Intrinsic Manifold Research Articles

Robust Object Tracking by Nonlinear Learning.

We propose a method that obtains a discriminative visual dictionary and a nonlinear classifier for visual tracking tasks in a sparse coding manner based on the globally linear approximation for a nonlinear learning theory. Traditional discriminative tracking methods based on sparse representation learn a dictionary in an unsupervised way and then train a classifier, which may not generate both descriptive and discriminative models for targets by treating dictionary learning and classifier learning separately. In contrast, the proposed tracking approach can construct a dictionary that fully reflects the intrinsic manifold structure of visual data and introduces more discriminative ability in a unified learning framework. Finally, an iterative optimization approach, which computes the optimal dictionary, the associated sparse coding, and a classifier, is introduced. Experiments on two benchmarks show that our tracker achieves a better performance compared with some popular tracking algorithms.

An improved Laplacian Eigenmaps method for machine nonlinear fault feature extraction

In the feature extraction of mechanical fault detection field, manifold learning is one of the effective nonlinear techniques. In this paper, aiming for the situations of noise sensitivity to manifold learning algorithms, an improved Laplacian Eigenmap (I-LapEig) algorithm is proposed and applied to the process of fault feature extraction. The new method takes advantage of local principal component analysis to eliminate the influence of noise points by reconstructing the neighborhood relation amongst the samples, and maintain the global intrinsic manifold structure, which enhances the performance of the feature extraction. To determine the parameters of I-LapEig algorithm, an adaptive neighborhood choose approach is presented. The K-nearest neighbor classifier is also adopted to implement feature classification and recognition. The experimental results on S-curve, rotor bed data, and compressor fault data show that the new method can effectively improve the performance of noise reduction in the feature extraction process when compared with the conventional local linear embedding and Laplacian Eigenmaps.

Nuclear Norm-Based 2DLPP for Image Classification

Two-dimensional locality preserving projections (2DLPP) that use 2D image representation in preserving projection learning can preserve the intrinsic manifold structure and local information of data. However, 2DLPP is based on the Euclidean distance, which is sensitive to noise and outliers in data. In this paper, we propose a novel locality preserving projection method called nuclear norm-based two-dimensional locality preserving projections (NN-2DLPP). First, NN-2DLPP recovers the noisy data matrix through low-rank learning. Second, noise in data is removed and the learned clean data points are projected on a new subspace. Without the disturbance of noise, data points belonging to the same class are kept as close to each other as possible in the new projective subspace. Experimental results on six public image databases with face recognition, object classification, and handwritten digit recognition tasks demonstrated the effectiveness of the proposed method.

Neighbourhood-preserving dimension reduction via localised multidimensional scaling

When high-dimensional data has an intrinsic lower-dimensional manifold structure, one can incorporate such structure knowledge into dimension reduction and design algorithms for special purposes, e.g., preserving the local neighbourhood or uncovering the global structure of data. Based on such assumption, we propose a neighbourhood-preserving dimension reduction algorithm, Localised Multidimensional Scaling with BFS (LMB), for generating low dimensional representation of data that has a latent manifold structure. LMB applies the Multidimensional Scaling (MDS) on the local neighbourhood of data and stitches the reduced neighbourhoods together to form a global reduction. By analysing the local structure of data, LMB can automatically find a well-fit space for reduction. We thoroughly compare the performance of LMB with other state-of-the-art linear or nonlinear algorithms on both synthetic data and real data. Numerical experiments show that LMB efficiently preserves the neighbourhood while uncovering the embedded structure of data. LMB also has a low complexity of O(n2) for a n-item data set.

Image Reconstruction via Manifold Constrained Convolutional Sparse Coding for Image Sets

Convolution sparse coding (CSC) has attracted much attention recently due to its advantages in image reconstruction and enhancement. However, the coding process suffers from perturbations caused by variations of input samples, as the consistence of features from similar input samples are not well addressed in the existing literature. In this paper, we will tackle this feature consistence problem from a set of samples via a proposed manifold constrained convolutional sparse coding (MCSC) method. The core idea of MCSC is to use the intrinsic manifold (Laplacian) structure of the input data to regularize the traditional CSC such that the consistence between features extracted from input samples can be well preserved. To implement the proposed MCSC method efficiently, the alternating direction method of multipliers (ADMM) approach is employed, which can consistently integrate the underlying Laplacian constraints during the optimization process. With this regularized data structure constraint, the MCSC can achieve a much better solution which is robust to the variance of the input samples against overcomplete filters. We demonstrate the capacity of MCSC by providing the state-of-the-art results when applied it to the task of reconstructing light fields. Finally, we show that the proposed MCSC is a generic approach as it also achieves better results than the state-of-the-art approaches based on convolutional sparse coding in other image reconstruction tasks, such as face reconstruction, digit reconstruction, and image restoration.

