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Graph-based semi-supervised feature selection has aroused continuous attention in processing high-dimensional data with most unlabeled and fewer data samples. Many graph-based models perform on a pre-defined graph, which is separated from the procedure of feature selection, making the model hard to select the discriminative features. To address this issue, we exploit a self-adjusted graph for semi-supervised embedded feature selection method (SAGFS), which learns an optimal sparse similarity graph to replace the pre-defined graph to alleviate the effect of data noise. SAGFS allows the learned graph itself to be adjusted according to the local geometric structure of the data and the procedure of selecting features to select the most representative features. Besides that, we introduce l 2 , p -norm to constrain the projection matrix for efficient feature selection. An efficient alternating optimization algorithm is presented, together with analyses on its convergence. Systematical experiments on several publicly datasets are performed to analyze the proposed model from several aspects, and demonstrate that our approaches outperform other comparison methods. [ABSTRACT FROM AUTHOR]

Autoencoders are widely used in machine learning for dimension reduction of high-dimensional data. The encoder embeds the input data manifold into a lower-dimensional latent space, while the decoder represents the inverse map, providing a parametrization of the data manifold by the manifold in latent space. We propose and analyze a novel regularization for learning the encoder component of an autoencoder: a loss functional that prefers isometric, extrinsically flat embeddings and allows to train the encoder on its own. To perform the training, it is assumed that the local Riemannian distance and the local Riemannian average can be evaluated for pairs of nearby points on the input manifold. The loss functional is computed via Monte Carlo integration. Our main theorem identifies a geometric loss functional of the embedding map as the Γ-limit of the sampling-dependent loss functionals. Numerical tests, using image data that encodes different explicitly given data manifolds, show that smooth manifold embeddings into latent space are obtained. Furthermore, due to the promotion of extrinsic flatness, interpolation between not too distant points on the manifold is well approximated by linear interpolation in latent space. [ABSTRACT FROM AUTHOR]

It has been hypothesized that the ventral streamprocessing for object recognition is based on a mechanism called cortically local subspace untangling. A mathematical abstraction of object recognition by the visual cortex is how to untangle the manifolds associated with different object categories. Such a manifold untangling problem is closely related to the celebrated kernel trick in metric space. In this paper, we conjecture that there is a more general solution to manifold untangling in the topological space without artificially defining any distance metric. Geometrically, we can either embed a manifold in a higher-dimensional space to promote selectivity or flatten a manifold to promote tolerance. General strategies of both global manifold embedding and local manifold flattening are presented and connected with existing work on the untangling of image, audio, and language data. We also discuss the implications of untangling the manifold into motor control and internal representations. [ABSTRACT FROM AUTHOR]

Generative models have received considerable attention in signal processing and compressive sensing for their ability to generate high-dimensional natural image using low-dimensional codes. In the context of compressive sensing, if the unknown image belongs to the range of a pretrained generative network, then we can recover the image by estimating the underlying compact latent code from the available measurements. In practice, however, a given pretrained generator can only reliably generate images that are similar to the training data. To overcome this challenge, a number of methods have been proposed recently to use untrained generator structure as prior while solving the signal recovery problem. In this paper, we propose a similar method for jointly updating the weights of the generator and latent codes while recovering a video sequence from compressive measurements. We use a single generator to generate the entire video. To exploit the temporal redundancy in a video sequence, we use a low-rank constraint on the latent codes that imposes a low-dimensional manifold model on the generated video sequence. We evaluate the performance of our proposed methods on different video compressive sensing problems under different settings and compared them against some state-of-the-art methods. Our results demonstrate that our proposed methods provide better or comparable accuracy and low computational and memory complexity compared to the existing methods.

Low-rank representation (LRR) aims to find the essential structural information of the original data. It can capture global information and has strong robustness to noise. However, the disadvantage of LRR is that the local similarity of the data is not considered. Most semi-supervised learning (SSL) methods infer unknown tags based on two-stage learning, in which the first stage is a graph construction, and the second stage is to perform SSL for classification. These methods do not share public information that is used to improve classification accuracy. This paper proposes a new semi-supervised learning classification algorithm termed adaptive distance penalty non-negative low-rank representation (ADP-NNLRR). The proposed method combines low rank representation, local constraints and SSL strategy, to make full use of label information and local manifold geometry structure from the data, which in turn, can capture the global subspace, and maintain the relationship between the local parts better. In the proposed method, distance penalty terms and non-negative constraints are introduced, and the obtained low-rank coefficient matrix is used as the similarity matrix of the graph, which can capture more discriminative information for the construction of the graph. Comparative experiments on some classical datasets and noisy datasets verify the superior performance of our proposed method. [ABSTRACT FROM AUTHOR]

