We study the problem of large-scale network embedding, which aims to learn latent representations for network mining applications. Previous research shows that 1) popular network embedding benchmarks, such as DeepWalk, are in essence implicitly factorizing a matrix with a closed form, and 2)the explicit factorization o…
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48 results for “matrix embeddings”
FREDE efficiently embeds graphs using linear space and guarantees quality.
problem Efficiently embedding graphs with quality guarantees and linear space complexity.
method FREDE combines matrix sketching with a nonlinear transform of PageRank similarities to achieve linear space and quality guarantees.
result FREDE provides column-covariance approximation guarantees that are nearly as good as SVD, even with limited node similarities.
Predict missing movie ratings or graph embeddings with low rank matrices.
problem Predicting missing entries in a ratings matrix or graph embeddings with known linear relations.
method Low rank matrix completion approach applied to graph embeddings.
result Effective methods for predicting missing entries in matrices and graph embeddings.
We simplify word embeddings by removing sigmoid in SGNS, revealing connections to hyperbolic spaces.
problem Improving word embeddings quality and understanding their relationship with hyperbolic spaces.
method Analyzing squashed shifted PMI matrix and its relation to graph properties and hyperbolic geometry.
result Word embeddings can be connected to hyperbolic spaces through squashed shifted PMI matrix.
Paper proposes a matrix optimization model for reliable Euclidean embedding from noisy data.
problem Challenges in Euclidean embedding from noisy observations containing outliers.
method Matrix optimization based embedding model to detect and remove outliers.
result The model provides high accuracy estimators and successfully identifies outliers.
Sparse OSEs achieve optimal embedding dimension of O(d).
problem Achieving optimal embedding dimension for sparse OSEs.
method Random sparsified matrix with non-zeros per column.
result Sparse OSEs can achieve embedding dimension , improving on previous .
This paper proposes novel algorithms for speaker embedding using subjective inter-speaker similarity based on deep neural networks (DNNs). Although conventional DNN-based speaker embedding such as a -vector can be applied to multi-speaker modeling in speech synthesis, it does not correlate with the subjective inter-…
As opposed to manual feature engineering which is tedious and difficult to scale, network representation learning has attracted a surge of research interests as it automates the process of feature learning on graphs. The learned low-dimensional node vector representation is generalizable and eases the knowledge discove…
Production recommendation systems rely on embedding methods to represent various features. An impeding challenge in practice is that the large embedding matrix incurs substantial memory footprint in serving as the number of features grows over time. We propose a similarity-aware embedding matrix compression method call…
Enhancing Network Embedding with Auxiliary Information: An Explicit Matrix Factorization Perspectivecs.SI
Recent advances in the field of network embedding have shown the low-dimensional network representation is playing a critical role in network analysis. However, most of the existing principles of network embedding do not incorporate auxiliary information such as content and labels of nodes flexibly. In this paper, we t…
Most of real-world graphs are dynamic, i.e., they change over time by a sequence of update operations. While the regression problem has been studied for static graphs and temporal graphs, it is not investigated for general dynamic graphs. In this paper, we study regression over dynamic graphs. First, we present the not…
Unified framework for hyperbolic embeddings from mixed data types.
problem Computing hyperbolic embeddings from noisy metric and non-metric data.
method Semidefinite programming and spectral factorization methods.
result Efficient computation of hyperbolic embeddings from arbitrary data.
Two new methods improve graph embedding without needing a complete graph structure.
problem Graph autoencoders' performance depends on the adjacency matrix quality.
method BAGE and VBAGE: unsupervised graph embedding via adaptive graph learning.
result The methods expand GAEs' applicability to datasets without graph structure.
Improves scalability and robustness of dynamic graph clustering.
problem Scalability and robustness issues in matrix factorization methods for dynamic graphs.
method Temporal separated matrix factorization, bi-clustering regularization, selective embedding updating.
result Demonstrated scalability, robustness, and effectiveness on synthetic and real-world benchmarks.
