40 research outputs found

    Efficient Nonlinear Dimensionality Reduction for Pixel-wise Classification of Hyperspectral Imagery

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    Classification, target detection, and compression are all important tasks in analyzing hyperspectral imagery (HSI). Because of the high dimensionality of HSI, it is often useful to identify low-dimensional representations of HSI data that can be used to make analysis tasks tractable. Traditional linear dimensionality reduction (DR) methods are not adequate due to the nonlinear distribution of HSI data. Many nonlinear DR methods, which are successful in the general data processing domain, such as Local Linear Embedding (LLE) [1], Isometric Feature Mapping (ISOMAP) [2] and Kernel Principal Components Analysis (KPCA) [3], run very slowly and require large amounts of memory when applied to HSI. For example, applying KPCA to the 512脳217 pixel, 204-band Salinas image using a modern desktop computer (AMD FX-6300 Six-Core Processor, 32 GB memory) requires more than 5 days of computing time and 28GB memory! In this thesis, we propose two different algorithms for significantly improving the computational efficiency of nonlinear DR without adversely affecting the performance of classification task: Simple Linear Iterative Clustering (SLIC) superpixels and semi-supervised deep autoencoder networks (SSDAN). SLIC is a very popular algorithm developed for computing superpixels in RGB images that can easily be extended to HSI. Each superpixel includes hundreds or thousands of pixels based on spatial and spectral similarities and is represented by the mean spectrum and spatial position of all of its component pixels. Since the number of superpixels is much smaller than the number of pixels in the image, they can be used as input for nonlinearDR, which significantly reduces the required computation time and memory versus providing all of the original pixels as input. After nonlinear DR is performed using superpixels as input, an interpolation step can be used to obtain the embedding of each original image pixel in the low dimensional space. To illustrate the power of using superpixels in an HSI classification pipeline,we conduct experiments on three widely used and publicly available hyperspectral images: Indian Pines, Salinas and Pavia. The experimental results for all three images demonstrate that for moderately sized superpixels, the overall accuracy of classification using superpixel-based nonlinear DR matches and sometimes exceeds the overall accuracy of classification using pixel-based nonlinear DR, with a computational speed that is two-three orders of magnitude faster. Even though superpixel-based nonlinear DR shows promise for HSI classification, it does have disadvantages. First, it is costly to perform out-of-sample extensions. Second, it does not generalize to handle other types of data that might not have spatial information. Third, the original input pixels cannot approximately be recovered, as is possible in many DR algorithms.In order to overcome these difficulties, a new autoencoder network - SSDAN is proposed. It is a fully-connected semi-supervised autoencoder network that performs nonlinear DR in a manner that enables class information to be integrated. Features learned from SSDAN will be similar to those computed via traditional nonlinear DR, and features from the same class will be close to each other. Once the network is trained well with training data, test data can be easily mapped to the low dimensional embedding. Any kind of data can be used to train a SSDAN,and the decoder portion of the SSDAN can easily recover the initial input with reasonable loss.Experimental results on pixel-based classification in the Indian Pines, Salinas and Pavia images show that SSDANs can approximate the overall accuracy of nonlinear DR while significantly improving computational efficiency. We also show that transfer learning can be use to finetune features of a trained SSDAN for a new HSI dataset. Finally, experimental results on HSI compression show a trade-off between Overall Accuracy (OA) of extracted features and PeakSignal to Noise Ratio (PSNR) of the reconstructed image

    Graph-based Semi-supervised Learning: Algorithms and Applications.

