arXiv research

There is much empirical evidence that item-item collaborative filtering works well in practice. Motivated to understand this, we provide a framework to design and analyze various recommendation algorithms. The setup amounts to online binary matrix completion, where at each time a random user requests a recommendation a…

A new algorithm estimates item parameters in item response theory models.

Recommender systems play a central role in providing individualized access to information and services. This paper focuses on collaborative filtering, an approach that exploits the shared structure among mind-liked users and similar items. In particular, we focus on a formal probabilistic framework known as Markov rand…

Joint analysis of data from multiple information repositories facilitates uncovering the underlying structure in heterogeneous datasets. Single and coupled matrix-tensor factorization (CMTF) has been widely used in this context for imputation-based recommendation from ratings, social network, and other user-item data. …

Let K be a knot in a closed orientable irreducible 3-manifold M and let P be a Heegaard splitting of the knot complement of genus at least two. Suppose Q is a bridge surface for K. Then either \begin{itemize} \item $d(P)\leq 2-χ(Q-K)$, or \item K can be isotoped to be disjoint from Q so that after the isotopy Q is a He…

We consider an online model for recommendation systems, with each user being recommended an item at each time-step and providing 'like' or 'dislike' feedback. Each user may be recommended a given item at most once. A latent variable model specifies the user preferences: both users and items are clustered into types. Al…

The paper models and predicts co-occurrence counts using Gamma regression.

Item-item collaborative filtering (CF) models are a well known and studied family of recommender systems, however current literature does not provide any theoretical explanation of the conditions under which item-based recommendations will succeed or fail. We investigate the existence of an ideal item-based CF method a…

Let $(M,g)$ be an open, oriented and incomplete riemannian manifold of dimension $m$. Under some general conditions we show that it is possible to build a Hilbert complex $(L^2Ω^i(M,g),d_{\mathfrak{M},i})$ such that its cohomology groups, labeled with $H^i_{2,\mathfrak{M}}(M,g)$, satisfy the following properties: \begi…

Let $f = (f_1,\ldots,f_m) : \R^n \longrightarrow \R^m$ be a polynomial map; $G^f(r) = \{x\in\R^n : |f_i(x)| \leq r,\ i =1,\ldots, m\}$. We show that if $f$ satisfies the Mikhailov - Gindikin condition then \begin{itemize} \item[(i)] $\text{Volume}\ G^f(r) \asymp r^θ(\ln r)^k$ \item[(ii)] $\text{Card}\left(G^f(r) \cap \…

Matrix factorization is a simple and effective solution to the recommendation problem. It has been extensively employed in the industry and has attracted much attention from the academia. However, it is unclear what the low-dimensional matrices represent. We show that matrix factorization can actually be seen as simult…

Optimal recommendation system using user and item clustering.

The paper is devoted to generalizations of Cencelj-Dranishnikov theorems relating extension properties of nilpotent CW complexes to its homology groups. Here are the main results of the paper: \par {\bf Theorem}. Suppose $L$ is a nilpotent CW complex and $F$ is the homotopy fiber of the inclusion $i$ of $L$ into its in…

We consider the problem of learning soft assignments of $N$ items to $K$ categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be assigned to categories they are dissimilar to), and an item-item similarity mat…

Improves search performance by transferring knowledge from recommender system.

Recommender systems are used in variety of domains affecting people's lives. This has raised concerns about possible biases and discrimination that such systems might exacerbate. There are two primary kinds of biases inherent in recommender systems: observation bias and bias stemming from imbalanced data. Observation b…

JoVA combines two VAEs to learn user and item representations for better recommendation.

We explore the task of local music recommendation: provide listeners with personalized playlists of relevant tracks by artists who play most of their live events within a small geographic area. Most local artists tend to be obscure, long-tail artists and generally have little or no available user preference data associ…

In recommender systems, the user-item interaction data is usually sparse and not sufficient for learning comprehensive user/item representations for recommendation. To address this problem, we propose a novel dual-bridging recommendation model (DBRec). DBRec performs latent user/item group discovery simultaneously with…

Fashion preference is a fuzzy concept that depends on customer taste, prevailing norms in fashion product/style, henceforth used interchangeably, and a customer's perception of utility or fashionability, yet fashion e-retail relies on algorithmically generated search and recommendation systems that process structured d…

CMF is a technique for simultaneously learning low-rank representations based on a collection of matrices with shared entities. A typical example is the joint modeling of user-item, item-property, and user-feature matrices in a recommender system. The key idea in CMF is that the embeddings are shared across the matrice…

A new framework evaluates large language models efficiently and accurately.

New estimators improve Rasch model item parameter estimation for sparse data.

New model improves recommendation systems by analyzing user-item interactions.

Model analyzes cooccurrence data for recommender systems and item relevance.

Preconditioned SGD accelerates convergence for ill-conditioned huge-scale matrix completion.

Study finds existence and non-uniqueness of cone spherical metrics on compact Riemann surfaces.

Three-layer networks learn complex hierarchical polynomials of multiple nonlinear features.

In this paper, we obtain several new intrinsic and extrinsic differential sphere theorems via Ricci flow. For intrinsic case, we show that a closed simply connected $n(\ge 4)$-dimensional Riemannian manifold $M$ is diffeomorphic to $S^n$ if one of the following conditions holds pointwisely: $$ (i)\ R_0>\left(1-\frac{24…

Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.

Proposes MGMN for end-to-end graph similarity learning.

The paper explores graphons of line graphs from sparse finite graphs.

MxPool learns graph features from diverse graphs using a hierarchical structure.

Study the geometry of graph product extension graphs.

Graph neural network learns graph distances effectively.

Quasi-transitive graphs quasi-isometric to planar graphs can be upgraded to Cayley graphs.

Customized-GNN generates model-specific for each graph.

Graph embedding leaks sensitive graph properties and subgraphs.

Characterizes graphs with leveled embeddings and introduces new graph invariants.

The paper shows conflict graphs of Petersen family graphs are mostly unbalanced.

Two new methods improve graph embedding without needing a complete graph structure.

We define a pseudo-inverse for line graphs using linear integer programming.

Develops method to create non-Abelian Ricci-flat graphs via bundles.

New method uses graph generative models for graph classification.

MathNet uses wavelets for graph representation and learning.

Unified framework for graph coarsening using node features and graph matrices.

A fast graph embedding method for large graphs.

Quadratic bounds found for graph dimensions.