Related papers: Leveraging Non-linear Dimension Reduction and Rand…

Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating…

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…

Network embedding, which maps graphs to distributed representations, is a unified framework for various graph inference tasks. According to the topology properties (e.g., structural roles and community memberships of nodes) to be preserved,…

Hyperbolic space can naturally embed hierarchies that often exist in real-world data and semantics. While high-dimensional hyperbolic embeddings lead to better representations, most hyperbolic models utilize low-dimensional embeddings, due…

Graph is an important data representation which occurs naturally in the real world applications \cite{goyal2018graph}. Therefore, analyzing graphs provides users with better insights in different areas such as anomaly detection…

Envelope methods offer targeted dimension reduction for various models. The overarching goal is to improve efficiency in multivariate parameter estimation by projecting the data onto a lower-dimensional subspace known as the envelope.…

Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including…

Popular node embedding methods such as DeepWalk follow the paradigm of performing random walks on the graph, and then requiring each node to be proximate to those appearing along with it. Though proved to be successful in various tasks,…

Standard Adjacency Spectral Embedding (ASE) relies on a global low-rank assumption often incompatible with the sparse, transitive structure of real-world networks, causing local geometric features to be 'smeared'. To address this, we…

Dimensionality reduction methods are employed to decrease data dimensionality, either to enhance machine learning performance or to facilitate data visualization in two or three-dimensional spaces. These methods typically fall into two…

High fidelity representation of shapes with arbitrary topology is an important problem for a variety of vision and graphics applications. Owing to their limited resolution, classical discrete shape representations using point clouds, voxels…

Community structures are critical for understanding the mesoscopic organization of networks, bridging local and global patterns. While methods such as DeepWalk and node2vec capture local positional information through random walks, they…

Many real-world problems are naturally modeled as heterogeneous graphs, where nodes and edges represent multiple types of entities and relations. Existing learning models for heterogeneous graph representation usually depend on the…

Node embeddings are a paradigm in non-parametric graph representation learning, where graph nodes are embedded into a given vector space to enable downstream processing. State-of-the-art node-embedding algorithms, such as DeepWalk and…

Embedding models can generate high-dimensional vectors whose similarity reflects semantic affinities. Thus, accurately and timely retrieving those vectors in a large collection that are similar to a given query has become a critical…

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…

We propose a novel approach to dimensionality reduction combining techniques of metric geometry and distributed persistent homology, in the form of a gradient-descent based method called DIPOLE. DIPOLE is a dimensionality-reduction…

As a pivotal branch of machine learning, manifold learning uncovers the intrinsic low-dimensional structure within complex nonlinear manifolds in high-dimensional space for visualization, classification, clustering, and gaining key…

In the Bag-of-Words (BoW) model based image retrieval task, the precision of visual matching plays a critical role in improving retrieval performance. Conventionally, local cues of a keypoint are employed. However, such strategy does not…

Community detection is a key aspect of network analysis, as it allows for the identification of groups and patterns within a network. With the ever-increasing size of networks, it is crucial to have fast algorithms to analyze them…