Local Embedding Research Articles

On local isometric embeddings of three-dimensional Lie groups

Due to Janet–Cartan’s theorem, any analytic Riemannian manifolds can be locally isometrically embedded into a sufficiently high dimensional Euclidean space. However, for an individual Riemannian manifold (M, g), it is in general hard to determine the least dimensional Euclidean space into which (M, g) can be locally isometrically embedded, even in the case where (M, g) is homogeneous. In this paper, when the space (M, g) is locally isometric to a three-dimensional Lie group equipped with a left-invariant Riemannian metric, we classify all such spaces that can be locally isometrically embedded into the four-dimensional Euclidean space. Two types of algebraic equations, the Gauss equation and the derived Gauss equation, play an essential role in this classification.

Local Embedding and Effective Downfolding in the Auxiliary-Field Quantum Monte Carlo Method.

A local embedding and effective downfolding scheme has been developed and implemented in the auxiliary-field quantum Monte Carlo (AFQMC) method. A local cluster in which electrons are fully correlated is defined, and the frozen orbital method is used on the remainder of the system to construct an effective Hamiltonian, which operates within the local cluster. Local embedding, which involves only the occupied sector, has previously been employed in the context of Co/graphene. Here, the methodology is extended in order to allow for effective downfolding of the virtual sector, thus allowing for significant reduction in the computational effort required for AFQMC calculations. The system size, which can be feasibly treated with AFQMC, is therefore greatly extended as only a single local cluster is explicitly correlated at the AFQMC level of theory. The approximation is controlled by the separate choice of the spatial size of the active occupied region ( Ro) and of the active virtual region ( Rv). The systematic dependence of the AFQMC energy on Ro and Rv is investigated, and it is found that relative AFQMC energies of physical and chemical interest converge rapidly to the full AFQMC treatment (i.e., using no embedding or downfolding).

Deep Imbalanced Learning for Face Recognition and Attribute Prediction.

Data for face analysis often exhibit highly-skewed class distribution, i.e., most data belong to a few majority classes, while the minority classes only contain a scarce amount of instances. To mitigate this issue, contemporary deep learning methods typically follow classic strategies such as class re-sampling or cost-sensitive training. In this paper, we conduct extensive and systematic experiments to validate the effectiveness of these classic schemes for representation learning on class-imbalanced data. We further demonstrate that more discriminative deep representation can be learned by enforcing a deep network to maintain inter-cluster margins both within and between classes. This tight constraint effectively reduces the class imbalance inherent in the local data neighborhood, thus carving much more balanced class boundaries locally. We show that it is easy to deploy angular margins between the cluster distributions on a hypersphere manifold. Such learned Cluster-based Large Margin Local Embedding (CLMLE), when combined with a simple k-nearest cluster algorithm, shows significant improvements in accuracy over existing methods on both face recognition and face attribute prediction tasks that exhibit imbalanced class distribution.

Recurrence relations for symplectic realization of (quasi)-Poisson structures

It is known that any Poisson manifold can be embedded into a bigger space which admits a description in terms of a global symplectic structure. Such a procedure is known as a symplectic realization and has a number of important applications like the quantization of the original Poisson manifold. In the present paper we extend the above idea to the case of quasi-Poisson structures which should not necessarily satisfy the Jacobi identity. For any given quasi-Poisson structure we provide a closed recursive formula for local embedding functions and Darboux coordinates. Our construction is illustrated for the examples of the constant R-flux algebra, quasi-Poisson structure isomorphic to the commutator algebra of imaginary octonions and the non-geometric M-theory R-flux background. In all cases we derive explicit formulas for the symplectic realization and the corresponding expression for Darboux coordinates.

