Graph-incorporated Latent Factor Analysis for High-dimensional and Sparse Matrices

A High-dimensional and sparse (HiDS) matrix is frequently encountered in a big data-related application like an e-commerce system or a social network services system. To perform highly accurate representation learning on it is of great significance owing to the great desire of extracting latent knowledge and patterns from it. Latent factor analysis (LFA), which represents an HiDS matrix by learning the low-rank embeddings based on its observed entries only, is one of the most effective and efficient approaches to this issue. However, most existing LFA-based models perform such embeddings on a HiDS matrix directly without exploiting its hidden graph structures, thereby resulting in accuracy loss. To address this issue, this paper proposes a graph-incorporated latent factor analysis (GLFA) model. It adopts two-fold ideas: 1) a graph is constructed for identifying the hidden high-order interaction (HOI) among nodes described by an HiDS matrix, and 2) a recurrent LFA structure is carefully designed with the incorporation of HOI, thereby improving the representa-tion learning ability of a resultant model. Experimental results on three real-world datasets demonstrate that GLFA outperforms six state-of-the-art models in predicting the missing data of an HiDS matrix, which evidently supports its strong representation learning ability to HiDS data

NGAT4Rec: Neighbor-Aware Graph Attention Network For Recommendation

Learning informative representations (aka. embeddings) of users and items is the core of modern recommender systems. Previous works exploit user-item relationships of one-hop neighbors in the user-item interaction graph to improve the quality of representation. Recently, the research of Graph Neural Network (GNN) for recommendation considers the implicit collaborative information of multi-hop neighbors to enrich the representation. However, most works of GNN for recommendation systems do not consider the relational information which implies the expression differences of different neighbors in the neighborhood explicitly. The influence of each neighboring item to the representation of the user's preference can be represented by the correlation between the item and neighboring items of the user. Symmetrically, for a given item, the correlation between one neighboring user and neighboring users can reflect the strength of signal about the item's characteristic. To modeling the implicit correlations of neighbors in graph embedding aggregating, we propose a Neighbor-Aware Graph Attention Network for recommendation task, termed NGAT4Rec. It employs a novel neighbor-aware graph attention layer that assigns different neighbor-aware attention coefficients to different neighbors of a given node by computing the attention among these neighbors pairwisely. Then NGAT4Rec aggregates the embeddings of neighbors according to the corresponding neighbor-aware attention coefficients to generate next layer embedding for every node. Furthermore, we combine more neighbor-aware graph attention layer to gather the influential signals from multi-hop neighbors. We remove feature transformation and nonlinear activation that proved to be useless on collaborative filtering. Extensive experiments on three benchmark datasets show that our model outperforms various state-of-the-art models consistently

Fast Partial Fourier Transform

Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications. Despite its pervasive use, all known FFT algorithms do not provide a fine-tuning option for the user to specify one's demand, that is, the output size (the number of Fourier coefficients to be computed) is algorithmically determined by the input size. This matters because not every application using FFT requires the whole spectrum of the frequency domain, resulting in an inefficiency due to extra computation. In this paper, we propose a fast Partial Fourier Transform (PFT), a careful modification of the Cooley-Tukey algorithm that enables one to specify an arbitrary consecutive range where the coefficients should be computed. We derive the asymptotic time complexity of PFT with respect to input and output sizes, as well as its numerical accuracy. Experimental results show that our algorithm outperforms the state-of-the-art FFT algorithms, with an order of magnitude of speedup for sufficiently small output sizes without sacrificing accuracy.Comment: 15 pages, 3 figure

Curriculum Pre-Training Heterogeneous Subgraph Transformer for Top-NN Recommendation

Due to the flexibility in modelling data heterogeneity, heterogeneous information network (HIN) has been adopted to characterize complex and heterogeneous auxiliary data in top-$N$ recommender systems, called \emph{HIN-based recommendation}. HIN characterizes complex, heterogeneous data relations, containing a variety of information that may not be related to the recommendation task. Therefore, it is challenging to effectively leverage useful information from HINs for improving the recommendation performance. To address the above issue, we propose a Curriculum pre-training based HEterogeneous Subgraph Transformer (called \emph{CHEST}) with new \emph{data characterization}, \emph{representation model} and \emph{learning algorithm}. Specifically, we consider extracting useful information from HIN to compose the interaction-specific heterogeneous subgraph, containing both sufficient and relevant context information for recommendation. Then we capture the rich semantics (\eg graph structure and path semantics) within the subgraph via a heterogeneous subgraph Transformer, where we encode the subgraph with multi-slot sequence representations. Besides, we design a curriculum pre-training strategy to provide an elementary-to-advanced learning process, by which we smoothly transfer basic semantics in HIN for modeling user-item interaction relation. Extensive experiments conducted on three real-world datasets demonstrate the superiority of our proposed method over a number of competitive baselines, especially when only limited training data is available.Comment: 26 page

GraphHINGE: Learning Interaction Models of Structured Neighborhood on Heterogeneous Information Network

Heterogeneous information network (HIN) has been widely used to characterize entities of various types and their complex relations. Recent attempts either rely on explicit path reachability to leverage path-based semantic relatedness or graph neighborhood to learn heterogeneous network representations before predictions. These weakly coupled manners overlook the rich interactions among neighbor nodes, which introduces an early summarization issue. In this paper, we propose GraphHINGE (Heterogeneous INteract and aggreGatE), which captures and aggregates the interactive patterns between each pair of nodes through their structured neighborhoods. Specifically, we first introduce Neighborhood-based Interaction (NI) module to model the interactive patterns under the same metapaths, and then extend it to Cross Neighborhood-based Interaction (CNI) module to deal with different metapaths. Next, in order to address the complexity issue on large-scale networks, we formulate the interaction modules via a convolutional framework and learn the parameters efficiently with fast Fourier transform. Furthermore, we design a novel neighborhood-based selection (NS) mechanism, a sampling strategy, to filter high-order neighborhood information based on their low-order performance. The extensive experiments on six different types of heterogeneous graphs demonstrate the performance gains by comparing with state-of-the-arts in both click-through rate prediction and top-N recommendation tasks.Comment: TOIS (Special Issue on Graph Technologies for User Modeling and Recommendation). arXiv admin note: text overlap with arXiv:2007.0021