We present an expectation-maximization (EM) based unified framework for
non-negative tensor decomposition that optimizes the Kullback-Leibler
divergence. To avoid iterations in each M-step and learning rate tuning, we
establish a general relationship between low-rank decomposition and many-body
approximation. Using this connection, we exploit that the closed-form solution
of the many-body approximation can be used to update all parameters
simultaneously in the M-step. Our framework not only offers a unified
methodology for a variety of low-rank structures, including CP, Tucker, and
Train decompositions, but also their combinations forming mixtures of tensors
as well as robust adaptive noise modeling. Empirically, we demonstrate that our
framework provides superior generalization for discrete density estimation
compared to conventional tensor-based approaches.

基于期望最大化 (EM) 的非负张量分解统一框架，通过优化 Kullback-Leibler 散度来避免在每次 M 步骤和学习率调整中的迭代，并建立了低秩分解和多体逼近之间的一般关系，进而利用了多体逼近的闭式解来同时更新所有参数。我们的框架不仅为各种低秩结构（包括 CP、Tucker 和 Train 分解）提供了统一的方法，还包括了张量的组合形成混合以及稳健的自适应噪声建模。实证方面，与传统的基于张量的方法相比，我们的框架在离散密度估计方面提供了更好的泛化。

离散密度估计的非负张量混合学习

Non-negative Tensor Mixture Learning for Discrete Density Estimation

Supervisory Control and Data Acquisition (SCADA) systems often serve as the
nervous system for substations within power grids. These systems facilitate
real-time monitoring, data acquisition, control of equipment, and ensure smooth
and efficient operation of the substation and its connected devices. Previous
work has shown that dimensionality reduction-based approaches, such as
Principal Component Analysis (PCA), can be used for accurate identification of
anomalies in SCADA systems. While not specifically applied to SCADA,
non-negative matrix factorization (NMF) has shown strong results at detecting
anomalies in wireless sensor networks. These unsupervised approaches model the
normal or expected behavior and detect the unseen types of attacks or anomalies
by identifying the events that deviate from the expected behavior. These
approaches; however, do not model the complex and multi-dimensional
interactions that are naturally present in SCADA systems. Differently,
non-negative tensor decomposition is a powerful unsupervised machine learning
(ML) method that can model the complex and multi-faceted activity details of
SCADA events. In this work, we novelly apply the tensor decomposition method
Canonical Polyadic Alternating Poisson Regression (CP-APR) with a probabilistic
framework, which has previously shown state-of-the-art anomaly detection
results on cyber network data, to identify anomalies in SCADA systems. We
showcase that the use of statistical behavior analysis of SCADA communication
with tensor decomposition improves the specificity and accuracy of identifying
anomalies in electrical grid systems. In our experiments, we model real-world
SCADA system data collected from the electrical grid operated by Los Alamos
National Laboratory (LANL) which provides transmission and distribution service
through a partnership with Los Alamos County, and detect synthetically
generated anomalies.

通过使用非负张量分解的统计行为分析方法，我们在聚变反应实验中展示了提高特异性和准确性的能力，从而能够识别出电网系统中的异常情况。