arXiv subjects

Menghan Wang

Publications and source records attributed to Menghan Wang.

27 records · Page 2Linked to original sources

arXiv2017

Collaborative Filtering with Social Exposure: A Modular Approach to Social Recommendation

This paper is concerned with how to make efficient use of social information to improve recommendations. Most existing social recommender systems assume people share similar preferences with their social friends. Which, however, may not hold true due to various motivations of making online friends and dynamics of online social networks. Inspired by recent causal process based recommendations that first model user exposures towards items and then use these exposures to guide rating prediction, we utilize social information to capture user exposures rather than user preferences. We assume that people get information of products from their online friends and they do not have to share similar preferences, which is less restrictive and seems closer to reality. Under this new assumption, in this paper, we present a novel recommendation approach (named SERec) to integrate social exposure into collaborative filtering. We propose two methods to implement SERec, namely social regularization and social boosting, each with different ways to construct social exposures. Experiments on four real-world datasets demonstrate that our methods outperform the state-of-the-art methods on top-N recommendations. Further study compares the robustness and scalability of the two proposed methods.

cs.IR↗

arXiv2016

Combinatorial rigidity of Incidence systems and Application to Dictionary learning

Given a hypergraph $H$ with $m$ hyperedges and a set $Q$ of $m$ \emph{pinning subspaces}, i.e.\ globally fixed subspaces in Euclidean space $\mathbb{R}^d$, a \emph{pinned subspace-incidence system} is the pair $(H, Q)$, with the constraint that each pinning subspace in $Q$ is contained in the subspace spanned by the point realizations in $\mathbb{R}^d$ of vertices of the corresponding hyperedge of $H$. This paper provides a combinatorial characterization of pinned subspace-incidence systems that are \emph{minimally rigid}, i.e.\ those systems that are guaranteed to generically yield a locally unique realization. Pinned subspace-incidence systems have applications in the \emph{Dictionary Learning (aka sparse coding)} problem, i.e.\ the problem of obtaining a sparse representation of a given set of data vectors by learning \emph{dictionary vectors} upon which the data vectors can be written as sparse linear combinations. Viewing the dictionary vectors from a geometry perspective as the spanning set of a subspace arrangement, the result gives a tight bound on the number of dictionary vectors for sufficiently randomly chosen data vectors, and gives a way of constructing a dictionary that meets the bound. For less stringent restrictions on data, but a natural modification of the dictionary learning problem, a further dictionary learning algorithm is provided. Although there are recent rigidity based approaches for low rank matrix completion, we are unaware of prior application of combinatorial rigidity techniques in the setting of Dictionary Learning. We also provide a systematic classification of problems related to dictionary learning together with various algorithms, their assumptions and performance.

cs.CG↗

arXiv2016

Symmetry in Sphere-based Assembly Configuration Spaces

Many remarkably robust, rapid and spontaneous self-assembly phenomena in nature can be modeled geometrically starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly processes. Since spheres within bunches could be identical and bunches could be identical as well, the underlying symmetry groups could be of large order that grows with the number of participating spheres and bunches. Thus, understanding symmetries and associated isomorphism classes of microstates correspond to various types of macrostates can significantly reduce the complexity of computing entropy and free energy, as well as paths and kinetics, in high dimensional configuration spaces. In addition, a precise understanding of symmetries is crucial for giving provable guarantees of algorithmic accuracy and efficiency in such computations. In particular, this may aid in predicting crucial assembly-driving interactions. This is a primarily expository paper that develops a novel, original framework for dealing with symmetries in configuration spaces of assembling spheres with the following goals. (1) We give new, formal definitions of various concepts relevant to sphere-based assembly that occur in previous work, and in turn, formal definitions of their relevant symmetry groups leading to the main theorem concerning their symmetries. These previously developed concepts include, for example, (a) assembly configuration spaces, (b) stratification of assembly configuration space into regions defined by active constraint graphs, (c) paths through the configurational regions, and (d) coarse assembly pathways. (2) We demonstrate the new symmetry concepts to compute sizes and numbers of orbits in two example settings appearing in previous work. (3) We give formal statements of a variety of open problems and challenges using the new conceptual definitions.

math.CO↗

arXiv2015

Optimal Decomposition and Recombination of Isostatic Geometric Constraint Systems for Designing Layered Materials

Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint systems, we describe an O(n^3) algorithm for a broad class of constraint systems that are isostatic or underconstrained. The algorithm achieves optimality by using the new notion of a canonical DR-plan that also meets various desirable, previously studied criteria. In addition, we leverage recent results on Cayley configuration spaces to show that the indecomposable systems---that are solved at the nodes of the optimal DR-plan by recombining solutions to child systems---can be minimally modified to become decomposable and have a small DR-plan, leading to efficient realization algorithms. We show formal connections to well-known problems such as completion of underconstrained systems. Well suited to these methods are classes of constraint systems that can be used to efficiently model, design and analyze quasi-uniform (aperiodic) and self-similar, layered material structures. We formally illustrate by modeling silica bilayers as body-hyperpin systems and cross-linking microfibrils as pinned line-incidence systems. A software implementation of our algorithms and videos demonstrating the software are publicly available online (visit http://cise.ufl.edu/~tbaker/drp/index.html.)

