Self-Learning Symmetric Multi-view Probabilistic Clustering

TL;DR

This work tackles incomplete multi-view clustering by introducing SLS-MPC, a unified probabilistic framework that combines a symmetric multi-view posterior with a hyper-parameter-free self-learning probability function. It advances the field by (i) decomposing joint view-posterior probabilities into per-view components, (ii) enforcing cross-view and multi-view consistency to learn each view’s distribution without prior knowledge, (iii) refining probabilities with graph-context information via path and co-neighbor propagation, and (iv) clustering samples in an unsupervised, parameter-free manner using refined posterior probabilities. Extensive experiments across multiple benchmarks demonstrate state-of-the-art performance in both complete and incomplete MVC scenarios, with strong robustness to missing views and noise. The approach offers practical benefits for real-world, multi-source data where view availability is imperfect and prior tuning is undesirable.

Abstract

Multi-view Clustering (MVC) has achieved significant progress, with many efforts dedicated to learn knowledge from multiple views. However, most existing methods are either not applicable or require additional steps for incomplete MVC. Such a limitation results in poor-quality clustering performance and poor missing view adaptation. Besides, noise or outliers might significantly degrade the overall clustering performance, which are not handled well by most existing methods. In this paper, we propose a novel unified framework for incomplete and complete MVC named self-learning symmetric multi-view probabilistic clustering (SLS-MPC). SLS-MPC proposes a novel symmetric multi-view probability estimation and equivalently transforms multi-view pairwise posterior matching probability into composition of each view's individual distribution, which tolerates data missing and might extend to any number of views. Then, SLS-MPC proposes a novel self-learning probability function without any prior knowledge and hyper-parameters to learn each view's individual distribution. Next, graph-context-aware refinement with path propagation and co-neighbor propagation is used to refine pairwise probability, which alleviates the impact of noise and outliers. Finally, SLS-MPC proposes a probabilistic clustering algorithm to adjust clustering assignments by maximizing the joint probability iteratively without category information. Extensive experiments on multiple benchmarks show that SLS-MPC outperforms previous state-of-the-art methods.

Figures (9)

• Figure 1: Illustration of the self-learning probability function. Given a multi-view dataset of $N$ samples with $M$ views $S=\{V^{(1)},V^{(2)},...,V^{(M)}\}$, $KNN^{(m)} \in R^{N*K}$ can be generated on the similarity matrix $W^{(m)} \in R^{N*N}$ of the $m$-th view. $KNN^{(m)}$ construct the training data including total $T$ pairwise samples $(p_t,q_t)$ and the corresponding similarity values $(w^{(1)}_{p_t,q_t},w^{(2)}_{p_t,q_t},...,w^{(M)}_{p_t,q_t})$. We divide each view's data $\{w^{(m)}_{p_t,q_t}\}$ of total $T$ length into $I$ parts in the order of $\{w^{(m)}_{p_t,q_t}\}$ from small to large defined in Eq. (\ref{['equ:f_function']}). $a$, $b$ and $c$ are three specific parts in the total of $I$ parts from three specific views. The light gray dotted boxes represent the single-view forms from different views. The dark gray dotted box represent the cross-view forms from different views. And the black dotted box represent the multi-view forms from different views. The single-view, cross-view and multi-view probability functions are defined in Eq. (\ref{['equ:f_single']}), Eq. (\ref{['equ:f_cross']}) and Eq. (\ref{['equ:f_multi']}) and the consistency constraint is defined in Eq. (\ref{['equ:loss_1']}). Then a self-learning probability function is proposed to learn the $P(e_{ij}=1|w^{(m)}_{ij})$ from the aspect of consistency in single-view, cross-view and multi-view without any prior knowledge and hyper-parameters. Finally, a multi-view pairwise posterior matching probability matrix is generated from the composition of each view's individual distribution.
• Figure 2: Our basic observation and motivation of self-learning probability function. Given the condition that the original similarity between the sample pairs in the first view is $x_a$, there are $t$ sample pairs including fixed $p$ positive sample pairs. Fix these $t$ sample pairs and find the original similarity between the sample pairs in the second view ($\{y_k|k \in \{1,...,t\}\}$). Due to the fixed sample pairs, the probability that the sample pairs belong to the same class in the first view ($f(x_a)$) and the second view ($g(y_k)$) should be consistent. In the same way, the probability that the sample pairs belong to the same class in the first view ($f(x_a)$) and multi-view ($h(x_a,y_k)$) should be also consistent.
• Figure 3: Illustration of the proposed graph-context-aware refinement including path propagation and co-neighbor propagation. As shown in path propagation, taken probability consistency information into consideration, $h$ sets up the probability path between $i$ and $j$ and the probability between $i$ and $j$ can be enhanced by finding the path with the maximum probability. Besides, in co-neighbor propagation, $b$ and $c$ are the noise in k-nearest-neighbors of $a$. Based on the number of common neighbours and the proportion of the common probabilities, co-neighbor propagation refinement adjusts the probability between $a$ and $b$ and the probability between $a$ and $c$ to a small value and the small value indicates that they are not linked. The probability between $a$ and $d$ can be further adjusted and enhanced.
• Figure 4: Illustration of the proposed probabilistic clustering. Each sample is assigned to its own clustering set at the beginning and each sample is moved to the neighbour clustering set in random sequential order by maximizing joint probability iteratively. Finally, a good clustering result can be generated in a convergent way.
• Figure 5: The clustering performance comparisons on Handwritten and 100Leaves with different missing rates. Three comparisons in the first row are experiments on Handwritten. Three comparisons in the second row are experiments on 100Leaves.