmines in different conditions: in Lab where specific source of light is used; in field where mines are covered by grass; and when mines are buried in soil. The results of this experiment are very interesting. The signature of two types of landmines are used in the simulations. They are a database necessary for supervised detection of landmines. Also we extracted some spectral characteristics of landmines that would help us to distinguish mines from background