Interpretable Multi-View Clustering Using Anchor Graph Tensor Factorization

Core Concepts

The core message of this paper is to propose an interpretable multi-view clustering model based on anchor graph tensor factorization (AGTF). The approach extends non-negative matrix factorization (NMF) to operate on third-order tensors, preserving more intrinsic spatial structure information across different views. It also utilizes the tensor Schatten p-norm to impose a low-rank constraint on the indicator tensor, effectively capturing the complementary information between views.

Abstract

The paper presents an interpretable multi-view clustering model based on anchor graph tensor factorization (AGTF). The key highlights are: The authors extend non-negative matrix factorization (NMF) to operate on third-order tensors, enabling direct processing of multi-view data and preserving more intrinsic spatial structure information across different views. They introduce the tensor Schatten p-norm to exploit complementary information across different views, facilitating the derivation of a common consensus indicator matrix. An optimization algorithm for non-negative tensor factorization (NTF) is proposed, and its convergence to the KKT stationary point is demonstrated both mathematically and experimentally. Extensive experiments on various datasets validate the superior clustering performance of the AGTF model compared to state-of-the-art multi-view clustering methods.

Stats

The anchor rate around 0.4 yields satisfactory clustering results across the MSRC, HandWritten4, and Mnist4 datasets. The tensor Schatten p-norm of the cluster label on the samples (∥H∥p Sp ⃝) is more important than that on the anchors (∥G∥p Sp ⃝) for improving clustering performance.

Quotes

"The core message of this paper is to propose an interpretable multi-view clustering model based on anchor graph tensor factorization (AGTF)." "The authors extend non-negative matrix factorization (NMF) to operate on third-order tensors, enabling direct processing of multi-view data and preserving more intrinsic spatial structure information across different views." "They introduce the tensor Schatten p-norm to exploit complementary information across different views, facilitating the derivation of a common consensus indicator matrix."

Key Insights Distilled From

Interpretable Multi-View Clustering Based on Anchor Graph Tensor Factorization

by Jing Li,Quan... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2404.00883.pdf

Deeper Inquiries

How can the proposed AGTF model be extended to handle dynamic or streaming multi-view data

To extend the proposed AGTF model to handle dynamic or streaming multi-view data, we can introduce an incremental learning approach. This involves updating the tensor factorization model as new data streams in, allowing the model to adapt to changes in the data distribution over time. One way to achieve this is by incorporating online learning techniques, where the model is updated iteratively as new data points arrive. Additionally, we can implement a sliding window mechanism to limit the memory usage and computational complexity of the model while still capturing the temporal dynamics of the data. By continuously updating the anchor graph tensors and retraining the model with incoming data, the AGTF framework can effectively handle dynamic or streaming multi-view data.

What are the potential limitations of the tensor Schatten p-norm regularization, and how can they be addressed

The tensor Schatten p-norm regularization, while effective in promoting low-rank structures and capturing complementary information across different views, may have some limitations. One potential limitation is the sensitivity to the choice of the parameter p. Selecting an inappropriate value for p can lead to suboptimal results or even convergence issues. To address this limitation, one approach is to perform hyperparameter tuning to find the optimal value of p through cross-validation or grid search. Additionally, incorporating adaptive or data-driven methods to dynamically adjust the value of p based on the characteristics of the data can help mitigate the sensitivity to this parameter and improve the robustness of the regularization technique.

Can the AGTF framework be adapted to other multi-view learning tasks, such as multi-view classification or regression

The AGTF framework can be adapted to other multi-view learning tasks, such as multi-view classification or regression, by modifying the objective function and constraints to suit the specific task requirements. For multi-view classification, the cluster indicator matrices obtained from the tensor factorization can be used as features for a classifier, such as a support vector machine or a neural network, to perform classification on the multi-view data. In the case of multi-view regression, the tensor factorization can be tailored to predict continuous target variables by incorporating regression loss functions and output constraints. By customizing the AGTF framework to the task at hand and integrating appropriate learning algorithms, the model can be extended to address a variety of multi-view learning tasks beyond clustering.