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    114 p.Graph-based semi-supervised learning have attracted large numbers of researchers and it is an important part of semi-supervised learning. Graph construction and semi-supervised embedding are two main steps in graph-based semi-supervised learning algorithms. In this thesis, we proposed two graph construction algorithms and two semi-supervised embedding algorithms. The main work of this thesis is summarized as follows:1. A new graph construction algorithm named Graph construction based on self-representativeness and Laplacian smoothness (SRLS) and several variants are proposed. Researches show that the coefficients obtained by data representation algorithms reflect the similarity between data samples and can be considered as a measurement of the similarity. This kind of measurement can be used for the weights of the edges between data samples in graph construction. Each column of the coefficient matrix obtained by data self-representation algorithms can be regarded as a new representation of original data. The new representations should have common features as the original data samples. Thus, if two data samples are close to each other in the original space, the corresponding representations should be highly similar. This constraint is called Laplacian smoothness.SRLS graph is based on l2-norm minimized data self-representation and Laplacian smoothness. Since the representation matrix obtained by l2 minimization is dense, a two phrase SRLS method (TPSRLS) is proposed to increase the sparsity of graph matrix. By extending the linear space to Hilbert space, two kernelized versions of SRLS are proposed. Besides, a direct solution to kernelized SRLS algorithm is also introduced.2. A new sparse graph construction algorithm named Sparse graph with Laplacian smoothness (SGLS) and several variants are proposed. SGLS graph algorithm is based on sparse representation and use Laplacian smoothness as a constraint (SGLS). A kernelized version of the SGLS algorithm and a direct solution to kernelized SGLS algorithm are also proposed. 3. SPP is a successful unsupervised learning method. To extend SPP to a semi-supervised embedding method, we introduce the idea of in-class constraints in CGE into SPP and propose a new semi-supervised method for data embedding named Constrained Sparsity Preserving Embedding (CSPE).4. The weakness of CSPE is that it cannot handle the new coming samples which means a cascade regression should be performed after the non-linear mapping is obtained by CSPE over the whole training samples. Inspired by FME, we add a regression term in the objective function to obtain an approximate linear projection simultaneously when non-linear embedding is estimated and proposed Flexible Constrained Sparsity Preserving Embedding (FCSPE).Extensive experiments on several datasets (including facial images, handwriting digits images and objects images) prove that the proposed algorithms can improve the state-of-the-art results

    Graph-based Semi-supervised Learning: Algorithms and Applications.

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    114 p.Graph-based semi-supervised learning have attracted large numbers of researchers and it is an important part of semi-supervised learning. Graph construction and semi-supervised embedding are two main steps in graph-based semi-supervised learning algorithms. In this thesis, we proposed two graph construction algorithms and two semi-supervised embedding algorithms. The main work of this thesis is summarized as follows:1. A new graph construction algorithm named Graph construction based on self-representativeness and Laplacian smoothness (SRLS) and several variants are proposed. Researches show that the coefficients obtained by data representation algorithms reflect the similarity between data samples and can be considered as a measurement of the similarity. This kind of measurement can be used for the weights of the edges between data samples in graph construction. Each column of the coefficient matrix obtained by data self-representation algorithms can be regarded as a new representation of original data. The new representations should have common features as the original data samples. Thus, if two data samples are close to each other in the original space, the corresponding representations should be highly similar. This constraint is called Laplacian smoothness.SRLS graph is based on l2-norm minimized data self-representation and Laplacian smoothness. Since the representation matrix obtained by l2 minimization is dense, a two phrase SRLS method (TPSRLS) is proposed to increase the sparsity of graph matrix. By extending the linear space to Hilbert space, two kernelized versions of SRLS are proposed. Besides, a direct solution to kernelized SRLS algorithm is also introduced.2. A new sparse graph construction algorithm named Sparse graph with Laplacian smoothness (SGLS) and several variants are proposed. SGLS graph algorithm is based on sparse representation and use Laplacian smoothness as a constraint (SGLS). A kernelized version of the SGLS algorithm and a direct solution to kernelized SGLS algorithm are also proposed. 3. SPP is a successful unsupervised learning method. To extend SPP to a semi-supervised embedding method, we introduce the idea of in-class constraints in CGE into SPP and propose a new semi-supervised method for data embedding named Constrained Sparsity Preserving Embedding (CSPE).4. The weakness of CSPE is that it cannot handle the new coming samples which means a cascade regression should be performed after the non-linear mapping is obtained by CSPE over the whole training samples. Inspired by FME, we add a regression term in the objective function to obtain an approximate linear projection simultaneously when non-linear embedding is estimated and proposed Flexible Constrained Sparsity Preserving Embedding (FCSPE).Extensive experiments on several datasets (including facial images, handwriting digits images and objects images) prove that the proposed algorithms can improve the state-of-the-art results

    The Multiplicative Zak Transform, Dimension Reduction, and Wavelet Analysis of LIDAR Data

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    This thesis broadly introduces several techniques within the context of timescale analysis. The representation, compression and reconstruction of DEM and LIDAR data types is studied with directional wavelet methods and the wedgelet decomposition. The optimality of the contourlet transform, and then the wedgelet transform is evaluated with a valuable new structural similarity index. Dimension reduction for material classification is conducted with a frame-based kernel pipeline and a spectral-spatial method using wavelet packets. It is shown that these techniques can improve on baseline material classification methods while significantly reducing the amount of data. Finally, the multiplicative Zak transform is modified to allow the study and partial characterization of wavelet frames

    Contribution to supervised representation learning: algorithms and applications.

