Recently graph based dimensionality reduction has received a lot of interests in many fields of information processing. Central to it is a graph structure which models the geometrical and discriminant structure of the data manifold. When label information is available, it is usually incorporated into the graph structure by modifying the weights between data points. In this paper, we propose a n...

Structural pattern recognition approaches offer the most expressive, convenient, powerful but computational expensive representations of underlying relational information. To benefit from mature, less expensive and efficient state-of-the-art machine learning models of statistical pattern recognition they must be mapped to a low-dimensional vector space. Our method of explicit graph embedding br...

Recently, more and more approaches are emerging to solve the cross-view matching problem where reference samples and query samples are from different views. In this paper, inspired by Graph Embedding, we propose a unified framework for these cross-view methods called Cross-view Graph Embedding. The proposed framework can not only reformulate most traditional cross-view methods (e.g., CCA, PLS a...

Commute time embedding involves computing eigenfunctions of the graph Laplacian matrix. Spectral decomposition requires computational burden proportional to 3 ( ) O n , which may not be suitable for large scale dataset. This paper proposes computationally efficient commute time embedding by applying Nyström method to the normalized graph Laplacian. The performance of the proposed algorithms is ...

In contrast with knots, whose properties depend only on their extrinsic topology in S3, there is a rich interplay between the intrinsic structure of a graph and the extrinsic topology of all embeddings of the graph in S3. For example, it was shown in [2] that every embedding of the complete graph K7 in S 3 contains a non-trivial knot. Later in [3] it was shown that for every m ∈ N, there is a c...

In [6], we introduced the notion of minor-embedding in adiabatic quantum optimization. A minor-embedding of a graph G in a quantum hardware graph U is a subgraph of U such that G can be obtained from it by contracting edges. In this paper, we describe the intertwined adiabatic quantum architecture design problem, which is to construct a hardware graph U that satisfies all known physical constra...

Laplacian embedding provides a lowdimensional representation for the nodes of a graph where the edge weights denote pairwise similarity among the node objects. It is commonly assumed that the Laplacian embedding results preserve the local topology of the original data on the low-dimensional projected subspaces, i.e., for any pair of graph nodes with large similarity, they should be embedded clo...

In network analysis, a community is typically considered of as a group of nodes with a great density of edges among themselves and a low density of edges relative to other network parts. Detecting a community structure is important in any network analysis task, especially for revealing patterns between specified nodes. There is a variety of approaches presented in the literature for overlapping...

In this paper, we study the problem of nonnegative graph embedding, originally investigated in [14] for reaping the benefits from both nonnegative data factorization and the specific purpose characterized by the intrinsic and penalty graphs [13]. Our contributions are two-fold. On the one hand, we present a multiplicative iterative procedure for nonnegative graph embedding, which significantly ...

Learning distributed representations for nodes in graphs has become an important problem that underpins a wide spectrum of applications. Existing methods to this problem learn representations by optimizing a softmax objective while constraining the dimension of embedding vectors. We argue that the generalization performance of these methods are probably not due to the dimensionality constraint ...