Embedding hospital-based medication review

PurposeThe purpose of this paper is to explore the embedding of hospital-based medication review attending to the conflictual and developmental nature of practice. Specifically, this paper examines manifestations of contradictions and how they play out in professional practices and local embedding processes.Design/methodology/approachUsing ethnographic methods, this paper employs the activity-theoretic notion of contradictions for analyzing the embedding of medication review. Data from participant observation (in total 290 h over 48 different workdays) and 31 semi-structured interviews with different healthcare professionals in two Swedish hospital-based settings (emergency department, department of surgery) are utilized.FindingsThe conflictual and developmental potential related to three interrelated characteristics (contested, fragmented and distributed) of the activity object is shown. The contested nature is illustrated showing different conceptualizations, interests and positions both within and across different professional groups. The fragmented character of medication review is shown by tensions related to the appraisal of the utility of the newly introduced practice. Finally, the distributed character is exemplified through tensions between individual and collective responsibility when engaging in multi-site work. Overall, the need for ongoing “repair” work is demonstrated.Originality/valueBy using a practice-theoretical approach and ethnographic methods, this paper presents a novel perspective for studying local embedding processes. Following the day-to-day work of frontline clinicians captures the ongoing processes of embedding medication review and highlights the opportunities to learn from contradictions inherent in routine work practices.

Hippocampus Segmentation Based on Iterative Local Linear Mapping With Representative and Local Structure-Preserved Feature Embedding.

Hippocampus segmentation plays a significant role in mental disease diagnoses, such as Alzheimer's disease, epilepsy, and so on. Patch-based multi-atlas segmentation (PBMAS) approach is a popular method for hippocampus segmentation and has achieved a promising result. However, the PBMAS approach needs high computation cost due to registration and the segmentation accuracy is subject to the registration accuracy. In this paper, we propose a novel method based on iterative local linear mapping (ILLM) with the representative and local structure-preserved feature embedding to achieve accurate and robust hippocampus segmentation with no need for registration. In the proposed approach, semi-supervised deep autoencoder (SSDA) exploits unsupervised deep autoencoder and local structure-preserved manifold regularization to nonlinearly transform the extracted magnetic resonance (MR) patch to embedded feature manifold, whose adjacent relationship is similar to the signed distance map (SDM) patch manifold. Local linear mapping is used to preliminarily predict SDM patch corresponding to the MR patch. Subsequently, threshold segmentation generates a preliminary segmentation. The ILLM refines the segmentation result iteratively by ensuring the local constraints of embedded feature manifold and SDM patch manifold using a space-constrained dictionary update. Thus, a refined segmentation is obtained with no need for registration. The experiments on 135 subjects from ADNI dataset show that the proposed approach is superior to the state-of-the-art PBMAS and classification-based approaches with mean Dice similarity coefficients of 0.8852±0.0203 and 0.8783 ± 0.0251 for bilateral hippocampus segmentation of 1.5T and 3.0T datasets, respectively.

A Novel Tri-Training Technique for the Semi-Supervised Classification of Hyperspectral Images Based on Regularized Local Discriminant Embedding Feature Extraction

This paper introduces a novel semi-supervised tri-training classification algorithm based on regularized local discriminant embedding (RLDE) for hyperspectral imagery. In this algorithm, the RLDE method is used for optimal feature information extraction, to solve the problems of singular values and over-fitting, which are the main problems in the local discriminant embedding (LDE) and local Fisher discriminant analysis (LFDA) methods. An active learning method is then used to select the most useful and informative samples from the candidate set. In the experiments undertaken in this study, the three base classifiers were multinomial logistic regression (MLR), k-nearest neighbor (KNN), and random forest (RF). To confirm the effectiveness of the proposed RLDE method, experiments were conducted on two real hyperspectral datasets (Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and Reflective Optics System Imaging Spectrometer (ROSIS)), and the proposed RLDE tri-training algorithm was compared with its counterparts of tri-training alone, LDE, and LFDA. The experiments confirmed that the proposed approach can effectively improve the classification accuracy for hyperspectral imagery.

Composition operators and embedding theorems for some function spaces of Dirichlet series

We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators. Following this, we perform a careful study of such composition operators generated by polynomial symbols $\varphi$ on a scale of Bergman--type Hilbert spaces $\mathcal{D}_\alpha$. We investigate the optimal $\beta$ such that the composition operator $\mathcal{C}_\varphi$ maps $\mathcal{D}_\alpha$ boundedly into $\mathcal{D}_\beta$. We also prove a new embedding theorem for the non-Hilbertian Hardy space $\mathcal H^p$ into a Bergman space in the half-plane and use it to consider composition operators generated by polynomial symbols on $\mathcal{H}^p$, finding the first non-trivial results of this type. The embedding also yields a new result for the functional associated to the multiplicative Hilbert matrix.