Deep learning methods have played a more important role in hyperspectral image classification. However, general deep learning methods mainly take advantage of the samplewise information to formulate the training loss while ignoring the intrinsic data structure of each class. Due to the high spectral dimension and great redundancy between different spectral channels in the hyperspectral image, these former training losses usually cannot work so well for the deep representation of the image. To tackle this problem, this work develops a novel deep manifold embedding method (DMEM) for deep learning in hyperspectral image classification. First, each class in the image is modeled as a specific nonlinear manifold, and the geodesic distance is used to measure the correlation between the samples. Then, based on the hierarchical clustering, the manifold structure of the data can be captured and each nonlinear data manifold can be divided into several subclasses. Finally, considering the distribution of each subclass and the correlation between different subclasses under data manifold, DMEM is constructed as the novel training loss to incorporate the special classwise information in the training process and obtain discriminative representation for the hyperspectral image. Experiments over four real-world hyperspectral image datasets have demonstrated the effectiveness of the proposed method when compared with general sample-based losses and showed superiority when compared with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Deep unsupervised learning extracts meaningful features from unlabeled images and simultaneously serves downstream tasks in computer vision. The basic process of deep clustering methods can include features learning and clustering assignment. To enhance the discriminative ability of the features and further improve the clustering performances, a new deep clustering method namely ACMEC (asymmetric convolutional denoising autoencoder with manifold spatial embedding clustering) is proposed. In this method, an asymmetric convolution denoising autoencoder is employed to extract visual features from images, and a manifold learning algorithm is used to obtain more distinctive features, followed by a Gaussian Mixture Model (GMM) is for clustering learning. The stability of feature space is guaranteed using separately training mechanism. In addition, reconstruction from noisy images enhances the robustness of feature networks. Experimental results on nine benchmark datasets demonstrate that the proposed ACMEC method can provide the better performances such as 0.979 clustering accuracy on the MNIST dataset and 0.668 on the fashion-MNIST dataset. ACMEC is a comparable competitor to the N2D (not too deep clustering) algorithm that is with 0.979 and 0.672 clustering accuracies respectively. Moreover, it is 16.1% higher than DEC algorithm on the fashion-MNIST dataset. [ABSTRACT FROM AUTHOR]

• A generally applicable dimensionality reduction method namely CKD has been proposed. • CKD leverages the differential characteristics of the data with respect to a reference data set. • Reference data can be obtained through an independent measurement or from the data themselves. • CKD shows superior performance over existing techniques. Dimensionality reduction and visualization of high dimensional data are fundamental tasks across scientific disciplines. Current dimensionality reduction methods rely on the use of some restrictive mathematical rules in projecting the data onto lower dimensions, which often leads to results of limited accuracy. Here, we present a generally applicable strategy of analyzing high-dimensional data by leveraging the differential characteristics of the data with respect to a reference data set. Depending on the problem, the reference data can be obtained either through an independent measurement or from the data themselves by finding a set of representative data points. The differentiating characteristics between the two sets of data are optimized by correlation transformation and scaling of the covariance matrices. We show the superior performance of the proposed method over existing techniques for a variety of data sets from different biomedical applications. [ABSTRACT FROM AUTHOR]

Passive non-line-of-sight (NLOS) imaging has drawn great attention in recent years. However, all existing methods are in common limited to simple hidden scenes, low-quality reconstruction, and small-scale datasets. In this paper, we propose NLOS-OT, a novel passive NLOS imaging framework based on manifold embedding and optimal transport, to reconstruct high-quality complicated hidden scenes. NLOS-OT converts the high-dimensional reconstruction task to a low-dimensional manifold mapping through optimal transport, alleviating the ill-posedness in passive NLOS imaging. Besides, we create the first large-scale passive NLOS imaging dataset, NLOS-Passive, which includes 50 groups and more than 3,200,000 images. NLOS-Passive collects target images with different distributions and their corresponding observed projections under various conditions, which can be used to evaluate the performance of passive NLOS imaging algorithms. It is shown that the proposed NLOS-OT framework achieves much better performance than the state-of-the-art methods on NLOS-Passive. We believe that the NLOS-OT framework together with the NLOS-Passive dataset is a big step and can inspire many ideas towards the development of learning-based passive NLOS imaging. Codes and dataset are publicly available (https://github.com/ruixv/NLOS-OT). [ABSTRACT FROM AUTHOR]