ℓ2,1 Norm and Hessian Regularized Non-Negative Matrix Factorization with Discriminability for Data Representation

Matrix factorization based methods have widely been used in data representation. Among them, Non-negative Matrix Factorization (NMF) is a promising technique owing to its psychological and physiological interpretation of spontaneously occurring data. On one hand, although traditional Laplacian regularization can enhance the performance of NMF, it still suffers from the problem of its weak extrapolating ability. On the other hand, standard NMF disregards the discriminative information hidden in the data and cannot guarantee the sparsity of the factor matrices. In this paper, a novel algorithm called ℓ 2 , 1 norm and Hessian Regularized Non-negative Matrix Factorization with Discriminability (ℓ 2 , 1 HNMFD), is developed to overcome the aforementioned problems. In ℓ 2 , 1 HNMFD, Hessian regularization is introduced in the framework of NMF to capture the intrinsic manifold structure of the data. ℓ 2 , 1 norm constraints and approximation orthogonal constraints are added to assure the group sparsity of encoding matrix and characterize the discriminative information of the data simultaneously. To solve the objective function, an efficient optimization scheme is developed to settle it. Our experimental results on five benchmark data sets have demonstrated that ℓ 2 , 1 HNMFD can learn better data representation and provide better clustering results.

Dynamical systems analysis of the Maasch–Saltzman model for glacial cycles

This article is concerned with the internal dynamics of a conceptual model proposed by Maasch and Saltzman (1990) to explain central features of the glacial cycles observed in the climate record of the Pleistocene Epoch. It is shown that, in most parameter regimes, the long-term system dynamics occur on certain intrinsic two-dimensional invariant manifolds in the three-dimensional state space. These invariant manifolds are slow manifolds when the characteristic time scales for the total global ice mass and the volume of the North Atlantic Deep Water are well separated, and they are center manifolds when these characteristic time scales are comparable. In both cases, the reduced dynamics on these manifolds are governed by Bogdanov–Takens singularities, and the bifurcation curves associated to these singularities organize the parameter regions in which the model exhibits glacial cycles. In addition, knowledge of the reduced systems and their bifurcations is useful for understanding the effects of slowly varying parameters, which cause passage through Hopf bifurcations, and of orbital (Milankovitch) forcing. Both are central to the mechanism proposed by Maasch and Saltzman for the mid-Pleistocene transition in their model.

Image retrieval framework based on texton uniform descriptor and modified manifold ranking

Image representation and ranking are crucial parts in image retrieval. These two steps are independently constructed in most retrieval models, but the compatibility between descriptors and ranking algorithms play an important role. Inspired by human vision perception and manifold learning, we propose a novel image retrieval framework in this paper. We first propose an image representation called texton uniform descriptor, and then illustrate the preservation of the intrinsic manifold structure through visualizing the distribution of image representations on the two-dimensional manifold. This characteristic provides the foundation for subsequent manifold-based ranking. To further improve the efficiency in image retrieval, we propose modified manifold ranking (MMR) which aims at selecting small-scale images randomly as landmarks to propagate adjacent similarity among images iteratively. The extensive experiments in four public datasets demonstrate that our framework has better performance than other state-of-the-art methods in image retrieval.

