Locally Linear Image Structural Embedding for Image Structure Manifold Learning
University of Waterloo（滑铁卢大学）
Benyamin Ghojogh, Fakhri Karray, Mark Crowley
备注：
This is the paper for the methods named "Locally Linear Image Structural Embedding (LLISE)" and "Kernel Locally Linear Image Structural Embedding (Kernel LLISE)"
发表信息：
International Conference on Image Analysis and Recognition, Springer, pp. 126-138, 2019
Most of existing manifold learning methods rely on Mean Squared Error (MSE) or $\ell_2$ norm. However, for the problem of image quality assessment, these are not promising measure. In this paper, we introduce the concept of an image structure manifold which captures image structure features and discriminates image distortions. We propose a new manifold learning method, Locally Linear Image Structural Embedding (LLISE), and kernel LLISE for learning this manifold. The LLISE is inspired by Locally Linear Embedding (LLE) but uses SSIM rather than MSE. This paper builds a bridge between manifold learning and image fidelity assessment and it can open a new area for future investigations.
Locally Linear Embedding (LLE) is a nonlinear spectral dimensionality reduction and manifold learning method. It has two main steps which are linear reconstruction and linear embedding of points in the input space and embedding space, respectively. In this work, we propose two novel generative versions of LLE, named Generative LLE (GLLE), whose linear reconstruction steps are stochastic rather than deterministic. GLLE assumes that every data point is caused by its linear reconstruction weights as latent factors. The proposed GLLE algorithms can generate various LLE embeddings stochastically wh…
This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we first cover LLE, kernel LLE, inverse LLE, and feature fusion with LLE. Then, we cover out-of-sample embedding using linear reconstruction, eigenfunctions, and kernel mapping. Incremental LLE is explained for embedding streaming data. Landmark LLE methods using the Nystrom approximation and locally linear landmarks are explained for big data embedding. We introduce the methods for parameter selection of numb…
Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE repeatedly to improve the results. Thirdly, we relax the kNN constraint of LLE and present a sparse similarity learning algorithm. The final Iterative LLE combines these three improvements. Extensive experiment results show that iterative LLE algorithm significantly improve both classification and clustering results.
We provide a new interpretation of Hessian locally linear embedding (HLLE), revealing that it is essentially a variant way to implement the same idea of locally linear embedding (LLE). Based on the new interpretation, a substantial simplification can be made, in which the idea of "Hessian" is replaced by rather arbitrary weights. Moreover, we show by numerical examples that HLLE may produce projection-like results when the dimension of the target space is larger than that of the data manifold, and hence one further modification concerning the manifold dimension is suggested. Combining all the …
Background: Functional magnetic resonance imaging (fMRI) provides non-invasive measures of neuronal activity using an endogenous Blood Oxygenation-Level Dependent (BOLD) contrast. This article introduces a nonlinear dimensionality reduction (Locally Linear Embedding) to extract informative measures of the underlying neuronal activity from BOLD time-series. The method is validated using the Leave-One-Out-Cross-Validation (LOOCV) accuracy of classifying psychiatric diagnoses using resting-state and task-related fMRI. Methods: Locally Linear Embedding of BOLD time-series (into each voxel's respec…
We demonstrate that locally linear embedding (LLE) inherently admits some unwanted results when no regularization is used, even for cases in which regularization is not supposed to be needed in the original algorithm. The existence of one special type of result, which we call ``projection pattern'', is mathematically proved in the situation that an exact local linear relation is achieved in each neighborhood of the data. These special patterns as well as some other bizarre results that may occur in more general situations are shown by numerical examples on the Swiss roll with a hole embedded i…
Locally Linear Embedding (LLE) is a nonlinear spectral dimensionality reduction and manifold learning method. It has two main steps which are linear reconstruction and linear embedding of points in the input space and embedding space, respectively. In this work, we look at the linear reconstruction step from a stochastic perspective where it is assumed that every data point is conditioned on its linear reconstruction weights as latent factors. The stochastic linear reconstruction of LLE is solved using expectation maximization. We show that there is a theoretical connection between three funda…
This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that the relationship between structural representations and node embeddings is analogous to that of a distribution and its samples. We prove that all tasks that can be performed by node embeddings can also be performed by structural representations and vice-versa. We also show that the concept of transductive and inductive learning is unrelated to node embeddings …
Tongji University（同济大学）；Google Research（谷歌研究院）；Intel Labs（英特尔实验室）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；The University of Chicago（芝加哥大学）；Northwestern University（西北大学）
Brain networks have received considerable attention given the critical significance for understanding human brain organization, for investigating neurological disorders and for clinical diagnostic applications. Structural brain network (e.g. DTI) and functional brain network (e.g. fMRI) are the primary networks of interest. Most existing works in brain network analysis focus on either structural or functional connectivity, which cannot leverage the complementary information from each other. Although multi-view learning methods have been proposed to learn from both networks (or views), these me…
University College London（伦敦大学学院）；Alan Turing Institute（艾伦·图灵研究所）
Linear chain conditional random fields (CRFs) combined with contextual word embeddings have achieved state of the art performance on sequence labeling tasks. In many of these tasks, the identity of the neighboring words is often the most useful contextual information when predicting the label of a given word. However, contextual embeddings are usually trained in a task-agnostic manner. This means that although they may encode information about the neighboring words, it is not guaranteed. It can therefore be beneficial to design the sequence labeling architecture to directly extract this inform…
Microsoft Research（微软研究院）；Indian Institute of Technology, Delhi（德里印度理工学院）
The objective in extreme multi-label learning is to train a classifier that can automatically tag a novel data point with the most relevant subset of labels from an extremely large label set. Embedding based approaches make training and prediction tractable by assuming that the training label matrix is low-rank and hence the effective number of labels can be reduced by projecting the high dimensional label vectors onto a low dimensional linear subspace. Still, leading embedding approaches have been unable to deliver high prediction accuracies or scale to large problems as the low rank assumpti…
Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of machine learning tasks. However, learning structural representations of nodes is a challenging problem, and it has typically involved manually specifying and tailoring topological features for each node. In this paper, we develop GraphWave, a method that represents each node's network neighborhood via a low-dimensional embedding by leveraging heat wavelet diffu…
Inferring the structural properties of a protein from its amino acid sequence is a challenging yet important problem in biology. Structures are not known for the vast majority of protein sequences, but structure is critical for understanding function. Existing approaches for detecting structural similarity between proteins from sequence are unable to recognize and exploit structural patterns when sequences have diverged too far, limiting our ability to transfer knowledge between structurally related proteins. We newly approach this problem through the lens of representation learning. We introd…
Recently, link prediction algorithms based on neural embeddings have gained tremendous popularity in the Semantic Web community, and are extensively used for knowledge graph completion. While algorithmic advances have strongly focused on efficient ways of learning embeddings, fewer attention has been drawn to the different ways their performance and robustness can be evaluated. In this work we propose an open-source evaluation pipeline, which benchmarks the accuracy of neural embeddings in situations where knowledge graphs may experience semantic and structural changes. We define relation-cent…
Jožef Stefan Institute（约瑟夫·斯蒂芬研究所）；Cosylab d.o.o.（Cosylab 公司）；National Institute of Chemistry（国家化学研究所）；Faculty of Computer and Information Science（计算机与信息科学学院）；University of Nova Gorica（新戈里察大学）
Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an autoencoder-based neural network architecture. The main advantages of the proposed Deep Node Ranking (DNR) algorithm are competitive or better classification performance, significantly higher learning speed and lower space requirements when compared to state-of-the-art approaches on 15 real-life node classification benchmarks. Furthermore, it enables exploration o…
