An Undirected Weighted Network (UWN) is frequently encountered in a
big-data-related application concerning the complex interactions among numerous
nodes, e.g., a protein interaction network from a bioinformatics application. A
Symmetric High-Dimensional and Incomplete (SHDI) matrix can smoothly illustrate
such an UWN, which contains rich knowledge like node interaction behaviors and
local complexes. To extract desired knowledge from an SHDI matrix, an analysis
model should carefully consider its symmetric-topology for describing an UWN's
intrinsic symmetry. Representation learning to an UWN borrows the success of a
pyramid of symmetry-aware models like a Symmetric Nonnegative Matrix
Factorization (SNMF) model whose objective function utilizes a sole Latent
Factor (LF) matrix for representing SHDI's symmetry rigorously. However, they
suffer from the following drawbacks: 1) their computational complexity is high;
and 2) their modeling strategy narrows their representation features, making
them suffer from low learning ability. Aiming at addressing above critical
issues, this paper proposes a Multi-constrained Symmetric Nonnegative
Latent-factor-analysis (MSNL) model with two-fold ideas: 1) introducing
multi-constraints composed of multiple LF matrices, i.e., inequality and
equality ones into a data-density-oriented objective function for precisely
representing the intrinsic symmetry of an SHDI matrix with broadened feature
space; and 2) implementing an Alternating Direction Method of Multipliers
(ADMM)-incorporated learning scheme for precisely solving such a
multi-constrained model. Empirical studies on three SHDI matrices from a real
bioinformatics or industrial application demonstrate that the proposed MSNL
model achieves stronger representation learning ability to an SHDI matrix than
state-of-the-art models do.

本文提出了一种多限制的对称非负潜因子分析模型，通过引入多种限制和实现交替方向乘子法的学习方案，有效解决了对称高维不完整矩阵在无向加权网络中的特征表达问题。实验证明该模型较现有模型具有更强的表征学习能力。

多约束对称非负隐变量分析大规模无向加权网络

Multi-constrained Symmetric Nonnegative Latent Factor Analysis for  Accurately Representing Large-scale Undirected Weighted Networks

An Undirected Weighted Network (UWN) is commonly found in big data-related
applications. Note that such a network's information connected with its nodes,
and edges can be expressed as a Symmetric, High-Dimensional and Incomplete
(SHDI) matrix. However, existing models fail in either modeling its intrinsic
symmetry or low-data density, resulting in low model scalability or
representation learning ability. For addressing this issue, a Proximal
Symmetric Nonnegative Latent-factor-analysis (PSNL) model is proposed. It
incorporates a proximal term into symmetry-aware and data density-oriented
objective function for high representation accuracy. Then an adaptive
Alternating Direction Method of Multipliers (ADMM)-based learning scheme is
implemented through a Tree-structured of Parzen Estimators (TPE) method for
high computational efficiency. Empirical studies on four UWNs demonstrate that
PSNL achieves higher accuracy gain than state-of-the-art models, as well as
highly competitive computational efficiency.

本文提出了一种名为 PSNL 的模型，它通过在面向数据密度和对称性的目标函数中加入接近项来提高表示准确性，并通过基于 ADMM 的自适应 TPE 方法实现高效的计算学习方案，从而实现了四个 UWN 上的模拟研究，证明了 PSNL 比最先进的模型实现更高的准确性提高，同时具有高度竞争的计算效率。