Enhancing spectral embedding for low-dimensional embeddings in rare disease cohorts
problem Representing clinical concepts and patients in electronic health records
method Spectral-based unsupervised learning with flexible knowledge transfer
result Outperforms competing approaches in challenging scenarios
Optimal Subspace Embeddings: Resolving Nelson-Nguyen Conjecture Up to Sub-Polylogarithmic Factorscs.DS
We prove optimal subspace embedding conjecture up to sub-polylogarithmic factors.
problem Optimal dimension and sparsity of subspace embeddings.
method Iterative decoupling technique to analyze higher-order trace moment bounds.
result Sub-polylogarithmic factors in dimension and sparsity of subspace embeddings.
This work optimizes induced correlation in joint graph embeddings.
problem Optimizing correlation across embedded networks in joint graph embeddings.
method Developed corr2Omni algorithm to estimate optimal Omnibus weights.
result corr2Omni algorithm improves inference fidelity compared to classical Omnibus construction.
Expected centre of mass for random embeddings is constant.
problem Understanding the expected centre of mass for random embeddings.
method Analyzing the Haar measure and Gaussian unitary ensemble on SL(N, C).
result The expectation of the centre of mass is a constant multiple of the identity matrix.
This work analyzes PPR-based node embeddings and their topological information.
problem Understanding and interpreting PPR-based node embeddings.
method Unified framework and two methods for topology recovery.
result PPR-based embeddings maintain more topological information than random walk-based embeddings.
Linear representations help embed manifolds into matrix spaces.
problem Embedding manifolds into matrix spaces with effective bounds.
method Defining linear representations of -manifolds as maps into matrix spaces, encoding -actions as matrix products.
result Explicit bounds for Mostow-Palais -equivariant embeddings of -manifolds into -modules , showing for compact .
Enhanced EEG classification using augmented covariance matrix.
problem Improving motor imagery classification from EEG signals.
method Proposes a new framework based on the augmented covariance matrix derived from an autoregressive model.
result The augmented covariance matrix outperformed state-of-the-art methods.
Estimates low-rank distributional matrices from incomplete samples.
problem Matrix completion for distributional entries with limited observed data.
method Kernel mean embeddings, Tucker rank, functional unfolding operators.
result Effective estimator for distributional matrix completion established.
Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factoriza…
Method reduces categorical data to lower dimensions using density matrices.
problem Dimensionality reduction for categorical data.
method Density-matrix construction from class-conditional frequencies; spectral embedding.
result Low-dimensional spectral embeddings with controlled rank.
Two algorithms estimate Wasserstein distance matrices from few entries for manifold learning.
problem Estimating Wasserstein distance matrices from limited data for manifold learning.
method Proposes two algorithms: matrix completion and Nyström completion for square Wasserstein matrices.
result Nyström completion can outperform matrix completion with a fixed sample budget and improve classification stability.
Explainable, Stable, and Scalable Graph Convolutional Networks for Learning Graph Representationcs.LG
New GCNs solve graph embedding problems efficiently and interpretably.
problem Graph embedding for scalable and interpretable machine learning.
method Proposed two GCNs: CAFE-GCN and sphere-GCN, based on constrained optimization.
result Both GCNs yield good approximations of dominant eigenvectors and perform dimensionality reduction.
We prove a central limit theorem for the components of the eigenvectors corresponding to the largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for stochastic blockmodel graphs, the rows of the spectral embedding of the normalized La…
Optimal subspace embedding with near-optimal sparsity for high-dimensional data.
problem Efficiently preserving norms of vectors in high-dimensional subspaces.
method Near-optimal sparsity oblivious subspace embedding with decoupling argument and cumulant method.
result Achieved near-optimal sparsity of non-zeros per column.
Point-of-Interest (POI) recommendation is one of the most important location-based services helping people discover interesting venues or services. However, the extreme user-POI matrix sparsity and the varying spatio-temporal context pose challenges for POI systems, which affects the quality of POI recommendations. To …
Survey of Laplacian-based methods for data dimensionality reduction and embedding.
problem Efficiently reducing high-dimensional data to lower dimensions while preserving important features and structures.
method Laplacian-based methods including spectral clustering, Laplacian eigenmap, locality preserving projection, graph embedding, and diffusion map.
result Comprehensive overview of various optimization variants and applications of Laplacian-based techniques.
