# Deep Multi-View Clustering Based on Reconstructed Self-Expressive Matrix
## 1 Introduction  
In recent years, with the widespread availability of advanced technologies and the accumulation of enormous amounts of data, multi-view data analysis has garnered great attention. Multi-view data refers to datasets where multiple sets of features or modalities are available for each sample, providing versatile information from different perspectives. Generally, each view of these datasets can be represented by distinct descriptors, such as color, edges, texture, etc. The application of multi-view data analysis is crucial in various fields, including recommender systems, medical diagnosis, image segmentation [1; 2; 3], image search result organization (ISRO) [4] and skew distribution datasets clustering [5]. However, when the dataset has high dimensionality and a large number of samples, several clustering methods can be limited when applying to these applications. The core idea behind multi-view subspace clustering is to capture consistent underlying representations of diverse views and group these data into distinct clusters. Recently, many multi-view clustering methods have been developed. Existing works about multi-view subspace clustering can be divided into different categories, i.e., non-negative matrix factorization (NMF) framework [6; 7; 8; 9], collaborative clustering methods [10; 11; 12], co-training methods [13; 14; 15], self-expressive based methods [16; 17] and deep-learning-based methods [18; 19]. NMF-based methods aim to obtain the partitioning of the data by a low-rank decomposition of the data matrix, and it is proved to be effective where the subspaces of data points are independent of each other. Co-training is a semi-supervised learningframework where two or more classifiers are trained on different subsets of features or views, and they collaboratively learn from each other by iteratively updating and refining their predictions. Since Deep Subspace Clustering Network (DSC-Net) [20] was proposed in 2017, several methods have been conducted with the combination of self-expressive methodology and deep learning. DSC-Net comprises a convolutional autoencoder architecture [21], where the encoder attempts to learn the compact and meaningful representations of the input images and the decoder learns to reconstruct the input images by these latent features. Meanwhile, by incorporating the self-expressive layer, DSC-Net goes beyond traditional clustering approaches that rely on predefined distance metrics or assumptions about the data distribution. Instead, it learns the intrinsic relationships directly from the data and acquires the affinity matrix to perform spectral clustering, enabling more accurate clustering results. While the multi-view model based on self-expression has demonstrated impressive performance and offers theoretical guarantees for correctness, it is hindered by two significant drawbacks: (1) The computational complexity associated with solving a self-expressive matrix of size \(N\times N\), makes it difficult when dealing with large-scale datasets. (2) They rarely consider the problem of fusing local and global representations, which is important for mining inherent relations between different views. To overcome these challenges, a new approach for deep multi-view subspace clustering based on reconstructing the self-expressive matrix (DCRSM) is proposed in this paper. We aim to reconstruct a set of self-expressive matrices from different latent features extracted by deep autoencoder. Principally, the number of network parameters does not need to match the number of samples in the dataset, which can help the network handle large-scale data readily and effectively. At the same time, we design a fusion network to learn global and local information from the extracted features and reconstruct the self-expressive matrices, which can integrate the common and specific information of different views simultaneously. Our research is of great practical importance.