The manifold learning for dimensionality reduction with hyperspectral image

The present paper put forward a non-destructive detection method which combines semi-transmission hyperspectral imaging technology with manifold learning dimension reduction algorithm and least squares support vector machine (LSSVM) to recognize internal and external defects in potatoes simultaneously. Three hundred fifteen potatoes were bought in farmers market as research object, and semi-transmission hyperspectral image acquisition system was constructed to acquire the hyperspectral images of normal external defects (bud and green rind) and internal defect (hollow heart) potatoes. In order to conform to the actual production, defect part is randomly put right, side and back to the acquisition probe when the hyperspectral images of external defects potatoes are acquired. The average spectrums (390-1,040 nm) were extracted from the region of interests for spectral preprocessing. Then three kinds of manifold learning algorithm were respectively utilized to reduce the dimension of spectrum data, including supervised locally linear embedding (SLLE), locally linear embedding (LLE) and isometric mapping (ISOMAP), the low-dimensional data gotten by manifold learning algorithms is used as model input, Error Correcting Output Code (ECOC) and LSSVM were combined to develop the multi-target classification model. By comparing and analyzing results of the three models, we concluded that SLLE is the optimal manifold learning dimension reduction algorithm, and the SLLE-LSSVM model is determined to get the best recognition rate for recognizing internal and external defects potatoes. For test set data, the single recognition rate of normal, bud, green rind and hollow heart potato reached 96.83%, 86.96%, 86.96% and 95% respectively, and he hybrid recognition rate was 93.02%. The results indicate that combining the semi-transmission hyperspectral imaging technology with SLLE-LSSVM is a feasible qualitative analytical method which can simultaneously recognize the internal and external defects potatoes and also provide technical reference for rapid on-line non-destructive detecting of the internal and external defects potatoes.

Hyperspectral remote sensing image (HRSI) can provide additional spectral information of objects and have been widely used in many fields. However, due to the complex environment of the HRSI gathering area, collecting the labeled samples of HRSI is time-consuming and labor-intensive. The scarcity of labeled samples is one of the major difficulties for HRSI analysis and processing. In this letter, a spatial–spectral prototypical network (SSPN) for HRSI is proposed for solving the problem of lack of labeled samples. The contribution of this letter is threefold. First, we design a novel local pattern coding algorithm to combine the spatial and spectral information of HRSI pixels based on spatial neighborhood correlation. Then, a spatial–spectral feature extraction algorithm based on 1-D convolutional neural network (1-D-CNN) is suggested to learn the spatial–spectral metric space where HRSI pixels can be correctly classified with only a few labeled samples. Finally, a novel prototype representation for HRSI in spatial–spectral metric space is proposed to better classify the mixed pixels existing in HRSI. The experimental results on three popular HRSI data sets demonstrate that the proposed SSPN is significantly better than the traditional algorithms.

At present, manifold learning is mainly applied to dimensionality reduction. However, from viewpoint of dimensionality reduction, manifold learning algorithms are only local feature preserving algorithms. For example, Local Linear Embedding is local linear preserving, Local Tangent Space Alignment is local homeomorphic preserving and Laplacian Eigenmap is local similarity preserving. The community of dimensionality reduction is now pursuing the algorithms which can preserve both local and global features of data during dimensionality reduction. In this paper, a new algorithm of dimensionality reduction, called Hilbert-Schmidt Independence Criterion Regularized Manifold Learning (HSIC-ML for short), is proposed, in which HSIC between the high dimensional data and the dimension-reduced data is added as a regularization term to the objective functions of manifold learning. The addition of HSIC regularization term makes HSIC-ML capable of preserving both local and global features during dimensionality reduction. HSIC is a criterion measuring the statistical dependence between two data sets and has been widely applied to machine learning in recent years. However, since HSIC was first proposed around 2005, there seems to have not been applied directly to dimensionality reduction, not applied as a regularization term either. The proposed HSIC-ML may be the first try in this respect. The experimental results presented in this paper show that the manifold learning with HSIC regularization performs better than that without HSIC regularization.

We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in two-dimensional/three-dimensional (2D/3D) Euclidean spaces and in higher-dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.

