TPA: Fast, Scalable, and Accurate Method for Approximate Random Walk with Restart on Billion Scale Graphs

Given a large graph, how can we determine similarity between nodes in a fast and accurate way? Random walk with restart (RWR) is a popular measure for this purpose and has been exploited in numerous data mining applications including ranking, anomaly detection, link prediction, and community detection. However, previous methods for computing exact RWR require prohibitive storage sizes and computational costs, and alternative methods which avoid such costs by computing approximate RWR have limited accuracy. In this paper, we propose TPA, a fast, scalable, and highly accurate method for computing approximate RWR on large graphs. TPA exploits two important properties in RWR: 1) nodes close to a seed node are likely to be revisited in following steps due to block-wise structure of many real-world graphs, and 2) RWR scores of nodes which reside far from the seed node are proportional to their PageRank scores. Based on these two properties, TPA divides approximate RWR problem into two subproblems called neighbor approximation and stranger approximation. In the neighbor approximation, TPA estimates RWR scores of nodes close to the seed based on scores of few early steps from the seed. In the stranger approximation, TPA estimates RWR scores for nodes far from the seed using their PageRank. The stranger and neighbor approximations are conducted in the preprocessing phase and the online phase, respectively. Through extensive experiments, we show that TPA requires up to 3.5x less time with up to 40x less memory space than other state-of-the-art methods for the preprocessing phase. In the online phase, TPA computes approximate RWR up to 30x faster than existing methods while maintaining high accuracy.Comment: 12pages, 10 figure

Application of Hellison's responsibility model in South Korea: a multiple case study of "at-risk" middle school students in Physical Education

Hellisons Teaching Personal and Social Responsibility (TPSR) model was developed in the United States but has been applied in many different countries. However, its application in East Asian cultural contexts has not been sufficiently examined. The current study describes and interprets the cultural translation of this value-based instructional model in the physical education program of a South Korean middle school. A multiple case study design was used to examine the relevance and impact of TPSR through the experiences and perceptions of six purposefully selected students who had been identified as at risk of school failure. Multiple data sources indicate that a 20-lesson TPSR unit was well-received by the students and contributed to numerous positive behavior changes. The core goals and life skills associated with TPSR appeared relevant and acceptable to case study participants, however, the concept of self-direction emerged as more challenging for them to understand and enact. This may relate to differences in cultural schemas and educational norms. Such issues, as well as implications for research and practice, are discussed. The current study expands the TPSR literature by being one of the first to examine and make a case for the implementation of TPSR in an East Asian countryEl modelo de Enseñanza de la Responsabilidad Personal y Social (TPSR) de Hellison fue desarrollado en los Estados Unidos de América pero se ha aplicado en muchos otros países. Sin embargo, su aplicación en contextos culturales de Asia oriental no ha sido suficientemente examinada. El presente estudio describe a interpreta la traducción cultural de dicho modelo de instrucción basado en valores dentro de un programa de EF en un centro de enseñanza media de Corea del Sur. Se escogió un diseño de estudio de casos multiple para examinar la relevancia y el impacto del TPSR a través de las experiencias y percepciones de seis alumnos, escogidos a propósito, que habían sido identificados como ¿en riesgo de fracaso académico¿. Múltiples fuentes de datos indican que el programa TPSR de 20 lecciones fue bien recibido por los alumnos y que contribuyó a numerosos cambios positivos de su comportamiento. Los participantes consideraron relevantes los objetivos centrales y las habilidades para la vida social asociadas al TPSR; sin embargo, el concepto de auto-direccion emergió como el más difícil de entender y llevar a cabo. Esto puede deberse a las diferencias relativas a los esquemas culturales y a las normas educativas. Se dicuten aquí estas cuestiones, así como sus implicaciones para la investigación y la práctica. Este estudio, al ser el primero que examina y propone la aplicación de TPSR en un país de Asia oriental, amplia la literatura sobre dicho modelo

Learning Disentangled Representations in Signed Directed Graphs without Social Assumptions

