LASE improves local network structure visualization by targeting locally low-dimensional regions.
problem Global spectral embedding fails to capture local geometric features in sparse, transitive networks.
method Local Adjacency Spectral Embedding (LASE) using weighted spectral decomposition.
result LASE reveals locally low-dimensional structure, improving local reconstruction and visualization.
New embeddings capture local structure in complex networks.
problem Embeddings cannot capture local structure in complex networks.
method Logistic Principal Component Analysis (LPCA) algorithm for exact low-rank representations.
result Exact low-rank representations of real-world networks are possible.
Two methods factor out prior knowledge from low-dimensional embeddings.
problem Visualizing data without considering background knowledge.
method JEDI for tSNE and CONFETTI for any embedding.
result Embeddings reveal meaningful structure hidden by prior knowledge.
The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional space into the original one, resulting in a more manageable optimization problem. S…
The paper analyzes side effects of learning from low-dimensional data embedded in a Euclidean space.
problem Learning from data distributed in a linear subspace of high-dimensional space.
method Derives estimates on the variation of the learning function and studies regularization effects.
result Potential regularization effects associated with network depth and noise in codimension of data manifold.
A new BO method tackles high-dimensional optimization without reconstruction.
problem Optimizing high-dimensional black-box functions is challenging, especially when low-dimensional structures are assumed.
method Tackles the problem in the original high-dimensional space using learned low-dimensional structure.
result Our method explores the high-dimensional space more effectively than existing approaches.
Kernel-spectral embedding learns low-dim. structures from noisy data.
problem Learning low-dimensional nonlinear structures from high-dimensional noisy data.
method Adaptive bandwidth spectral embedding using integral operators.
result Convergence to noiseless embeddings and eigenfunctions of integral operators.
The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique, widely used due to its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in the low-dimensional embedding. W…
Word embedding maps words into a low-dimensional continuous embedding space by exploiting the local word collocation patterns in a small context window. On the other hand, topic modeling maps documents onto a low-dimensional topic space, by utilizing the global word collocation patterns in the same document. These two …
Paper presents a new method for learning hyperbolic representations using tree structures.
problem Learning faithful low-dimensional hyperbolic embeddings of data.
method Metric-first approach to learn tree structure, then embed into hyperbolic manifold.
result Novel fast algorithm TreeRep learns tree approximating original metric.
Mercat preserves angles to create accurate low-dimensional embeddings.
problem Reconstructing global relationships in low-dimensional embeddings.
method Reconstructing angles between data points to preserve both local and global structures.
result Mercat yields good reconstruction across various experiments and metrics.
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
We describe a new method called t-ETE for finding a low-dimensional embedding of a set of objects in Euclidean space. We formulate the embedding problem as a joint ranking problem over a set of triplets, where each triplet captures the relative similarities between three objects in the set. By exploiting recent advance…
Generates low-dimensional node vectors for graphs with privacy while preserving structural preferences.
problem Publishing graph node vectors can leak sensitive individual information.
method SE-PrivGEmb, a skip-gram based technique with a unified noise tolerance mechanism and negative sampling probabilities.
result Our method outperforms existing methods in structural equivalence and link prediction tasks.
Optimizes optimal transport distances using low-dimensional embeddings.
problem High computational cost of optimal transport distances in high dimensions.
method Approximate OT distances using 1-Lipschitz maps in a lower-dimensional space.
result Efficiently approximates optimal transport distances with lower computational cost.
Kernel method embeds noisy datasets, capturing shared structures.
problem Limited power in capturing nonlinear structures, noisiness, high-dimensionality, and interpretability issues.
method Kernel spectral joint embeddings using duo-landmark integral operators.
result Consistent recovery of low-dimensional noiseless signals and convergence to eigenfunctions of integral operators.
We propose a general framework for policy representation for reinforcement learning tasks. This framework involves finding a low-dimensional embedding of the policy on a reproducing kernel Hilbert space (RKHS). The usage of RKHS based methods allows us to derive strong theoretical guarantees on the expected return of t…
Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and visualization. Most existing approaches represent graph nodes as point vectors i…
dtSNE preserves local densities in low-dimensional embeddings.
problem Local density differences are not accurately preserved in tSNE and UMAP.
method dtSNE, which approximately conserves local densities.
result dtSNE provides more accurate local density depictions.
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based …
This paper studies how to find compact state embeddings from high-dimensional Markov state trajectories, where the transition kernel has a small intrinsic rank. In the spirit of diffusion map, we propose an efficient method for learning a low-dimensional state embedding and capturing the process's dynamics. This idea a…
This work improves KG embeddings by integrating hyperbolic and attention mechanisms.
problem Preserving hierarchical and logical patterns in KGs with low-dimensional embeddings.
method Combines hyperbolic reflections/rotations with attention mechanisms to capture complex relational patterns.
result Improves MRR by up to 6.1% on standard benchmarks and new state-of-the-art results in high dimensions.
How can we effectively encode evolving information over dynamic graphs into low-dimensional representations? In this paper, we propose DyRep, an inductive deep representation learning framework that learns a set of functions to efficiently produce low-dimensional node embeddings that evolves over time. The learned embe…
In this paper, we aim to learn a low-dimensional Euclidean representation from a set of constraints of the form "item j is closer to item i than item k". Existing approaches for this "ordinal embedding" problem require expensive optimization procedures, which cannot scale to handle increasingly larger datasets. To addr…
Parametric UMAP learns a mapping from data to embeddings.
problem Representing and learning from structured data.
method Parametric optimization over neural network weights for UMAP.
result Parametric UMAP performs comparably to non-parametric UMAP with faster online embeddings.