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    278 p.In this thesis, we focus on supervised learning methods for pattern categorization. In this context, itremains a major challenge to establish efficient relationships between the discriminant properties of theextracted features and the inter-class sparsity structure.Our first attempt to address this problem was to develop a method called "Robust Discriminant Analysiswith Feature Selection and Inter-class Sparsity" (RDA_FSIS). This method performs feature selectionand extraction simultaneously. The targeted projection transformation focuses on the most discriminativeoriginal features while guaranteeing that the extracted (or transformed) features belonging to the sameclass share a common sparse structure, which contributes to small intra-class distances.In a further study on this approach, some improvements have been introduced in terms of theoptimization criterion and the applied optimization process. In fact, we proposed an improved version ofthe original RDA_FSIS called "Enhanced Discriminant Analysis with Class Sparsity using GradientMethod" (EDA_CS). The basic improvement is twofold: on the first hand, in the alternatingoptimization, we update the linear transformation and tune it with the gradient descent method, resultingin a more efficient and less complex solution than the closed form adopted in RDA_FSIS.On the other hand, the method could be used as a fine-tuning technique for many feature extractionmethods. The main feature of this approach lies in the fact that it is a gradient descent based refinementapplied to a closed form solution. This makes it suitable for combining several extraction methods andcan thus improve the performance of the classification process.In accordance with the above methods, we proposed a hybrid linear feature extraction scheme called"feature extraction using gradient descent with hybrid initialization" (FE_GD_HI). This method, basedon a unified criterion, was able to take advantage of several powerful linear discriminant methods. Thelinear transformation is computed using a descent gradient method. The strength of this approach is thatit is generic in the sense that it allows fine tuning of the hybrid solution provided by different methods.Finally, we proposed a new efficient ensemble learning approach that aims to estimate an improved datarepresentation. The proposed method is called "ICS Based Ensemble Learning for Image Classification"(EM_ICS). Instead of using multiple classifiers on the transformed features, we aim to estimate multipleextracted feature subsets. These were obtained by multiple learned linear embeddings. Multiple featuresubsets were used to estimate the transformations, which were ranked using multiple feature selectiontechniques. The derived extracted feature subsets were concatenated into a single data representationvector with strong discriminative properties.Experiments conducted on various benchmark datasets ranging from face images, handwritten digitimages, object images to text datasets showed promising results that outperformed the existing state-ofthe-art and competing methods

    Semi-Supervised Normalized Embeddings for Fusion and Land-Use Classification of Multiple View Data

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    Land-use classification from multiple data sources is an important problem in remote sensing. Data fusion algorithms like Semi-Supervised Manifold Alignment (SSMA) and Manifold Alignment with Schroedinger Eigenmaps (SEMA) use spectral and/or spatial features from multispectral, multimodal imagery to project each data source into a common latent space in which classification can be performed. However, in order for these algorithms to be well-posed, they require an expert user to either directly identify pairwise dissimilarities in the data or to identify class labels for a subset of points from which pairwise dissimilarities can be derived. In this paper, we propose a related data fusion technique, which we refer to as Semi-Supervised Normalized Embeddings (SSNE). SSNE is defined by modifying the SSMA/SEMA objective functions to incorporate an extra normalization term that enables a latent space to be well-defined even when no pairwise-dissimilarities are provided. Using publicly available data from the 2017 IEEE GRSS Data Fusion Contest, we show that SSNE enables similar land-use classification performance to SSMA/SEMA in scenarios where pairwise dissimilarities are available, but that unlike SSMA/SEMA, it also enables land-use classification in other scenarios. We compare the effect of applying different classification algorithms including a support vector machine (SVM), a linear discriminant analysis classifier (LDA), and a random forest classifier (RF); we show that SSMA/SEMA and SSNE robust to the use of different classifiers. In addition to comparing the classification performance of SSNE to SSMA/SEMA and comparing classification algorithm, we utilize manifold alignment to classify unknown views