cs.CG↗

arXiv2015

An Incidence Geometry approach to Dictionary Learning

We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a sparse representation of data points, by learning \emph{dictionary vectors} upon which the data points can be written as sparse linear combinations. We view this problem from a geometry perspective as the spanning set of a subspace arrangement, and focus on understanding the case when the underlying hypergraph of the subspace arrangement is specified. For this Fitted Dictionary Learning problem, we completely characterize the combinatorics of the associated subspace arrangements (i.e.\ their underlying hypergraphs). Specifically, a combinatorial rigidity-type theorem is proven for a type of geometric incidence system. The theorem characterizes the hypergraphs of subspace arrangements that generically yield (a) at least one dictionary (b) a locally unique dictionary (i.e.\ at most a finite number of isolated dictionaries) of the specified size. We are unaware of prior application of combinatorial rigidity techniques in the setting of Dictionary Learning, or even in machine learning. We also provide a systematic classification of problems related to Dictionary Learning together with various algorithms, their assumptions and performance.

cs.LG↗

arXiv2015

Combinatorial rigidity and independence of generalized pinned subspace-incidence constraint systems

Given a hypergraph $H$ with $m$ hyperedges and a set $X$ of $m$ \emph{pins}, i.e.\ globally fixed subspaces in Euclidean space $\mathbb{R}^d$, a \emph{pinned subspace-incidence system} is the pair $(H, X)$, with the constraint that each pin in $X$ lies on the subspace spanned by the point realizations in $\mathbb{R}^d$ of vertices of the corresponding hyperedge of $H$. We are interested in combinatorial characterization of pinned subspace-incidence systems that are \emph{minimally rigid}, i.e.\ those systems that are guaranteed to generically yield a locally unique realization. As is customary, this is accompanied by a characterization of generic independence as well as rigidity. In a previous paper \cite{sitharam2014incidence}, we used pinned subspace-incidence systems towards solving the \emph{fitted dictionary learning} problem, i.e.\ dictionary learning with specified underlying hypergraph, and gave a combinatorial characterization of minimal rigidity for a more restricted version of pinned subspace-incidence system, with $H$ being a uniform hypergraph and pins in $X$ being 1-dimension subspaces. Moreover in a recent paper \cite{Baker2015}, the special case of pinned line incidence systems was used to model biomaterials such as cellulose and collagen fibrils in cell walls. In this paper, we extend the combinatorial characterization to general pinned subspace-incidence systems, with $H$ being a non-uniform hypergraph and pins in $X$ being subspaces with arbitrary dimension. As there are generally many data points per subspace in a dictionary learning problem, which can only be modeled with pins of dimension larger than $1$, such an extension enables application to a much larger class of fitted dictionary learning problems.

cs.CG↗

arXiv2014

Dynamic Decision Process Modeling and Relation-line Handling in Distributed Cooperative Modeling System

The Distributed Cooperative Modeling System (DCMS) solves complex decision problems involving a lot of participants with different viewpoints by network based distributed modeling and multi-template aggregation. This thesis aims at extending the system with support for dynamic decision making process. First, the thesis presents a discussion of characteristics and optimal policy finding Markov Decision Process as well as a brief introduction to dynamic Bayesian decision network, which is inherently equal to MDP. After that, discussion and implementation of prediction in Markov process for both discrete and continuous random variable are given, as well as several different kinds of correlation analysis among multiple indices which could help decision-makers to realize the interaction of indices and design appropriate policy. Appending history data of Macau industry, as the foundation of extending DCMS, is introduced. Additional works include rearrangement of graphical class hierarchy in DCMS, which in turn allows convenient implementation of curve relation-line, which makes template modeling clearer and friendlier.

cs.AI↗

arXiv2014

Cayley Analysis of Mechanism Configuration Spaces using CayMos: Software Functionalities and Architecture

For a common class of 2D mechanisms called 1-dof tree decomposable linkages, we present a software CayMos which uses new theoretical results to implement efficient algorithmic solutions for: (a) meaningfully representing and visualizing the connected components in the Euclidean realization space; (b) finding a path of continuous motion between two realizations in the same connected component, with or without restricting the realization type (sometimes called orientation type); (c) finding two ``closest'' realizations in different connected components.

cs.CG↗

arXiv2012

Cayley Configuration Spaces of 1-dof Tree-decomposable Linkages, Part II: Combinatorial Characterization of Complexity

We continue to study Cayley configuration spaces of 1-dof linkages in 2D begun in Part I of this paper, i.e. the set of attainable lengths for a non-edge. In Part II, we focus on the algebraic complexity of describing endpoints of the intervals in the set, i.e., the Cayley complexity. Specifically, We focus on Cayley configuration spaces of a natural class of 1-dof linkages, called 1-dof tree-decomposable linkages. The underlying graphs G satisfy the following: for some base non-edge f, G \cup f is quadratic-radically solvable (QRS), meaning that G \cup f is minimally rigid, and given lengths \bar{l} of all edges, the corresponding linkage (G \cup f, \bar{l}) can be simply realized by ruler and compass starting from f. It is clear that the Cayley complexity only depends on the graph G and possibly the non-edge f. Here we ask whether the Cayley complexity depends on the choice of a base non-edge f. We answer this question in the negative, thereby showing that low Cayley complexity is a property of the graph G (independent of the non-edge f). Then, we give a simple characterization of graphs with low Cayley complexity, leading to an efficient algorithmic characterization, i.e. an efficient algorithm for recognizing such graphs. Next, we show a surprising result that (graph) planarity is equivalent to low Cayley complexity for a natural subclass of 1-dof triangle-decomposable graphs. While this is a finite forbidden minor graph characterization of low Cayley complexity, we provide counterexamples showing impossibility of such finite forbidden minor characterizations when the above subclass is enlarged.

cs.CG↗