Fault diagnosis is essentially the identification of multiple fault modes. How to extract sensitive features and improve diagnostic accuracy is the key to fault diagnosis. In this paper, a new manifold learning method (Mass Laplacian Discriminant Analysis, MLDA) is proposed. Firstly, it is assumed that each data point in the space is a point with mass, and the mass is defined as the number of data points in a certain area. Then, the idea of universal gravitation is introduced to calculate the virtual universal gravitation between data points. Based on the Laplace eigenmaps algorithm, the gravitational Laplacian matrix between the same kind of data and the heterogeneous data is obtained, and the discriminant function is constructed by the ratio of the virtual gravitation between the heterogeneous data and the virtual gravitation between the similar data; the projection function with the largest discriminant function value is the optimal feature mapping function. Finally, based on the mapping function, the eigenvalues of the training data and the test data are calculated, and the softmax algorithm is used to classify the test data. Experiments on gear fault diagnosis show that this method has higher diagnostic accuracy than other manifold learning algorithms.

Spinal cord injuries (SCI) occur when the spinal cord is damaged due to any trauma. Treatment of this condition typically involves a long and challenging rehabilitation process. Brain-computer interface (BCI) controlled rehabilitation systems show promise for people with SCI, as they offer repetitive and controlled treatment in the home environment without requiring a specialist. There is a growing demand for electroencephalography (EEG)–based BCI rehabilitation systems, particularly for patients with SCI. In this study, EEG signals from ten SCI patients were analyzed. At the same time, they imagined performing rehabilitation movements for five different hand and arm actions (pronation, supination, palmar grasp, lateral grasp, and hand opening). The study tested manifold learning algorithms, feature extraction, and classification methods in EEG analysis to improve usability in real-time applications. Manifold learning algorithms were used to represent complex and high-dimensional data in a lower-dimensional space, allowing for better representation and separation of the temporal and spatial characteristics of brain activity. The spectral embedding algorithm was used in this study, which, to the best of our knowledge, is the first time this algorithm has been applied to the data of SCI patients. Additionally, we conducted a comparative analysis of commonly encountered methods in the literature, including multi-dimensional scaling (MDS), isometric feature mapping (ISOMAP), local linear embedding (LLE), and t-distributed stochastic neighbor embedding (t-SNE). Machine learning algorithms, such as k-nearest neighbor (k-NN), support vector machine (SVM), and Naive Bayes methods, were used to obtain classification results for both multi-class and binary classes. The combination of pronation and hand open was found to yield the best performance for binary classification of the movements. The study determined that the ISOMAP manifold learning method with the k-NN algorithm is the optimal method for processing times of both the train and the test. The method also demonstrated a high accuracy value of 0.967 and a short time of 0.088 units in multiple classifications, which is promising. The study utilized the spectral embedding method for the first time and achieved an accuracy rate of 0.649 in multi-class classification and 0.933 ± 0.049 in binary-class classification.

Dimensionality reduction is a key step in hyperspectral image processing. Recent investigations are looking into nonlinear manifold learning for dimensionality reduction in hyperspectral imagery. Nonlinear manifold learning methods such as Isomap, and Local Linear Embedding are use to recover the low dimensional representation of an unknown nonlinear manifold for high dimensional data where it is important to retain the neighborhood structure of the manifold. Although these algorithms use different philosophies for recovering the nonlinear manifold, they all incorporate neighborhood information from each data point to construct a weighted graph having the data points as vertices. Thus the performance of these methods highly depends on how well these neighborhoods are selected, since all subsequent steps rely on it. The k -NN algorithm is the most widely used technique for neighbor selection in manifold learning. However, it can result in a disconnected graph and it does not fully exploit spatial neighborhood information from the image in selecting points to form the neighborhoods. In this paper, recently proposed methods for constructing the weighted graph in manifold learning are studied: k -VC, k -EC and k -MST, which have the advantage of creating connected graphs and have performed well in artificial data sets. Spatial information of the hyperspectral images is included in the manifold learning process by using spatial coherence. Experiments are conducted with artificial data and hyperspectral images. For hyperspectral images, classification accuracy was used as an indirect measure to understand how the low dimensional embedding of the data reduces dimensionality while still maintaining good discrimination performance.