• A novel dimensionality reduction method namely GSE has been proposed. • GSE preserves both local and global geometry of the data while reducing dimension. • GSE preserves statistical properties of the data in low dimension. • GSE offers dimension reduction based on position information of the data. • GSE offers superior dimensionality reduction compared to the traditional methods. Nonlinear dimensionality reduction based on preservation of geometry is an imperative task in many scientific applications such as face recognition, object detection, data visualization, and classification. The traditional methods such as Isomap, locally linear embedding (LLE), and Laplacian eigen map (LEM) preserve local or global geometry or both with several limitations such as topological instability in the presence of noise or large neighborhood, inability to deal with ill-connected data points, high sensitivity of embedding performance to selected neighbor number. They also fail to retain the statistical properties of the data such as mean and variance while reducing the data dimensionality. In this paper, we propose a novel method, referred to as geometry and statistics-preserving embedding (GSE), which preserves both geometry and statistics of the data as well as overcomes some critical limitations of the above-mentioned methods. Moreover, GSE offers nonlinear mapping based on position information of the geometry, which is not possible by any other available method. We run experiments with GSE on several datasets including facial images and single cell RNA sequence data, where the GSE has been found to provide significantly better manifold embedding results than the traditional methods. The implementation codes of GSE are available at https://github.com/tauhidstanford/GSE. [ABSTRACT FROM AUTHOR]

Hashing based methods for cross-modal retrieval has been widely explored in recent years. However, most of them mainly focus on the preservation of neighborhood relationship and label consistency, while ignore the proximity of neighbors and proximity of classes, which degrades the discrimination of hash codes. And most of them learn hash codes and hashing functions simultaneously, which limits the flexibility of algorithms. To address these issues, in this article, we propose a two-step cross-modal retrieval method named Manifold-Embedded Semantic Hashing (MESH). It exploits Local Linear Embedding to model the neighborhood proximity and uses class semantic embeddings to consider the proximity of classes. By so doing, MESH can not only extract the manifold structure in different modalities, but also can embed the class semantic information into hash codes to further improve the discrimination of learned hash codes. Moreover, the two-step scheme makes MESH flexible to various hashing functions. Extensive experimental results on three datasets show that MESH is superior to 10 state-of-the-art cross-modal hashing methods. Moreover, MESH also demonstrates superiority on deep features compared with the deep cross-modal hashing method.

Flexible manifold embedding (FME) has been recognized as an effective method for face recognition by integrating both class label information from labeled data and manifold structure information of all data. In order to achieve better performance, this particular method usually requires sufficient samples to make manifold smooth. However, it is often hard to provide enough samples for FME in practice. In view of facial symmetry, we utilize left/right mirror face images to address the deficiency of samples in manifold embedding. These mirror images enable to reflect variations of illuminations, or poses or both them that the original face images cannot provide. Therefore, we propose a robust manifold embedding (RME) algorithm in this paper, which can fully use the class label information and correctly capture the underlying manifold structure. The proposed RME algorithm integrates two complementary characteristics of the label fitness and the manifold smoothness. Moreover, the original face images and its left/right mirror images are jointly used in the learning of RME, which shows better robustness against the variations of both illuminations and poses. Extensive experiments on several public face databases demonstrate that the proposed RME algorithm is promising for higher recognition accuracy than other compared methods in reference.

We propose a new embedding method, named Quantile–Quantile Embedding (QQE), for distribution transformation and manifold embedding with the ability to choose the embedding distribution. QQE, which uses the concept of quantile–quantile plot from visual statistical tests, can transform the distribution of data to any theoretical desired distribution or empirical reference sample. Moreover, QQE gives the user a choice of embedding distribution in embedding the manifold of data into the low dimensional embedding space. It can also be used for modifying the embedding distribution of other dimensionality reduction methods, such as PCA, t-SNE, and deep metric learning, for better representation or visualization of data. We propose QQE in both unsupervised and supervised forms. QQE can also transform a distribution to either an exact reference distribution or its shape. We show that QQE allows for better discrimination of classes in some cases. Our experiments on different synthetic and image datasets show the effectiveness of the proposed embedding method.

