Tensor clustering has become an important topic, specifically in
spatio-temporal modeling, due to its ability to cluster spatial modes (e.g.,
stations or road segments) and temporal modes (e.g., time of the day or day of
the week). Our motivating example is from subway passenger flow modeling, where
similarities between stations are commonly found. However, the challenges lie
in the innate high-dimensionality of tensors and also the potential existence
of anomalies. This is because the three tasks, i.e., dimension reduction,
clustering, and anomaly decomposition, are inter-correlated to each other, and
treating them in a separate manner will render a suboptimal performance. Thus,
in this work, we design a tensor-based subspace clustering and anomaly
decomposition technique for simultaneously outlier-robust dimension reduction
and clustering for high-dimensional tensors. To achieve this, a novel low-rank
robust subspace clustering decomposition model is proposed by combining Tucker
decomposition, sparse anomaly decomposition, and subspace clustering. An
effective algorithm based on Block Coordinate Descent is proposed to update the
parameters. Prudent experiments prove the effectiveness of the proposed
framework via the simulation study, with a gain of +25% clustering accuracy
than benchmark methods in a hard case. The interrelations of the three tasks
are also analyzed via ablation studies, validating the interrelation
assumption. Moreover, a case study in the station clustering based on real
passenger flow data is conducted, with quite valuable insights discovered.

本研究提出了一种基于张量的子空间聚类和异常分解技术，旨在同时实现高维张量的异常鲁棒降维和聚类。通过结合 Tucker 分解、稀疏异常分解和子空间聚类，提出了一个新的低秩鲁棒子空间聚类分解模型，并通过块坐标下降算法更新参数。实验证明，该方法在模拟研究中相比基准方法在难案例中提高了 + 25% 的聚类准确率，同时通过消融研究分析了三个任务之间的相互关系，并通过基于真实乘客流量数据的车站聚类案例研究发现了有价值的见解。

地铁客流建模的低秩稳健子空间张量聚类

Low-Rank Robust Subspace Tensor Clustering for Metro Passenger Flow  Modeling

Anchor-based large-scale multi-view clustering has attracted considerable
attention for its effectiveness in handling massive datasets. However, current
methods mainly seek the consensus embedding feature for clustering by exploring
global correlations between anchor graphs or projection matrices.In this paper,
we propose a simple yet efficient scalable multi-view tensor clustering
(S^2MVTC) approach, where our focus is on learning correlations of embedding
features within and across views. Specifically, we first construct the
embedding feature tensor by stacking the embedding features of different views
into a tensor and rotating it. Additionally, we build a novel tensor
low-frequency approximation (TLFA) operator, which incorporates graph
similarity into embedding feature learning, efficiently achieving smooth
representation of embedding features within different views. Furthermore,
consensus constraints are applied to embedding features to ensure inter-view
semantic consistency. Experimental results on six large-scale multi-view
datasets demonstrate that S^2MVTC significantly outperforms state-of-the-art
algorithms in terms of clustering performance and CPU execution time,
especially when handling massive data. The code of S^2MVTC is publicly
available at this https URL

提出了一种简单而高效的可扩展多视图张量聚类方法（S^2MVTC），专注于学习嵌入特征在视图内部和视图之间的相关性，利用嵌入特征的张量低频近似操作实现嵌入特征的平滑表示，采用共识约束确保视图间的语义一致性，实验证明该方法在聚类性能和 CPU 执行时间方面显著优于当前最先进的算法。

S^2MVTC：一种简单而高效的可扩展多视图张量聚类

S^2MVTC: a Simple yet Efficient Scalable Multi-View Tensor Clustering

Tensor clustering, which seeks to extract underlying cluster structures from
noisy tensor observations, has gained increasing attention. One extensively
studied model for tensor clustering is the tensor block model, which postulates
the existence of clustering structures along each mode and has found broad
applications in areas like multi-tissue gene expression analysis and multilayer
network analysis. However, currently available computationally feasible methods
for tensor clustering either are limited to handling i.i.d. sub-Gaussian noise
or suffer from suboptimal statistical performance, which restrains their
utility in applications that have to deal with heteroskedastic data and/or low
signal-to-noise-ratio (SNR).
To overcome these challenges, we propose a two-stage method, named
$\mathsf{High\text{-}order~HeteroClustering}$ ($\mathsf{HHC}$), which starts by
performing tensor subspace estimation via a novel spectral algorithm called
$\mathsf{Thresholded~Deflated\text{-}HeteroPCA}$, followed by approximate
$k$-means to obtain cluster nodes. Encouragingly, our algorithm provably
achieves exact clustering as long as the SNR exceeds the computational limit
(ignoring logarithmic factors); here, the SNR refers to the ratio of the
pairwise disparity between nodes to the noise level, and the computational
limit indicates the lowest SNR that enables exact clustering with polynomial
runtime. Comprehensive simulation and real-data experiments suggest that our
algorithm outperforms existing algorithms across various settings, delivering
more reliable clustering performance.

基于张量的聚类方法中存在一些挑战，为了克服这些挑战，我们提出了一种名为高阶异质聚类（HHC）的两阶段方法，通过创新的谱算法进行张量子空间估计，然后使用近似 k-means 算法获得聚类节点，模拟和实际数据实验证明我们的算法在各种情境下都优于现有算法，提供更可靠的聚类性能。