Local Geometric Structure Feature for Dimensionality Reduction of Hyperspectral Imagery

Marginal Fisher analysis (MFA) exploits the margin criterion to compact the intraclass data and separate the interclass data, and it is very useful to analyze the high-dimensional data. However, MFA just considers the structure relationships of neighbor points, and it cannot effectively represent the intrinsic structure of hyperspectral imagery (HSI) that possesses many homogenous areas. In this paper, we propose a new dimensionality reduction (DR) method, termed local geometric structure Fisher analysis (LGSFA), for HSI classification. Firstly, LGSFA uses the intraclass neighbor points of each point to compute its reconstruction point. Then, an intrinsic graph and a penalty graph are constructed to reveal the intraclass and interclass properties of hyperspectral data. Finally, the neighbor points and corresponding intraclass reconstruction points are used to enhance the intraclass-manifold compactness and the interclass-manifold separability. LGSFA can effectively reveal the intrinsic manifold structure and obtain the discriminating features of HSI data for classification. Experiments on the Salinas, Indian Pines, and Urban data sets show that the proposed LGSFA algorithm achieves the best classification results than other state-of-the-art methods.

Global similarity preserving hashing

Hashing learning has attracted increasing attention these years with the explosive increase in data volume. Most existing hashing learning methods can be divided into two stages. Firstly, obtain low-dimensional representation of the original data. Secondly, quantize the low-dimensional representation of each sample and map them to binary codes. This two-stage hashing framework separates projection operation and quantization operation apart, and the original data structure cannot be well preserved after this kind of two-stage operation. Considering this, global similarity preserving hashing (GSPH) is proposed, which utilizes a joint hashing framework to directly project the original data to hamming space, and reduces the projection error and the quantization loss simultaneously. Moreover, GSPH presents a global similarity-based data sample reconstruction method, which describes the intrinsic manifold structure of original data more precisely. The image retrieval experimental results on Corel, CIFAR, LabelMe and NUS-WIDE datasets illustrate that our algorithm outperforms several other state-of-the-art methods.

Fault Diagnosis for Rolling Bearings under Variable Conditions Based on Visual Cognition.

Fault diagnosis for rolling bearings has attracted increasing attention in recent years. However, few studies have focused on fault diagnosis for rolling bearings under variable conditions. This paper introduces a fault diagnosis method for rolling bearings under variable conditions based on visual cognition. The proposed method includes the following steps. First, the vibration signal data are transformed into a recurrence plot (RP), which is a two-dimensional image. Then, inspired by the visual invariance characteristic of the human visual system (HVS), we utilize speed up robust feature to extract fault features from the two-dimensional RP and generate a 64-dimensional feature vector, which is invariant to image translation, rotation, scaling variation, etc. Third, based on the manifold perception characteristic of HVS, isometric mapping, a manifold learning method that can reflect the intrinsic manifold embedded in the high-dimensional space, is employed to obtain a low-dimensional feature vector. Finally, a classical classification method, support vector machine, is utilized to realize fault diagnosis. Verification data were collected from Case Western Reserve University Bearing Data Center, and the experimental result indicates that the proposed fault diagnosis method based on visual cognition is highly effective for rolling bearings under variable conditions, thus providing a promising approach from the cognitive computing field.

Locality similarity and dissimilarity preserving support vector machine

Support vector machines (SVMs) are well-known machine learning algorithms, however they may not effectively detect the intrinsic manifold structure of data and give a lower classification performance when learning from structured data sets. To mitigate the above deficiency, in this article, we propose a novel method termed as Locality similarity and dissimilarity preserving support vector machine (LSDPSVM). Compared to SVMs, LSDPSVM successfully inherits the characteristics of SVMs, moreover, it exploits the intrinsic manifold structure of data from both inter-class and intra-class to improve the classification accuracy. In our LSDPSVM a squared loss function is used to reduce the complexity of the model, and an algorithm based on concave-convex procedure method is used to solve the optimal problem. Experimental results on UCI benchmark datasets and Extend Yaleface datasets demonstrate LSDPSVM has better performance than other similar methods.

Analysis of the approximate slow invariant manifold method for reactive flow equations

The Approximate Slow Invariant Manifold method of Singh, Powers and Paolucci is a useful method for addressing model reduction in systems of reactive flow equations. It exploits separations of time scales between slow and fast species, and it generalizes the Intrinsic Low-Dimensional Manifold method, which was developed for model reduction in the context of reaction kinetics, to systems with diffusive and active transport. In this article, we present a mathematical analysis of the Approximate Slow Invariant Manifold method in the context of systems of reaction–diffusion equations with slow and fast reaction kinetics. Beginning with systems of two species (one slow and one fast), and then treating general systems with multiple slow and fast species, we explicitly determine the accuracy of the Approximate Slow Invariant Manifold method. We find that it is correct up to and including the terms of first order in the small parameter that measures the separation of the kinetics time scales, and that it captures many of the terms at second order, as well. Our analysis includes precise statements of the errors at second order, and we find that these are proportional to the slow components of the reaction–diffusion equation, as well as to the curvature of the critical manifold. We illustrate the results analytically on two prototypical examples, the Michaelis–Menten–Henri model with diffusion of the slow species and the Davis–Skodje model in which both the slow and fast species diffuse.