Passive non-line-of-sight (NLOS) imaging has drawn great attention in recent years. However, all existing methods are in common limited to simple hidden scenes, low-quality reconstruction, and small-scale datasets. In this paper, we propose NLOS-OT, a novel passive NLOS imaging framework based on manifold embedding and optimal transport, to reconstruct high-quality complicated hidden scenes. NLOS-OT converts the high-dimensional reconstruction task to a low-dimensional manifold mapping through optimal transport, alleviating the ill-posedness in passive NLOS imaging. Besides, we create the first large-scale passive NLOS imaging dataset, NLOS-Passive, which includes 50 groups and more than 3,200,000 images. NLOS-Passive collects target images with different distributions and their corresponding observed projections under various conditions, which can be used to evaluate the performance of passive NLOS imaging algorithms. It is shown that the proposed NLOS-OT framework achieves much better performance than the state-of-the-art methods on NLOS-Passive. We believe that the NLOS-OT framework together with the NLOS-Passive dataset is a big step and can inspire many ideas towards the development of learning-based passive NLOS imaging. Codes and dataset are publicly available (https://github.com/ruixv/NLOS-OT). [ABSTRACT FROM AUTHOR]

This paper investigates the problem of treating embedding and clustering simultaneously to uncover data structure reliably by constraining manifold embedding through clustering. Conversely, most existing methods perform embedding sequentially, followed by clustering, which leads to a clustering that sometimes pushes data towards a direction induced by embedding. Instead, we perform them simultaneously through an original formulation, which allows for preserving the data's original structure in the embedding space and producing a better clustering assignment. To achieve this goal, we introduce a novel algorithm that unifies manifold embedding and clustering (UEC). The proposed UEC algorithm is based on a bi-objective loss function that combines data embedding and clustering, which is optimised using three different ways: (1) Comma Variant, (2) Plus Variant, and (3) Light Plus Variant. The experimental results with several real-world datasets show that UEC is competitive with the state-of-the-art embedding and clustering methods showing in particular that UEC allows for better preservation of the structure of the dataset resulting in better clustering performance. • UEC performs jointly manifold embedding and clustering of data. • The learning process is performed using three different optimisation ways. • We conduct extensive experiments on a public dataset e.g. images, document text, etc. • UEC is effective and competitive to deep and manifold clustering techniques. [ABSTRACT FROM AUTHOR]

Principal component analysis is a widely used technique. However, it is sensitive to noise and considers data samples to be linearly distributed globally. To tackle these challenges, a novel technique robust to noise termed deflated manifold embedding PCA is proposed. In this framework, we unify PCA with manifold embedding to preserve both global and local geometric structures of linear and non-linear data in sub-manifolds. Additionally, a scaling-factor is imposed in the instance space to mitigate the impact of noise in pursuing projections. By using cosine similarity and total distance approaches, we iteratively learn the relationships between instances and projections in order to discriminate between authentic and corrupt instances. Further, a deflation technique is applied to establish multi-relationships between instances and every pursued projection for thorough discrimination. Experimental evaluation of the proposed methods on five datasets show great improvements in their performances over six state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

Domain adaptation (DA) aims to train a robust predictor by transferring rich knowledge from a well-labeled source domain to annotate a newly coming target domain; however, the two domains are usually drawn from very different distributions. Most current methods either learn the common features by matching inter-domain feature distributions and training the classifier separately or align inter-domain label distributions to directly obtain an adaptive classifier based on the original features despite feature distortion. Moreover, intra-domain information may be greatly degraded during the DA process; i.e., the source data samples from different classes might grow closer. To this end, this paper proposes a novel DA approach, referred to as inter-class distribution alienation and inter-domain distribution alignment based on manifold embedding (IDAME). Specifically, IDAME commits to adapting the classifier on the Grassmann manifold by using structural risk minimization, where inter-domain feature distributions are aligned to mitigate feature distortion, and the target pseudo labels are exploited using the distances on the Grassmann manifold. During the classifier adaptation process, we simultaneously consider the inter-class distribution alienation, the inter-domain distribution alignment, and the manifold consistency. Extensive experiments validate that IDAME can outperform several comparative state-of-the-art methods on real-world cross-domain image datasets. [ABSTRACT FROM AUTHOR]