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for Weingarten's formula, the Ricci curvature and the Codazzi-Mainardi equations. For ma…
Manifold learning and dimensionality reduction techniques are ubiquitous in science and engineering, but can be computationally expensive procedures when applied to large data sets or when similarities are expensive to compute. To date, little work has been done to investigate the tradeoff between computational resourc…
The paper shows how to recover true node positions from a graph or similarity matrix.
problem Recovering true distances and positions from a graph or similarity matrix.
method Two steps: matrix factorisation followed by nonlinear dimension reduction.
result Nonlinear dimension reduction can recover latent positions close to a manifold where geodesic distance is encoded.
This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We r…
The paper analyzes DeepWalk and node2vec for community detection in stochastic blockmodels.
problem Theoretical understanding of community detection in stochastic blockmodels.
method Matrix factorization perspective on DeepWalk and node2vec.
result Node2vec and DeepWalk can perfectly recover community memberships in sparse graphs.
New method transfers word embeddings from large to small datasets efficiently.
problem Challenges in learning word embeddings from new domains with limited data.
method Group-sparse matrix factorization for transfer learning.
result Efficiently learns domain-specific word embeddings with less data.
A framework for stable dynamic network embeddings using static methods.
problem Dynamic network embedding in a nascent field.
method Using static network embedding methods on dilated unfolded adjacency matrices.
result Stable embeddings that preserve latent node behavior across time.
Speaker diarization with session-level speaker embedding refinement using graph neural networkseess.AS
Graph neural networks refine speaker embeddings for better session-level diarization.
problem Local speaker distinction in meeting sessions using deep embeddings.
method Graph Neural Networks (GNNs) refine speaker embeddings using session-level structural information.
result Spectral clustering on refined embeddings outperforms original embeddings significantly.
Low-Rank Plus Sparse Matrix Transfer Learning under Growing Representations and Ambient Dimensionscs.LG
The paper tackles transfer learning for growing matrix representations, improving estimation accuracy.
problem Structured matrix estimation under growing ambient dimensions and latent representations.
method Proposes a general transfer framework decomposing target parameters into embedded source components, low-rank innovations, and sparse edits. Develops an anchored alternating projection estimator.
result Establishes deterministic error bounds that separate target noise, representation growth, and source estimation error, yielding improved rates.
New method uses MHN for associative learning in network embedding.
problem Represent nodes in networks as low-dimensional vectors while incorporating topological and structural information.
method Introduces Modern Hopfield Networks (MHN) for associative learning between node content and neighbors.
result Competitive performance on node classification and linkage prediction tasks.
Signed Network Embedding with Application to Simultaneous Detection of Communities and Anomaliescs.SI
Unified model for signed networks separates balance and anomaly effects.
problem Ignoring sign information in signed networks leads to inaccurate analysis.
method Low rank plus sparse matrix decomposition with regularized formulation.
result The model accurately detects communities and anomalies in signed networks.
Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix factorization and random walk-based models. In this paper, we aim to bring toge…
A new method uses matrix sketches for efficient graph clustering in dynamic environments.
problem Efficiently clustering large, dynamic graphs in distributed memory systems.
method Inspired by spectral clustering, the approach uses random dimension-reducing projections to derive matrix sketches.
result The method produces embeddings that yield performant clustering results in a fully-dynamic stochastic block model stream.
We introduce Gaussian Process Topic Models (GPTMs), a new family of topic models which can leverage a kernel among documents while extracting correlated topics. GPTMs can be considered a systematic generalization of the Correlated Topic Models (CTMs) using ideas from Gaussian Process (GP) based embedding. Since GPTMs w…
The Joint Optimization of Fidelity and Commensurability (JOFC) manifold matching methodology embeds an omnibus dissimilarity matrix consisting of multiple dissimilarities on the same set of objects. One approach to this embedding optimizes the preservation of fidelity to each individual dissimilarity matrix together wi…
The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning computation-efficient kernel embeddings from specific data. In the framework, the h…
Bridging the Gap between Community and Node Representations: Graph Embedding via Community Detectioncs.SI
Graph embedding has become a key component of many data mining and analysis systems. Current graph embedding approaches either sample a large number of node pairs from a graph to learn node embeddings via stochastic optimization or factorize a high-order proximity/adjacency matrix of the graph via computationally expen…
In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to large-scale graphs. Our contribution consists of reformulating spect…