Hyper-graph regularized discriminative concept factorization for data representation

For the tasks of pattern analysis and recognition, nonnegative matrix factorization and concept factorization (CF) have attracted much attention due to its effective application to find the meaningful low-dimensional representation of data. However, they neglect the geometry information embedded in the local neighborhoods of the data and fail to exploit the prior knowledge. In this paper, a novel semi-supervised learning algorithm named hyper-graph regularized discriminative concept factorization (HDCF) is proposed. For the sake of exploring intrinsic geometrical structure of the data and making use of label information, HDCF incorporates hyper-graph regularizer into CF framework and uses the label information to train a classifier for the classification task. HDCF can learn a new concept factorization with respect to the intrinsic manifold structure of the data and also simultaneously adapted to the classification task and a classifier built on the low-dimensional representations. Moreover, an iterative updating optimization scheme is developed to solve the objective function of the proposed HDCF and the convergence proof of our optimization scheme is also provided. Experimental results on ORL, Yale and USPS image databases demonstrate the effectiveness of our proposed algorithm.

Unsupervised rank diffusion for content-based image retrieval

Despite the continuous development of features and mid-level representations, effectively and reliably measuring the similarity among images remains a challenging problem in image retrieval tasks. Once traditional measures consider only pairwise analysis, context-sensitive measures capable of exploiting the intrinsic manifold structure became indispensable for improving the retrieval performance. In this scenario, diffusion processes and rank-based methods are the most representative approaches. This paper proposes a novel hybrid method, named rank diffusion, which uses a diffusion process based on ranking information. The proposed method consists in a diffusion-based re-ranking approach, which propagates contextual information through a diffusion process defined in terms of top-ranked objects, reducing the computational complexity of the proposed algorithm. Extensive experiments considering a rigorous experimental protocol were conducted on six public image datasets and several different descriptors. Experimental results and comparison with state-of-the-art methods demonstrate that high effectiveness gains can be obtained, despite the low-complexity of the algorithm proposed.

Scalable graph based non-negative multi-view embedding for image ranking

Abstract Due to the well-known semantic gap, content based image retrieval task is still a challenge problem. The performance of image ranking highly depends on feature representation. In this paper, trying to make a more discriminative feature, we propose a multi-graph based non-negative feature embedding framework for image ranking. In this framework, various image features are embedded into a unified latent space by a learned graph based non-negative multi-view embedding model. In this model, a multi-graph based regularization term, which discovers the intrinsic geometrical and the discriminating structure of the data space, is imposed into the non-negative matrix factorization. The framework learns to find an optimized combination of different Laplacian matrices to approximate the intrinsic manifold automatically. Meanwhile, multiple anchor graphs are utilized to reduce the complexity of computational. Finally, ranking is conducted according to the relevance score inferred by a Markov random field. Extensive experiments prove the effectiveness of proposed method.

Intrinsic Manifold SLIC: A Simple and Efficient Method for Computing Content-Sensitive Superpixels.

Superpixels are perceptually meaningful atomic regions that can effectively capture image features. Among various methods for computing uniform superpixels, simple linear iterative clustering (SLIC) is popular due to its simplicity and high performance. In this paper, we extend SLIC to compute content-sensitive superpixels, i.e., small superpixels in content-dense regions with high intensity or colour variation and large superpixels in content-sparse regions. Rather than using the conventional SLIC method that clusters pixels in , we map the input image to a 2-dimensional manifold , whose area elements are a good measure of the content density in . We propose a simple method, called intrinsic manifold SLIC (IMSLIC), for computing a geodesic centroidal Voronoi tessellation (GCVT)-a uniform tessellation-on , which induces the content-sensitive superpixels in . In contrast to the existing algorithms, IMSLIC characterizes the content sensitivity by measuring areas of Voronoi cells on . Using a simple and fast approximation to a closed-form solution, the method can compute the GCVT at a very low cost and guarantees that all Voronoi cells are simply connected. We thoroughly evaluate IMSLIC and compare it with eleven representative methods on the BSDS500 dataset and seven representative methods on the NYUV2 dataset. Computational results show that IMSLIC outperforms existing methods in terms of commonly used quality measures pertaining to superpixels such as compactness, adherence to boundaries, and achievable segmentation accuracy. We also evaluate IMSLIC and seven representative methods in an image contour closure application, and the results on two datasets, WHD and WSD, show that IMSLIC achieves the best foreground segmentation performance.