Probabilistic topic modelings, such as latent Dirichlet allocation (LDA) and correlated topic models (CTM), have recently emerged as powerful statistical tools for processing video content. They share an important property, i.e., using a common set of topics to model all data. However, such property can be too restrictive for modeling complex visual data such as crowd scenes where multiple fields of heterogeneous data jointly provide rich information about objects and events. This paper proposes graph-based extensions of LDA and CTM, referred to as GLDA and GCTM, to learn and analyze motion patterns by trajectory clustering in a highly cluttered and crowded environment. Unlike previous works that relied on a scene prior, we apply a spatio-temporal graph to uncover the spatial and temporal coherence between the trajectories of crowd motion during the learning process. The presented models advance the conventional approaches by integrating a manifold-based clustering as initialization and iterative statistical inference as optimization. The output of GLDA and GCTM are mid-level features that represent the motion patterns used later to generate trajectory clusters. Experiments on three different datasets show the effectiveness of the approaches in trajectory clustering and crowd motion modeling. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of large-scale graph-based semi-supervised learning for multi-class classification. Most existing scalable graph-based semi-supervised learning methods are based on the hard linear constraint or cannot cope with the unseen samples, which limits their applications and learning performance. To this end, we build upon our previous work flexible manifold embedding (FME) and propose two novel linear-complexity algorithms called fast flexible manifold embedding (f-FME) and reduced flexible manifold embedding (r-FME). Both of the proposed methods accelerate FME and inherit its advantages. Specifically, our methods address the hard linear constraint problem by combining a regression residue term and a manifold smoothness term jointly, which naturally provides the prediction model for handling unseen samples. To reduce computational costs, we exploit the underlying relationship between a small number of anchor points and all data points to construct the graph adjacency matrix, which leads to simplified closed-form solutions. The resultant f-FME and r-FME algorithms not only scale linearly in both time and space with respect to the number of training samples but also can effectively utilize information from both labeled and unlabeled data. Experimental results show the effectiveness and scalability of the proposed methods. [ABSTRACT FROM AUTHOR]

Hyperspectral remote sensing image classification has drawn a great attention in recent years due to the development of remote sensing technology. To build a high confident classifier, the large number of labeled data is very important, e.g., the success of deep learning technique. Indeed, the acquisition of labeled data is usually very expensive, especially for the remote sensing images, which usually needs to survey outside. To address this problem, in this letter, we propose a domain adaptation method by learning the manifold embedding and matching the discriminative distribution in source domain with neural networks for hyperspectral image classification. Specifically, we use the discriminative information of source image to train the classifier for the source and target images. To make the classifier can work well on both domains, we minimize the distribution shift between the two domains in an embedding space with prior class distribution in the source domain. Meanwhile, to avoid the distortion mapping of the target domain in the embedding space, we try to keep the manifold relation of the samples in the embedding space. Then, we learn the embedding on source domain and target domain by minimizing the three criteria simultaneously based on a neural network. The experimental results on two hyperspectral remote sensing images have shown that our proposed method can outperform several baseline methods. [ABSTRACT FROM AUTHOR]

Abstract Zero-Shot Recognition (ZSR) has gained its popularity recently owing to its promising characteristic that extends the classifiers to the unseen classes. It is typically addressed by resorting to a class semantic space to transfer the knowledge from the seen classes to unseen ones. Therefore, constructing the effective interactions between the visual space and the class semantic space is the key for ZSR. In this paper, under the assumption that the distribution of the semantic categories in the semantic space has an intrinsic manifold structure, we propose two manifold embedding-based ZSR approaches to capture the intrinsic structures of both the visual space and the class semantic space, i.e., ME-ZSR and MCCA-ZSR. Specifically, ME-ZSR builds embedding from visual space to semantic space, while MCCA-ZSR explores to embed both visual and semantic features into a common space. The linear, closed-form solutions make both methods efficient to optimize. Extensive experiments on three popular datasets AwA, CUB and NAB validate the effectiveness of both methods. [ABSTRACT FROM AUTHOR]

Spectra from a single intimate (nonlinear) mixture can be modeled as data points drawn from a smooth manifold. Spectral data sets containing hyperspectral observations of multiple intimate mixtures with some constituent materials in common can, therefore, be modeled as data clouds, in which each point is drawn from a union of manifolds that share a boundary. Two important steps in the processing of such data are to: 1) identify the different mixture manifolds present in the data and 2) invert the nonlinear mixing function by mapping each mixture manifold into some low-dimensional Euclidean space (manifold embedding). The present state-of-the-art algorithms for joint manifold clustering and embedding perform poorly for hyperspectral data, particularly in the embedding task. We propose a novel reconstruction-based algorithm for the improved clustering and the embedding of mixture manifolds. The algorithm attempts to reconstruct each target point as an affine combination of its nearest neighbors with an additional rank penalty on the neighborhood to ensure that only the neighbors on the same manifold as the target point are used in the reconstruction. The reconstruction matrix generated by this technique is both block diagonal and neighborhood-based, leading to improved clustering and embedding. The improved performance of the algorithm against its competitors is exhibited on a variety of simulated and real mixture data sets. [ABSTRACT FROM AUTHOR]