The local embedding of low carbon technologies and the agency of user-side intermediaries

‘Local embedding’ is a term increasingly used by transition researchers but in a variety of ways. As a concept it is emotive but lacks clarity. The first contribution of this paper is to explore and substantiate the concept of local embedding by drawing on three theoretical fields: socio-technical transitions, domestication studies and research on innovation intermediaries. Emphasis is placed on the work required to integrate low carbon technologies into local contexts of use by aligning multiple system elements into configurations that work. This points to a particular form of actor – those performing relational work between multiple actors and technologies, commonly known as intermediaries – as being central to the process. Three key intermediary processes – of facilitating, configuring and brokering - are thought to define the work that intermediary organisations do. Nonetheless, understanding how these key intermediary processes relate as well as the agency of intermediary organisations in local embedding is still largely uncharted territory. The paper's second contribution is the development of a process perspective on the agency of intermediary organisations in local embedding. The resulting perspective offers a means to situate and understand the agency of user-side intermediaries in local embedding and insights into later phases of transition processes.

Integrating leaf and flower by local discriminant CCA for plant species recognition

Plant species recognition using a single organ, such as flower and leaf, is not sufficiently reliable, because different species may have very similar flowers or leaves, while the same species may have rather different flowers or leaves. Combining leaves and flowers to recognize plant species can produce positive results. Based on multi-modal learning scheme, an automatic plant species recognition method is proposed by combining leaves and flowers of plant. In the method, a modified local discriminant canonical correlation analysis (MLDCCA) is designed by incorporating the idea of local discriminant embedding (LDE) into canonical correlation analysis (CCA). Firstly, two neighbor graphs are constructed based on the exploration of the manifold that the input data lie on. Then, two projection matrices for dimensionality reduction are obtained by making the within-class neighbor samples most correlated and between-class neighbor samples least correlated, and meanwhile keeping the correlation between leaves and flowers of the same species maximum. Finally, 1-nearest neighbor classifier with geodesic distance is used to recognize the plant species. MLDCCA is a powerful supervised multi-modal dimensional reduction method which can extract the discriminant features from two plant organs, meanwhile preserve the discriminant information and the data structure well. Experimental results on a real leaf and flower image dataset validate the effectiveness of the proposed method.

On the local isometric embedding of trapped surfaces into three-dimensional Riemannian manifolds

We study trapped surfaces from the point of view of local isometric embedding into 3D Riemannian manifolds. When a two-surface is embedded into 3D Euclidean space, the problem of finding all surfaces applicable upon it gives rise to a non-linear partial differential equation of the Monge–Ampère type, first discovered by Darboux, and later reformulated by Weingarten. Even today, this problem remains very difficult, despite some remarkable results. We find an original way of generalizing the Darboux technique, which leads to a coupled set of six non-linear partial differential equations. For the 3-manifolds occurring in Friedmann–(Lemaitre)–Robertson–Walker cosmologies, we show that the local isometric embedding of trapped surfaces into them can be proved by solving just one non-linear equation. Such an equation is here solved for the three kinds of Friedmann model associated with positive, zero, negative curvature of spatial sections, respectively.

Generalized ratiometric fluorescence nanosensors based on carbon dots and an advanced chemometric model

Probe encapsulated by biologically localized embedding (PEBBLE) has emerged as a new type of sensing technique for complex systems. Generalized ratiometric PEBBLE nanosensors prepared by encapsulating an intensity-based probe and an inert reference dye inside the pores of stable matrix possess advantages of easy synthesis, immunity to interference, lower toxicity, and robustness to variations in probe loading. However, the selection of appropriate reference dyes used in generalized ratiometric PEBBLE nanosensors is a rather difficult task since they should satisfy some stringent requirements. In this contribution, the feasibility of using carbon dots (C-dots) as generic inert references in synthesizing PEBBLE nanosensors was first investigated in detail. And a dual-wavelength monitoring strategy and the quantitative fluorescence model for generalized ratiometric probes (QFMGRP) were adopted to solve the problems brought by the use of carbon dots as inert references. C-dots doped PEBBLE nanosensors (C-PEBBLE nanosensors) for the quantification of NO2− and free Ca2+ were synthesized by encapsulating C-dots and intensity based fluorescence probes (i.e., acriflavine for NO2−, and Rhod-2 for Ca2+, respectively) inside the pores of stable matrix. Experimental results showed that the combination of C-PEBBLEs, the QFMGRP model and the dual-wavelength monitoring strategy achieved accurate quantification of NO2− and the free Ca2+ in real-world samples. Their quantitative results were in good consistence with those determined by HPLC and atomic absorption spectrophotometer, respectively. The strategies proposed in this contribution have generic applicability in the synthesis of PEBBLE nanosensors and their quantitative applications.