    Doctor of Philosophy

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    dissertationWith the ever-increasing amount of available computing resources and sensing devices, a wide variety of high-dimensional datasets are being produced in numerous fields. The complexity and increasing popularity of these data have led to new challenges and opportunities in visualization. Since most display devices are limited to communication through two-dimensional (2D) images, many visualization methods rely on 2D projections to express high-dimensional information. Such a reduction of dimension leads to an explosion in the number of 2D representations required to visualize high-dimensional spaces, each giving a glimpse of the high-dimensional information. As a result, one of the most important challenges in visualizing high-dimensional datasets is the automatic filtration and summarization of the large exploration space consisting of all 2D projections. In this dissertation, a new type of algorithm is introduced to reduce the exploration space that identifies a small set of projections that capture the intrinsic structure of high-dimensional data. In addition, a general framework for summarizing the structure of quality measures in the space of all linear 2D projections is presented. However, identifying the representative or informative projections is only part of the challenge. Due to the high-dimensional nature of these datasets, obtaining insights and arriving at conclusions based solely on 2D representations are limited and prone to error. How to interpret the inaccuracies and resolve the ambiguity in the 2D projections is the other half of the puzzle. This dissertation introduces projection distortion error measures and interactive manipulation schemes that allow the understanding of high-dimensional structures via data manipulation in 2D projections

    Nonlinear Dimensionality Reduction by Manifold Unfolding

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    Every second, an enormous volume of data is being gathered from various sources and stored in huge data banks. Most of the time, monitoring a data source requires several parallel measurements, which form a high-dimensional sample vector. Due to the curse of dimensionality, applying machine learning methods, that is, studying and analyzing high-dimensional data, could be difficult. The essential task of dimensionality reduction is to faithfully represent a given set of high-dimensional data samples with a few variables. The goal of this thesis is to develop and propose new techniques for handling high-dimensional data, in order to address contemporary demand in machine learning applications. Most prominent nonlinear dimensionality reduction methods do not explicitly provide a way to handle out-of-samples. The starting point of this thesis is a nonlinear technique, called Embedding by Affine Transformations (EAT), which reduces the dimensionality of out-of-sample data as well. In this method, a convex optimization is solved for estimating a transformation between the high-dimensional input space and the low-dimensional embedding space. To the best of our knowledge, EAT is the only distance-preserving method for nonlinear dimensionality reduction capable of handling out-of-samples. The second method that we propose is TesseraMap. This method is a scalable extension of EAT. Conceptually, TesseraMap partitions the underlying manifold of data into a set of tesserae and then unfolds it by constructing a tessellation in a low-dimensional subspace of the embedding space. Crucially, the desired tessellation is obtained through solving a small semidefinite program; therefore, this method can efficiently handle tens of thousands of data points in a short time. The final outcome of this thesis is a novel method in dimensionality reduction called Isometric Patch Alignment (IPA). Intuitively speaking, IPA first considers a number of overlapping flat patches, which cover the underlying manifold of the high-dimensional input data. Then, IPA rearranges the patches and stitches the neighbors together on their overlapping parts. We prove that stitching two neighboring patches aligns them together; thereby, IPA unfolds the underlying manifold of data. Although this method and TesseraMap have similar approaches, IPA is more scalable; it embeds one million data points in only a few minutes. More importantly, unlike EAT and TesseraMap, which unfold the underlying manifold by stretching it, IPA constructs the unfolded manifold through patch alignment. We show this novel approach is advantageous in many cases. In addition, compared to the other well-known dimensionality reduction methods, IPA has several important characteristics; for example, it is noise tolerant, it handles non-uniform samples, and it can embed non-convex manifolds properly. In addition to these three dimensionality reduction methods, we propose a method for subspace clustering called Low-dimensional Localized Clustering (LDLC). In subspace clustering, data is partitioned into clusters, such that the points of each cluster lie close to a low-dimensional subspace. The unique property of LDLC is that it produces localized clusters on the underlying manifold of data. By conducting several experiments, we show this property is an asset in many machine learning tasks. This method can also be used for local dimensionality reduction. Moreover, LDLC is a suitable tool for forming the tesserae in TesseraMap, and also for creating the patches in IPA.1 yea
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