Conventionally, the similarity between two images is measured by the easy-calculating Euclidean distance between their corresponding image feature representations for image retrieval. However, this kind of direct similarity measurement ignores the local geometry structure of the intrinsic data manifold, which is not discriminative enough for robust image retrieval. Some works have proposed to tackle this problem by re-ranking with manifold learning. While benefiting better performance, algorithms of this category suffer from non-trivial computational complexity, which is unfavorable for its application to large-scale retrieval tasks. To address the above problems, in this paper, we propose to learn a robust feature embedding with the guidance of manifold relationships. Specifically, the manifold relationship is used to guide the automatic selection of training image pairs. A fine-tuning network with those selected image pairs transfers such manifold relationships into the fine-tuned feature embedding. With the fine-tuned feature embedding, the Euclidean distance can be directly used to measure the pairwise similarity between images, where the manifold structure is implicitly embedded. Thus, we maintain both the efficiency of Euclidean distance-based similarity measurement and the effectiveness of manifold information in the new feature embedding. Extensive experiments on three benchmark datasets demonstrate the robustness of our proposed method, where our approach significantly outperforms the baselines and exceeds or is comparable to the state-of-the-art methods.

With the rapid development of artificial intelligence, how to take advantage of deep learning and big data to classify polarimetric synthetic aperture radar (PolSAR) imagery is a hot topic in the field of remote sensing. As a key step for PolSAR image classification, feature extraction technology based on target decomposition is relatively mature, and how to extract discriminative spatial features and integrate these features with polarized information to maximize the classification accuracy is the core issue. In this context, this paper proposes a PolSAR image classification algorithm based on fully convolutional networks (FCNs) and a manifold graph embedding model. First, to describe different types of land objects more comprehensively, various polarized features of PolSAR images are extracted through seven kinds of traditional decomposition methods. Afterwards, drawing on transfer learning, the decomposed features are fed into multiple parallel and pre-trained FCN-8s models to learn deep multi-scale spatial features. Feature maps from the last layer of each FCN model are concatenated to obtain spatial polarization features with high dimensions. Then, a manifold graph embedding model is adopted to seek an effective and compact representation for spatially polarized features in a manifold subspace, simultaneously removing redundant information. Finally, a support vector machine (SVM) is selected as the classifier for pixel-level classification in a manifold subspace. Extensive experiments on three PolSAR datasets demonstrate that the proposed algorithm achieves a superior classification performance.

The low-rank representation (LRR) can get essential row-representation of data and it is robust to illumination variation, occlusions and other types of noise. This paper presents a novel manifold embedding classification algorithm based on nonnegative low-rank representation for semi-supervised learning (MEC-NNLRR). In the proposed algorithm, label fitness, manifold smoothness and low-rank representation are integrated, and the label information from the labeled data and the manifold structure from all data are fully and effectively utilized. Based on LRR and manifold learning, the proposed MEC-NNLRR can capture the global and local structure information of the observed data. The obtained nonnegative low-rank representation coefficients can be used as a graph similarity matrix. Considering the physical interpretation of the graph matrix, we impose the non-negativity constraint on the coefficients. In addition, no matter whether the training samples or test samples are corrupted, the proposed MEC-NNLRR is little affected by noise. Extensive experiments on public image databases demonstrate that the proposed MEC-NNLRR is an excellent algorithm and achieves satisfactory results. [ABSTRACT FROM AUTHOR]

Recent advances in hyperspectral imaging have made it a promising solution for intra-operative tissue characterization, with the advantages of being non-contact, non-ionizing, and non-invasive. Working with hyperspectral images in vivo, however, is not straightforward as the high dimensionality of the data makes real-time processing challenging. In this paper, a novel dimensionality reduction scheme and a new processing pipeline are introduced to obtain a detailed tumor classification map for intra-operative margin definition during brain surgery. However, existing approaches to dimensionality reduction based on manifold embedding can be time consuming and may not guarantee a consistent result, thus hindering final tissue classification. The proposed framework aims to overcome these problems through a process divided into two steps: dimensionality reduction based on an extension of the T-distributed stochastic neighbor approach is first performed and then a semantic segmentation technique is applied to the embedded results by using a Semantic Texton Forest for tissue classification. Detailed in vivo validation of the proposed method has been performed to demonstrate the potential clinical value of the system. [ABSTRACT FROM AUTHOR]