Dynamic graph fusion label propagation for semi-supervised multi-modality classification

The key of label propagation heavily depends on how to capture the manifold structure of the data, which usually is represented by the graph. In the semi-supervised multi-modality classification, exiting methods often optimize the linear relation of multi-graph for label propagation. However, the intrinsic manifold structure is not completely revealed by the linear fusion of multi-graph because the label changes in each iterating propagation dynamically influence the fusion relation of multi-graph. In other words, the fusion relation of multi-graph should be nonlinear because of the label changes in the propagation process, and can not be precisely described by the fixed linear relation in existing methods. To evaluate this nonlinear relationship influence on the classification performance of label propagation, we propose dynamic graph fusion label propagation (DGFLP) for the semi-supervised multi-modality classification. DGFLP is able to jointly consider the relation of multi-graph and the unique distribution of each graph, and models the various relevance of multi-graph in the propagation process. Moreover, the DGFLP alternately integrates the tradition label propagation and the new model function to describe the interaction between the multi-graph and label. The DGFLP solution provides not only the classification label but also the nonlinear relation that encodes the dynamical multi-graph relationship changes in label propagation. The experimental results demonstrate that DGFLP outperforms state-of-art methods on the ORL, AR, scenes 15, Caltech 101, and Caltech 256 databases.

Multi-view learning via multiple graph regularized generative model

Topic models, such as probabilistic latent semantic analysis (PLSA) and latent Dirichlet allocation (LDA), have shown impressive success in many fields. Recently, multi-view learning via probabilistic latent semantic analysis (MVPLSA), is also designed for multi-view topic modeling. These approaches are instances of generative model, whereas they all ignore the manifold structure of data distribution, which is generally useful for preserving the nonlinear information. In this paper, we propose a novel multiple graph regularized generative model to exploit the manifold structure in multiple views. Specifically, we construct a nearest neighbor graph for each view to encode its corresponding manifold information. A multiple graph ensemble regularization framework is proposed to learn the optimal intrinsic manifold. Then, the manifold regularization term is incorporated into a multi-view topic model, resulting in a unified objective function. The solutions are derived based on the Expectation Maximization optimization framework. Experimental results on real-world multi-view data sets demonstrate the effectiveness of our approach.

GSEAD: Graphical Scoring Estimation for Hyperspectral Anomaly Detection

Hyperspectral anomaly detection has been the subject of increased attention in the past 20 years. One obvious trend for scholars is seeking an appropriate data description in the hyperspectral anomaly detection domain. However, a specific predetermined data model in a given detector may not be able to fit all the other cases of hyperspectral images. Hence, can we construct a hyperspectral anomaly detector from a data-adaptive analysis perspective that can implement detection processing only with the characteristics of the data itself? In our manuscript, we propose a graphical scoring estimation based anomaly detector (GSEAD) that utilizes graphical data description to achieve a data-adaptive analysis-based anomaly detection procedure. First, potential anomalies are screened out by a predicted connected component graph (pcc-graph). The remaining pixels constitute the robust background dataset. Second, an embedded locality preserving graph (elp-graph) is generated with the robust background dataset in an intrinsic manifold space by locality preserving graph embedding. Finally, a k-nearest neighbor graphical scoring estimation is undertaken to output the detection result. A target-embedded hyperspectral dataset and three real hyperspectral images were utilized to validate the detection performance of the proposed method. The experimental results show that GSEAD achieves superior receiver operating characteristic curves, area under ROC curves values, and background-anomaly separation than some of the other state-of-the-art anomaly detection methods. A sensitivity analysis of the relevant parameters was also undertaken in the experimental analysis.