Dimensionality Reduction of Hyperspectral Image Using Spatial Regularized Local Graph Discriminant Embedding

Dimensionality reduction (DR) is an important preprocessing step for hyperspectral image (HSI) classification. Recently, graph-based DR methods have been widely used. Among various graph-based models, the local graph discriminant embedding (LGDE) model has shown its effectiveness due to the complete use of label information. Besides spectral information, an HSI also contains rich spatial information. In this paper, we propose a regularization method to incorporate the spatial information into the LGDE model. Specifically, an oversegmentation method is first employed to divide the original HSI into nonoverlapping superpixels. Then, based on the observation that pixels in a superpixel often belong to the same class, intraclass graphs are constructed to describe such spatial information. Finally, the constructed superpixel-level intraclass graphs are used as a regularization term, which can be naturally incorporated into the LGDE model. Besides, to sufficiently capture the nonlinear property of an HSI, the linear LGDE model is further extended into its kernel counterpart. To demonstrate the effectiveness of the proposed method, experiments have been established on three widely used HSIs acquired by different hyperspectral sensors. The obtained results show that the proposed method can achieve higher classification performance than many state-of-the-art graph embedding models, and the kernel extension model can further improve the classification performance.

Local word vectors guiding keyphrase extraction

Automated keyphrase extraction is a fundamental textual information processing task concerned with the selection of representative phrases from a document that summarize its content. This work presents a novel unsupervised method for keyphrase extraction, whose main innovation is the use of local word embeddings (in particular GloVe vectors), i.e., embeddings trained from the single document under consideration. We argue that such local representation of words and keyphrases are able to accurately capture their semantics in the context of the document they are part of, and therefore can help in improving keyphrase extraction quality. Empirical results offer evidence that indeed local representations lead to better keyphrase extraction results compared to both embeddings trained on very large third corpora or larger corpora consisting of several documents of the same scientific field and to other state-of-the-art unsupervised keyphrase extraction methods.

On optimal embeddings and trees

We apply the theory of Bruhat–Tits trees to the study of optimal embeddings from orders of rank two and three to quaternion algebras. Specifically, we determine how many conjugacy classes of global Eichler orders in an indefinite quaternion algebra yield optimal representations of such orders. This completes previous work by C. Maclachlan, who considered only Eichler orders of square free level and integral domains as suborders. The same technique is used in the second part of this work to compute local embedding numbers, which extends previous results by J. Brzezinski.

Local compressed convex spectral embedding for bird species identification.

This paper proposes a multi-layer alternating sparse-dense framework for bird species identification. The framework takes audio recordings of bird vocalizations and produces compressed convex spectral embeddings (CCSE). Temporal and frequency modulations in bird vocalizations are ensnared by concatenating frames of the spectrogram, resulting in a high dimensional and highly sparse super-frame-based representation. Random projections are then used to compress these super-frames. Class-specific archetypal analysis is employed on the compressed super-frames for acoustic modeling, obtaining the convex-sparse CCSE representation. This representation efficiently captures species-specific discriminative information. However, many bird species exhibit high intra-species variations in their vocalizations, making it hard to appropriately model the whole repertoire of vocalizations using only one dictionary of archetypes. To overcome this, each class is clustered using Gaussian mixture models (GMM), and for each cluster, one dictionary of archetypes is learned. To calculate CCSE for any compressed super-frame, one dictionary from each class is chosen using the responsibilities of individual GMM components. The CCSE obtained using this GMM-archetypal analysis framework is referred to as local CCSE. Experimental results corroborate that local CCSE either outperforms or exhibits comparable performances to existing methods including support vector machine powered by dynamic kernels and deep neural networks.