Recently, learning-based hashing methods which are designed to preserve the semantic information, have shown promising results for approximate nearest neighbor (ANN) search problems. However, most of these methods require a large number of labeled data which are difficult to access in many real applications. With very limited labeled data available, in this paper we propose a semi-supervised hashing method by integrating manifold embedding, feature representation and classifier learning into a joint framework. Specifically, a semi-supervised manifold embedding is explored to simultaneously optimize feature representation and classifier learning to make the learned binary codes optimal for classification. A two-stage hashing strategy is proposed to effectively address the corresponding optimization problem. At the first stage, an iterative algorithm is designed to obtain a relaxed solution. At the second stage, the hashing function is refined by introducing an orthogonal transformation to reduce the quantization error. Extensive experiments on three benchmark databases demonstrate the effectiveness of the proposed method in comparison with several state-of-the-art hashing methods. [ABSTRACT FROM AUTHOR]

This paper focuses on learning a smooth skeleton structure from noisy data-an emerging topic in the fields of computer vision and computational biology. Many dimensionality reduction methods have been proposed, but none are specially designed for this purpose. To achieve this goal, we propose a unified probabilistic framework that directly models the posterior distribution of data points in an embedding space so as to suppress data noise and reveal the smooth skeleton structure. Within the proposed framework, a sparse positive similarity matrix is obtained by solving a box-constrained convex optimization problem, in which the sparsity of the matrix represents the learned neighborhood graph and the positive weights stand for the new similarity. Embedded data points are then obtained by applying the maximum a posteriori estimation to the posterior distribution expressed by the learned similarity matrix. The embedding process naturally provides a probabilistic interpretation of Laplacian eigenmap and maximum variance unfolding. Extensive experiments on various datasets demonstrate that our proposed method obtains the embedded points that accurately uncover inherent smooth skeleton structures in terms of data visualization, and the method yields superior clustering performance compared to various baselines. [ABSTRACT FROM AUTHOR]

Based on collaborative representation, a novel supervised dimensionality reduction method called collaborative discriminative manifold embedding (CDME) is proposed for hyperspectral imagery. In the proposed CDME, we construct both an intraclass manifold graph and an interclass manifold graph based on two structured dictionaries. In the intraclass manifold graph, the neighborhood points are selected from the dictionary with the same class. Interclass manifold graph calculates the edge weight using all points that are sampled from the dictionary with the different classes. The goal of CDME is to learn a low-dimensional feature space by preserving the intraclass reconstructive structure and the interclass geometric structure simultaneously. Finally, the 1-NN classifier is employed to verify the performance of the CDME. Experimental results demonstrate that CDME outperforms other state-of-the-art dimensionality reduction methods. [ABSTRACT FROM PUBLISHER]

It has been hypothesized that the ventral stream processing for object recognition is based on a mechanism called cortically local subspace untangling. A mathematical abstraction of object recognition by the visual cortex is how to untangle the manifolds associated with different object categories. Such a manifold untangling problem is closely related to the celebrated kernel trick in metric space. In this paper, we conjecture that there is a more general solution to manifold untangling in the topological space without artificially defining any distance metric. Geometrically, we can either embed a manifold in a higher-dimensional space to promote selectivity or flatten a manifold to promote tolerance. General strategies of both global manifold embedding and local manifold flattening are presented and connected with existing work on the untangling of image, audio, and language data. We also discuss the implications of untangling the manifold into motor control and internal representations., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Li and Wang.)

In this paper, we study the problem of face identification from only one training sample per person (OSPP). For a face identification system, the most critical obstacles towards real-world applications are often caused by the disguised, corrupted and varying illuminated images in limited sample sets. Meanwhile, storing fewer training samples would essentially reduce the cost for collecting, storing and processing data. Unfortunately, most methods in the literature basically need large training sets for good representation and generation abilities and would fail if there is only one training sample per person. In this paper, we propose a two-step scheme for the OSPP problem by posing it as a representation and matching problem. For the representation step, we present a novel manifold embedding algorithm, namely sparse discriminative multi-manifold embedding (SDMME), to learn the intrinsic representation beneath the raw data. We construct two sparse graphs to measure the sample similarity, based on two structured dictionaries. Multiple feature spaces are learned to simultaneously minimize the bias from the subspace of the same class and maximize the distances to the subspaces of other classes. For the matching step, we use a distance metric based on the manifold structure to identify the person. Extensive experiments demonstrate that the proposed method outperforms other state-of-the-art methods for the problem of one-sample face identification, while the robustness with occlusion and illumination variances highlights the contribution of our work. [ABSTRACT FROM AUTHOR]