Signed graphs are complex systems that represent trust relationships or preferences in various domains. Learning node representations in such graphs is crucial for many mining tasks. Although real-world signed relationships can be influenced by multiple latent factors, most existing methods often oversimplify the modeling of signed relationships by relying on social theories and treating them as simplistic factors. This limits their expressiveness and their ability to capture the diverse factors that shape these relationships. In this paper, we propose DINES, a novel method for learning disentangled node representations in signed directed graphs without social assumptions. We adopt a disentangled framework that separates each embedding into distinct factors, allowing for capturing multiple latent factors. We also explore lightweight graph convolutions that focus solely on sign and direction, without depending on social theories. Additionally, we propose a decoder that effectively classifies an edge's sign by considering correlations between the factors. To further enhance disentanglement, we jointly train a self-supervised factor discriminator with our encoder and decoder. Throughout extensive experiments on real-world signed directed graphs, we show that DINES effectively learns disentangled node representations, and significantly outperforms its competitors in the sign prediction task.Comment: 26 pages, 11 figure

Time-aware Random Walk Diffusion to Improve Dynamic Graph Learning

How can we augment a dynamic graph for improving the performance of dynamic graph neural networks? Graph augmentation has been widely utilized to boost the learning performance of GNN-based models. However, most existing approaches only enhance spatial structure within an input static graph by transforming the graph, and do not consider dynamics caused by time such as temporal locality, i.e., recent edges are more influential than earlier ones, which remains challenging for dynamic graph augmentation. In this work, we propose TiaRa (Time-aware Random Walk Diffusion), a novel diffusion-based method for augmenting a dynamic graph represented as a discrete-time sequence of graph snapshots. For this purpose, we first design a time-aware random walk proximity so that a surfer can walk along the time dimension as well as edges, resulting in spatially and temporally localized scores. We then derive our diffusion matrices based on the time-aware random walk, and show they become enhanced adjacency matrices that both spatial and temporal localities are augmented. Throughout extensive experiments, we demonstrate that TiaRa effectively augments a given dynamic graph, and leads to significant improvements in dynamic GNN models for various graph datasets and tasks.Comment: 16 page

TensorCodec: Compact Lossy Compression of Tensors without Strong Data Assumptions

Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor compression algorithms are available, many of them rely on strong data assumptions regarding its order, sparsity, rank, and smoothness. In this work, we propose TENSORCODEC, a lossy compression algorithm for general tensors that do not necessarily adhere to strong input data assumptions. TENSORCODEC incorporates three key ideas. The first idea is Neural Tensor-Train Decomposition (NTTD) where we integrate a recurrent neural network into Tensor-Train Decomposition to enhance its expressive power and alleviate the limitations imposed by the low-rank assumption. Another idea is to fold the input tensor into a higher-order tensor to reduce the space required by NTTD. Finally, the mode indices of the input tensor are reordered to reveal patterns that can be exploited by NTTD for improved approximation. Our analysis and experiments on 8 real-world datasets demonstrate that TENSORCODEC is (a) Concise: it gives up to 7.38x more compact compression than the best competitor with similar reconstruction error, (b) Accurate: given the same budget for compressed size, it yields up to 3.33x more accurate reconstruction than the best competitor, (c) Scalable: its empirical compression time is linear in the number of tensor entries, and it reconstructs each entry in logarithmic time. Our code and datasets are available at https://github.com/kbrother/TensorCodec.Comment: Accepted to ICDM 2023 - IEEE International Conference on Data Mining 202

NeuKron: Constant-Size Lossy Compression of Sparse Reorderable Matrices and Tensors

Many real-world data are naturally represented as a sparse reorderable matrix, whose rows and columns can be arbitrarily ordered (e.g., the adjacency matrix of a bipartite graph). Storing a sparse matrix in conventional ways requires an amount of space linear in the number of non-zeros, and lossy compression of sparse matrices (e.g., Truncated SVD) typically requires an amount of space linear in the number of rows and columns. In this work, we propose NeuKron for compressing a sparse reorderable matrix into a constant-size space. NeuKron generalizes Kronecker products using a recurrent neural network with a constant number of parameters. NeuKron updates the parameters so that a given matrix is approximated by the product and reorders the rows and columns of the matrix to facilitate the approximation. The updates take time linear in the number of non-zeros in the input matrix, and the approximation of each entry can be retrieved in logarithmic time. We also extend NeuKron to compress sparse reorderable tensors (e.g. multi-layer graphs), which generalize matrices. Through experiments on ten real-world datasets, we show that NeuKron is (a) Compact: requiring up to five orders of magnitude less space than its best competitor with similar approximation errors, (b) Accurate: giving up to 10x smaller approximation error than its best competitors with similar size outputs, and (c) Scalable: successfully compressing a matrix with over 230 million non-zero entries.Comment: Accepted to WWW 2023 - The Web Conference 202