Privacy-Preserving Predictive Modeling: Harmonization of Contextual Embeddings From Different Sources.

BackgroundData sharing has been a big challenge in biomedical informatics because of privacy concerns. Contextual embedding models have demonstrated a very strong representative capability to describe medical concepts (and their context), and they have shown promise as an alternative way to support deep-learning applications without the need to disclose original data. However, contextual embedding models acquired from individual hospitals cannot be directly combined because their embedding spaces are different, and naive pooling renders combined embeddings useless.ObjectiveThe aim of this study was to present a novel approach to address these issues and to promote sharing representation without sharing data. Without sacrificing privacy, we also aimed to build a global model from representations learned from local private data and synchronize information from multiple sources.MethodsWe propose a methodology that harmonizes different local contextual embeddings into a global model. We used Word2Vec to generate contextual embeddings from each source and Procrustes to fuse different vector models into one common space by using a list of corresponding pairs as anchor points. We performed prediction analysis with harmonized embeddings.ResultsWe used sequential medical events extracted from the Medical Information Mart for Intensive Care III database to evaluate the proposed methodology in predicting the next likely diagnosis of a new patient using either structured data or unstructured data. Under different experimental scenarios, we confirmed that the global model built from harmonized local models achieves a more accurate prediction than local models and global models built from naive pooling.ConclusionsSuch aggregation of local models using our unique harmonization can serve as the proxy for a global model, combining information from a wide range of institutions and information sources. It allows information unique to a certain hospital to become available to other sites, increasing the fluidity of information flow in health care.

Learning local embedding deep features for person re-identification in camera networks

In this paper, we propose a novel feature learning method named local embedding deep features (LEDF) for person re-identification in camera networks. In order to learn the structural information of pedestrian, we first utilize the verification network that does not require explicit identity labels to obtain the local summing maps. We then combine all local summing maps of a pedestrian image to form the holistic summing map which has the same identity label with the original pedestrian image. Finally, we take the holistic summing maps as the input to train the identification network, and then obtain the LEDF from the last fully connected layer. The proposed LEDF fully considers the structural information by learning the local features and meanwhile possesses strong discriminative ability by learning global features. The experimental results on two large-scale datasets (Market-1501 and CUHK03) demonstrate that the proposed LEDF achieves better results than the state-of-the-art methods.

Learned local similarity prior embedding active contour model for choroidal neovascularization segmentation in optical coherence tomography images

Learned local similarity prior embedding active contour model for choroidal neovascularization segmentation in optical coherence tomography images

Supervised Polarimetric SAR Image Classification Using Tensor Local Discriminant Embedding.

Feature extraction is a very important step for polarimetric synthetic aperture radar (PolSAR) image classification. Many dimensionality reduction (DR) methods have been employed to extract features for supervised PolSAR image classification. However, these DR-based feature extraction methods only consider each single pixel independently and thus fail to take into account the spatial relationship of the neighboring pixels, so their performance may not be satisfactory. To address this issue, we introduce a novel tensor local discriminant embedding (TLDE) method for feature extraction for supervised PolSAR image classification. The proposed method combines the spatial and polarimetric information of each pixel by characterizing the pixel with the patch centered at this pixel. Then each pixel is represented as a third-order tensor, of which the first two modes indicate the spatial information of the patch (i.e. the row and the column of the patch) and the third mode denotes the polarimetric information of the patch. Based on the label information of samples and the redundance of the spatial and polarimetric information, a supervised tensor-based dimensionality reduction technique, called TLDE, is introduced to find three projections which project each pixel, that is, the third-order tensor into the low-dimensional feature. Finally, classification is completed based on the extracted features using the nearest neighbor (NN) classifier and the support vector machine (SVM) classifier. The proposed method is evaluated on two real PolSAR data sets and the simulated PolSAR data sets with various number of looks. The experimental results demonstrate that the proposed method not only improves the classification accuracy greatly, but also alleviates the influence of speckle noise on classification.