A nonlinear version of discriminative elastic embedding (DEE) algorithm is presented, called kernel discriminative elastic embedding (KDEE). In this paper, we concretely fulfill the following works: (1) class labels and linear projection matrix are integrated into the kernel-based objective function; (2) two different strategies are adopted for optimizing the objective function of KDEE, and accordingly the final algorithms are termed as KDEE1 and KDEE2 respectively; (3) a deliberately selected Laplacian search direction is adopted in KDEE1 for faster convergence. Experimental results on several publicly available databases demonstrate that the proposed algorithm achieves powerful pattern revealing capability for complex manifold data. [ABSTRACT FROM AUTHOR]

The capabilities and application range of cryogenic electron microscopy (cryo-EM) method have expanded vastly in the last two years, thanks to the advances provided by direct detection devices and computational classification tools. We take this review as an opportunity to sketch out promising developments of cryo-EM in two important directions: (i) imaging of short-lived states (10-1000 ms) of biological molecules by using timeresolved cryo-EM, particularly the mixing-spraying method and (ii) recovering an entire continuum of coexisting states from the same sample by employing a computational technique called manifold embedding. It is tempting to think of combining these two methods, to elucidate the way the states of a molecular machine such as the ribosome branch and unfold. This idea awaits further developments of both methods, particularly by increasing the data yield of the time-resolved cryo-EM method and by developing the manifold embedding technique into a user-friendly workbench. [ABSTRACT FROM AUTHOR]

A crucial step in many manifold clustering and embedding algorithms involves selecting the neighbors of a data point. In this paper, a non-negative representation learning algorithm is proposed to select the neighbors of a data point, so that they are almost always lying in the tangent space of the manifold at the given query point. This is very important to multi-manifold clustering and manifold embedding. Convex geometry theory states that a data point on a face of a convex polytope can be a convex combination of the vertices of the polytope, and that the non-zero combination scalars correspond to the vertices of the face the point lies on. The intent of this paper is to use points that that are near to a point as the vertices of a convex polytope, and select the vertices on the same face as this point to be the neighbors. Clearly, the point can be a convex combination of its neighbors. We can observe that these neighbors almost always lie in the tangent space of the manifold at the query point and can preserve the local manifold structure well. Based on this basic idea, we construct an objective function. Moreover, an augmented Lagrange multipliers method is proposed for solving it to derive a non-negative representation, and then the neighbors of a data point can be obtained. The result of our neighbor selection algorithm can be used by other clustering methods such as LEM or manifold embedding methods such as LLE. We demonstrate the effectiveness and efficiency of the proposed method through experiments on synthetic data and a real-world problem. [ABSTRACT FROM AUTHOR]

Three-dimensional head pose estimation from a single 2D image is a challenging task with extensive applications. Existing approaches lack the capability to deal with multiple pose-related and -unrelated factors in a uniform way. Most of them can provide only one-dimensional yaw estimation and suffer from limited representation ability for out-of-sample testing inputs. These drawbacks lead to limited performance when extensive variations exist on faces in-the-wild. To address these problems, we propose a coarse-to-fine pose estimation framework, where the unit circle and 3-sphere are employed to model the manifold topology on the coarse and fine layer respectively. It can uniformly factorize multiple factors in an instance parametric subspace, where novel inputs can be synthesized under a generative framework. Moreover, our approach can effectively avoid the manifold degradation problem when 3D pose estimation is performed. The results on both experimental and in-the-wild databases demonstrate the validity and superior performance of our approach compared with the state-of-the-arts. [ABSTRACT FROM AUTHOR]

We present a family of kernels for analysis of data generated by dynamical systems. These so-called cone kernels feature a dependence on the dynamical vector field operating in the phase space manifold, estimated empirically through finite differences of time-ordered data samples. In particular, cone kernels assign strong affinity to pairs of samples whose relative displacement vector lies within a narrow cone aligned with the dynamical vector field. The outcome of this explicit dependence on the dynamics is that, in a suitable asymptotic limit, Laplace-Beltrami operators for data analysis constructed from cone kernels generate diffusions along the integral curves of the dynamical vector field. This property is independent of the observation modality, and endows these operators with invariance under a weakly restrictive class of transformations of the data (including conformal transformations), while it also enhances their capability to extract intrinsic dynamical timescales via eigenfunctions. Here, we study these features by establishing the Riemannian metric tensor induced by cone kernels in the limit of large data. We find that the corresponding Dirichlet energy is governed by the directional derivative of functions along the dynamical vector field, giving rise to a measure of roughness of functions that favors slowly varying observables. We demonstrate the utility of cone kernels in nonlinear flows on the 2-torus and North Pacific sea surface temperature data generated by a comprehensive climate model. [ABSTRACT FROM AUTHOR]