The success of machine learning methods heavily relies on having an appropriate representation for data at hand. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural information about data. However, recently there has been a surge in approaches that learn …
We propose a novel method to embed a functional magnetic resonance imaging (fMRI) dataset in a low-dimensional space. The embedding optimally preserves the local functional coupling between fMRI time series and provides a low-dimensional coordinate system for detecting activated voxels. To compute the embedding, we bui…
SA-REMBO adapts to nonstationary high-dimensional optimization.
problem Bayesian Optimization in high-dimensional spaces is limited by the curse of dimensionality and rigidity of global assumptions.
method SA-REMBO uses multiple random Gaussian embeddings and an index variable to adaptively select the best embedding for the optimization problem.
result SA-REMBO outperforms traditional REMBO and other low-rank BO methods across synthetic and real-world benchmarks.
Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge prediction and handle more complex logical queries, which might involve multiple un…
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation…
In this paper we consider self-supervised representation learning to improve sample efficiency in reinforcement learning (RL). We propose a forward prediction objective for simultaneously learning embeddings of states and action sequences. These embeddings capture the structure of the environment's dynamics, enabling e…
Sensor data analysis plays a key role in health assessment of critical equipment. Such data are multivariate and exhibit nonlinear relationships. This paper describes how one can exploit nonlinear dimension reduction techniques, such as the t-distributed stochastic neighbor embedding (t-SNE) and kernel principal compon…
For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric according to angular changes along a geodesic line, thereby reflecting the underlying …
We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density function over a measurable space. Furthermore, we analyze the connection between th…
Network embedding, which learns low-dimensional vector representation for nodes in the network, has attracted considerable research attention recently. However, the existing methods are incapable of handling billion-scale networks, because they are computationally expensive and, at the same time, difficult to be accele…
Real world data often exhibit low-dimensional geometric structures, and can be viewed as samples near a low-dimensional manifold. This paper studies nonparametric regression of Hölder functions on low-dimensional manifolds using deep ReLU networks. Suppose n training data are sampled from a Hölder function in $\mathc…
This paper proposes a variant of the method of Guédon and Verhynin for estimating the cluster matrix in the Mixture of Gaussians framework via Semi-Definite Programming. A clustering oriented embedding is deduced from this estimate. The procedure is suitable for very high dimensional data because it is based on pairwis…
Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed, finite-dimensional feature representation. Here we consider a different setting. We as…
Classifies fake surfaces up to complexity 5.
problem Classifying fake surfaces for low-dimensional topology.
method Derived properties of fake surfaces, classified up to complexity 5.
result Proved conjectures about fake surfaces up to complexity 5.
This paper proposes an embedding-based neural network for more accurate investment return prediction.
problem Accurately predicting investment returns requires understanding industry knowledge and news, as well as leveraging relevant theories.
method The approach uses embedding to encode investment IDs into low-dimensional vectors, leveraging dual branches to separate different information, and employs the swish activation function.
result The proposed embedding-based dual branch model outperforms traditional machine learning models like Xgboost, Lightgbm, and Catboost on the Ubiquant Market Prediction dataset.
A graph embedding is a representation of graph vertices in a low-dimensional space, which approximately preserves properties such as distances between nodes. Vertex sequence-based embedding procedures use features extracted from linear sequences of nodes to create embeddings using a neural network. In this paper, we pr…
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…
Proposes MR-SNE for multimodal data visualization.
problem Visualizing data from multiple domains with relations across them.
method Extends t-SNE to compute augmented relations and jointly embed them in a low-dimensional space.
result Demonstrates promising performance in visualizing Flickr and Animal with Attributes 2 datasets.
Proposes a novel approach using vector cross product to preserve directional edges in directed graphs.
problem Preserving directional edges in directed graphs for tasks like link prediction and node recommendation.
method Integrates the non-commutative property of vector cross product into a Siamese neural network to learn N-dimensional embeddings.
result Low-dimensional embeddings effectively preserve directional properties and outperform state-of-the-art methods.
SILBO optimizes high-dimensional Bayesian optimization using semi-supervised embedding learning.
problem Bayesian optimization struggles with high-dimensional search spaces.
method SILBO uses semi-supervised dimension reduction to find a low-dimensional space for iterative optimization.
result SILBO outperforms existing methods on high-dimensional Bayesian optimization tasks.
Network embedding has become a hot research topic recently which can provide low-dimensional feature representations for many machine learning applications. Current work focuses on either (1) whether the embedding is designed as an unsupervised learning task by explicitly preserving the structural connectivity in the n…
We show how to learn low-dimensional representations (embeddings) of patient visits from the corresponding electronic health record (EHR) where International Classification of Diseases (ICD) diagnosis codes are removed. We expect that these embeddings will be useful for the construction of predictive statistical models…
Word2Vec (W2V) and GloVe are popular, fast and efficient word embedding algorithms. Their embeddings are widely used and perform well on a variety of natural language processing tasks. Moreover, W2V has recently been adopted in the field of graph embedding, where it underpins several leading algorithms. However, despit…