Related papers: Uncovering Locally Low-dimensional Structure in Ne…

We put forth a principled design of a neural architecture to learn nodal Adjacency Spectral Embeddings (ASE) from graph inputs. By bringing to bear the gradient descent (GD) method and leveraging the principle of algorithm unrolling, we…

We introduce Locally Linear Embedding (LLE) to the astronomical community as a new classification technique, using SDSS spectra as an example data set. LLE is a nonlinear dimensionality reduction technique which has been studied in the…

Dynamic relational data arise in many machine learning applications, yet their evolving structure poses challenges for learning representations that remain consistent and interpretable over time. A common approach is to learn time varying…

Motivated by collaborative localization in robotic sensor networks, we consider the problem of large-scale network localization where location estimates are derived from inter-node radio signals. Well-established methods for network…

Spectral clustering is a popular tool in network data analysis, with applications in a variety of scientific application areas. However, many studies have shown that classical spectral clustering does not perform well on certain network…

Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…

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…

In this paper we propose Structuring AutoEncoders (SAE). SAEs are neural networks which learn a low dimensional representation of data which are additionally enriched with a desired structure in this low dimensional space. While traditional…

Stability for dynamic network embeddings ensures that nodes behaving the same at different times receive the same embedding, allowing comparison of nodes in the network across time. We present attributed unfolded adjacency spectral…

We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a dataset in lower dimension and registers them to obtain a global embedding. The local views are…

Adding attributes for nodes to network embedding helps to improve the ability of the learned joint representation to depict features from topology and attributes simultaneously. Recent research on the joint embedding has exhibited a…

Medical images acquired from standardized protocols show consistent macroscopic or microscopic anatomical structures, and these structures consist of composable/decomposable organs and tissues, but existing self-supervised learning (SSL)…

Learning low-dimensional representations of networks has proved effective in a variety of tasks such as node classification, link prediction and network visualization. Existing methods can effectively encode different structural properties…

Manifold learning techniques, such as Locally linear embedding (LLE), are designed to preserve the local neighborhood structures of high-dimensional data during dimensionality reduction. Traditional LLE employs Euclidean distance to define…

Low-dimensional embeddings (LDEs) of high-dimensional data are ubiquitous in science and engineering. They allow us to quickly understand the main properties of the data, identify outliers and processing errors, and inform the next steps of…

Autoencoders (AE) are simple yet powerful class of neural networks that compress data by projecting input into low-dimensional latent space (LS). Whereas LS is formed according to the loss function minimization during training, its…

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…

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…

We introduce the Graph Sylvester Embedding (GSE), an unsupervised graph representation of local similarity, connectivity, and global structure. GSE uses the solution of the Sylvester equation to capture both network structure and…

Anomaly detection in multivariate time series is a critical task across a wide range of real-world applications, where abnormal behaviour is rare, labels are unavailable, and the cost of a miss is high. The central challenge is learning a…