Hyperspectral images comprise, by design, high dimensional image data. However, research has shown that for a d-dimensional hyperspectral image, it is typical for the data to inherently occupy an m-dimensional space, with m << d. In the remote sensing community, this has led to a recent increase in the use of non-linear manifold learning, which aims to characterize the embedded lower-dimensional, non-linear manifold upon which the hyperspectral data inherently lie. Classic hyperspectral data models include statistical, linear subspace, and linear mixture models, but these can place restrictive assumptions on the distribution of the data. With graph theory and manifold learning based models, the only assumption is that the data reside on an underlying manifold. In previous publications, we have shown that manifold coordinate approximation using locally linear embedding (LLE) is a viable pre-processing step for target detection with the Adaptive Cosine/Coherence Estimator (ACE) algorithm. Here, we improve upon that methodology using a more rigorous, data-driven implementation of LLE that incorporates the injection of a cloud" of target pixels and the Spectral Angle Mapper (SAM) detector. The LLE algorithm, which holds that the data is locally linear, is typically governed by a user defined parameter k, indicating the number of nearest neighbors to use in the initial graph model. We use an adaptive approach to building the graph that is governed by the data itself and does not rely upon user input. This implementation of LLE can yield greater separation between the target pixels and the background pixels in the manifold space. We present an analysis of target detection performance in the manifold coordinates using scene-derived target spectra and laboratory-measured target spectra across two different data sets.

In order to extract sensitive features of face images from high dimensional image data and facilitate the recognition speed, this paper has proposed a novel method based on the manifold learning and genetic-chaos algorithm optimized kernel extreme learning machine (KELM) for the application of face recognition. The locally linear embedding (LLE) algorithm has been employed to extract distinct features by projecting the original high dimensionality of the face image into a low dimensionality space. Then the KELM is introduced to provide quick and accurate pattern recognition on the extracted features. The only parameter need to be determined in KELM is the neuron number of hidden layer. Literature review indicates that very limited work has addressed the optimization of this parameter. Hence, the genetic-chaos algorithm was used for the first time to optimize the KELM parameter in this paper. A robust KELM structure may be attained after the genetic-chaos optimization. In order to evaluate and verify the proposed method, experiment tests have been carried out using standard face expressions. The experimental analysis results indicate that the performance of the proposed LLE- genetic-chaos-KELM method outperforms its rivals in terms of both recognition accuracy and training speed. Index Terms—face recognition, feature extraction, GA Chaos, KELM.

In machine learning, a group of high-dimensional data point set which represents an image set can be looked upon as the point set distributing on a nonlinear manifold. Typically, the manifold dimension is much lower than the dimension of data points. Therefore, it is important to explore the real dimension and the real geometry of high-dimensional data point set. Based on this objective, researchers put forward the concept of manifold learning. Traditional manifold learning can achieve dramatic dimensional reduction on high-dimension points, but there are still some problems of it. In the aspect of processing a large amount of data currently, traditional manifold learning algorithm reveals many weaknesses mainly in time consumption. To improve the deficiency, the paper puts forward a new algorithm, aiming at simplifying the time process of manifold learning algorithm which is also abbreviated as SLEP. In the part of the experiment, the study makes a comparative experiment between the synthetic data set and the real data set. The result shows that the proposed algorithm improves time efficiency.

The field of manifold learning provides powerful tools for parameterizing high-dimensional data points with a small number of parameters when this data lies on or near some manifold. Images can be thought of as points in some high-dimensional image space where each coordinate represents the intensity value of a single pixel. These manifold learning techniques have been successfully applied to simple image sets, such as handwriting data and a statue in a tightly controlled environment. However, they fail in the case of natural image sets, even those that only vary due to a single degree of freedom, such as a person walking or a heart beating. Parameterizing data sets such as these will allow for additional constraints on traditional computer vision problems such as segmentation and tracking. This dissertation explores the reasons why classical manifold learning algorithms fail on natural image sets and proposes new algorithms for parameterizing this type of data. Type of Report: Other Department of Computer Science & Engineering Washington University in St. Louis Campus Box 1045 St. Louis, MO 63130 ph: (314) 935-6160 WASHINGTON UNIVERSITY THE HENRY EDWIN SEVER GRADUATE SCHOOL DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING MANIFOLD LEARNING FOR NATURAL IMAGE SETS by Richard M. Souvenir, M.S. Computer Science, B.S. Applied Science Prepared under the direction of Professor Robert Pless A dissertation presented to the Henry Edwin Sever Graduate School of Washington University in partial fulfillment of the requirements for the degree of DOCTOR OF SCIENCE August 2006 Saint Louis, Missouri WASHINGTON UNIVERSITY THE HENRY EDWIN SEVER GRADUATE SCHOOL DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING

Image processing and machine learning communities have long addressed the problems involved in the analysis of large high-dimensional data sets. To deal with high-dimensional data efficiently, learning core properties of given data set is important. The manifold learning methods such as ISOMap try to identify a low-dimensional manifold from a set of unorganized samples. ISOMap method is an extension of the classical multidimensional scaling method for dimension reduction, which find a linear subspace in which dissimilarity between data points is preserved. In order to measure dissimilarity, ISOMap uses the geodesic distances on the manifold instead of Euclidean distance. In this paper, we propose a modification of ISOMap using class information, which is often given in company with input data in many applications such as pattern classification. Since the conventional ISOMap does not use class information in approximating true geodesic distance between each pair of data points, it is difficult to construct a data structure related to class-membership that may give important information for given task such as data visualization and classification. The proposed method utilizes class-membership for measuring distance of data pair so as to find a low-dimensional manifold preserving the distance between classes as well as the distance between data points. Through computational experiments on artificial data sets and real facial data sets, we confirm that the proposed method gives better performance than the conventional ISOMap.

Locally Linear Embedding (LLE) is a recently proposed algorithm for non-linear dimensionality reduction and manifold learning. However, it may not be optimal for classification problem. In this paper, an improved version of LLE, namely KFDA-LLE, is proposed using kernel Fisher discriminant analysis (KFDA) method, combined with SVM classifier for face recognition task. Firstly, the input training samples are projected into the low-dimensional space by LLE. Then KFDA is introduced for finding the optimal projection direction. Finally, SVM classifier is used for face recognition. Experimental results on face database demonstrate that the extended LLE method is more efficient and robust.

To effectively utilize the rich spectral information of hyperspectral remote sensing images (HRSIs), the fractional Fourier transform (FRFT) feature of HRSIs is proposed to reflect the time-domain and frequency-domain characteristics of a spectral pixel simultaneously, and an FRFT order selection criterion is also proposed based on maximizing separability. Firstly, FRFT is applied to the spectral pixels, and the amplitude spectrum is taken as the FRFT feature of HRSIs. The FRFT feature is mixed with the pixel spectral to form the presented spectral and fractional Fourier transform mixed feature (SF2MF), which contains time–frequency mixing information and spectral information of pixels. K-nearest neighbor, logistic regression, and random forest classifiers are used to verify the superiority of the proposed feature. A 1-dimensional convolutional neural network (1D-CNN) and a two-branch CNN network (Two-CNNSF2MF-Spa) are designed to extract the depth SF2MF feature and the SF2MF-spatial joint feature, respectively. Moreover, to compensate for the defect that CNN cannot effectively capture the long-range features of spectral pixels, a long short-term memory (LSTM) network is introduced to be combined with CNN to form a two-branch network C-CLSTMSF2MF for extracting deeper and more efficient fusion features. A 3D-CNNSF2MF model is designed, which firstly performs the principal component analysis on the spa-SF2MF cube containing spatial information and then feeds it into the 3-dimensional convolutional neural network 3D-CNNSF2MF to extract the SF2MF-spatial joint feature effectively. The experimental results of three real HRSIs show that the presented mixed feature SF2MF can effectively improve classification accuracy.

Hyperspectral band selection (BS) is an important technique to reduce data dimensionality for the classification applications of hyperspectral remote sensing images (HSIs). Recently, searching-based BS methods have received increasing attention for their ability to select the best subset of bands while preserving the essential information of the original data. However, existing searching-based BS methods neglect effective exploitation of the spatial and spectral prior information inherent in the data, thus limiting their performance. To address this problem, in this study, a novel unsupervised BS method called Spectral–Spatial Iterative Greedy Algorithm (SSIGA) is proposed. Specifically, to facilitate efficient local search using spectral information, SSIGA conducts clustering on all the bands by employing a K-means clustering method with balanced cluster size constraints and constructs a K-nearest neighbor graph for each cluster. Based on the nearest neighbor graphs, SSIGA can effectively explore the neighborhood solutions in local search. In addition, to efficiently evaluate the discriminability and information redundancy of the solution given by SSIGA using the spatial and spectral information of HSIs, we designed an effective objective function for SSIGA. The value of the objective function is derived by calculating the Fisher score for each band in the solution based on the results of the superpixel segmentation performed on the target HSI, as well as by computing the average information entropy and mutual information of the bands in the solution. Experimental results on three publicly available real HSI datasets demonstrate that the SSIG algorithm achieves superior performance compared to several state-of-the-art methods.