相关论文: Equivalence between LINE and Matrix Factorization

Low-dimensional embedding techniques such as tSNE and UMAP allow visualizing high-dimensional data and therewith facilitate the discovery of interesting structure. Although they are widely used, they visualize data as is, rather than in…

The training dynamics of linear networks are well studied in two distinct setups: the lazy regime and balanced/active regime, depending on the initialization and width of the network. We provide a surprisingly simple unifying formula for…

Matrix factorization-based recommender system is in effect an angle preserving dimensionality reduction technique. Since the frequency of items follows power-law distribution, most vectors in the original dimension of user feature vectors…

We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L^2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein…

Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph…

Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…

Large Language Models (LLMs) have shown human-like reasoning abilities but still face challenges in solving complex logical problems. Existing unidirectional chaining methods, such as forward chaining and backward chaining, suffer from…

MIMO interference network optimization is important for increasingly crowded wireless communication networks. We provide a new algorithm, named Dual Link algorithm, for the classic problem of weighted sum-rate maximization for MIMO…

Inferring trust relations between social media users is critical for a number of applications wherein users seek credible information. The fact that available trust relations are scarce and skewed makes trust prediction a challenging task.…

Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…

Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…

Given a totally positive matrix, can one insert a line (row or column) between two given lines while maintaining total positivity? This question was first posed and solved by Johnson and Smith who gave an algorithm that results in one…

Neural networks typically exhibit permutation symmetries which contribute to the non-convexity of the networks' loss landscapes, since linearly interpolating between two permuted versions of a trained network tends to encounter a high loss…

In this letter, a novel linear transmission strategy to design the linear precoding matrix~(PM) at base station~(BS) and the beamforming matrix~(BM) at relay station~(RS) for multiple-input multiple-output~(MIMO) relaying broadcast channels…

The knowledge of end-to-end network distances is essential to many Internet applications. As active probing of all pairwise distances is infeasible in large-scale networks, a natural idea is to measure a few pairs and to predict the other…

Weight tying, i.e. sharing parameters between input and output embedding matrices, is common practice in language model design, yet its impact on the learned embedding space remains poorly understood. In this paper, we show that tied…

In this paper, we propose a method that has foundations in the line search sequential quadratic programming paradigm for solving general nonlinear equality constrained optimization problems. The method employs a carefully designed modified…

Visualizing network data is applicable in domains such as biology, engineering, and social sciences. We report the results of a study comparing the effectiveness of the two primary techniques for showing network data: node-link diagrams and…

Matrix factorization is a common machine learning technique for recommender systems. Despite its high prediction accuracy, the Bayesian Probabilistic Matrix Factorization algorithm (BPMF) has not been widely used on large scale data because…

Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the…