Non-negative matrix factorization (NMF) and its variants have been widely employed in clustering and classification tasks (Long, & Jian , 2021). However, noises can seriously affect the results of our experiments. Our research is dedicated to investigating the noise robustness of non-negative matrix factorization (NMF) in the face of different types of noise. Specifically, we adopt three different NMF algorithms, namely L1 NMF, L2 NMF, and L21 NMF, and use the ORL and YaleB data sets to simulate a series of experiments with salt-and-pepper noise and Block-occlusion noise separately. In the experiment, we use a variety of evaluation indicators, including root mean square error (RMSE), accuracy (ACC), and normalized mutual information (NMI), to evaluate the performance of different NMF algorithms in noisy environments. Through these indicators, we quantify the resistance of NMF algorithms to noise and gain insights into their feasibility in practical applications.

Recent multi-view subspace clustering achieves impressive results utilizing deep networks, where the self-expressive correlation is typically modeled by a fully connected (FC) layer. However, they still suffer from two limitations. i) The parameter scale of the FC layer is quadratic to sample numbers, resulting in high time and memory costs that significantly degrade their feasibility in large-scale datasets. ii) It is under-explored to extract a unified representation that simultaneously satisfies minimal sufficiency and discriminability. To this end, we propose a novel deep framework, termed Efficient and Effective deep Multi-View Subspace Clustering (E$^2$MVSC). Instead of a parameterized FC layer, we design a Relation-Metric Net that decouples network parameter scale from sample numbers for greater computational efficiency. Most importantly, the proposed method devises a multi-type auto-encoder to explicitly decouple consistent, complementary, and superfluous information from every view, which is supervised by a soft clustering assignment similarity constraint. Following information bottleneck theory and the maximal coding rate reduction principle, a sufficient yet minimal unified representation can be obtained, as well as pursuing intra-cluster aggregation and inter-cluster separability within it. Extensive experiments show that E$^2$MVSC yields comparable results to existing methods and achieves state-of-the-art performance in various types of multi-view datasets.

Existing state-of-the-art 3D point clouds understanding methods only perform well in a fully supervised manner. To the best of our knowledge, there exists no unified framework which simultaneously solves the downstream high-level understanding tasks, especially when labels are extremely limited. This work presents a general and simple framework to tackle point clouds understanding when labels are limited. We propose a novel unsupervised region expansion based clustering method for generating clusters. More importantly, we innovatively propose to learn to merge the over-divided clusters based on the local low-level geometric property similarities and the learned high-level feature similarities supervised by weak labels. Hence, the true weak labels guide pseudo labels merging taking both geometric and semantic feature correlations into consideration. Finally, the self-supervised reconstruction and data augmentation optimization modules are proposed to guide the propagation of labels among semantically similar points within a scene. Experimental Results demonstrate that our framework has the best performance among the three most important weakly supervised point clouds understanding tasks including semantic segmentation, instance segmentation, and object detection even when limited points are labeled, under the data-efficient settings for the large-scale 3D semantic scene parsing. The developed techniques have postentials to be applied to downstream tasks for better representations in robotic manipulation and robotic autonomous navigation. Codes and models are publicly available at: https://github.com/KangchengLiu.

The block diagonal structure of an affinity matrix is a commonly desired property in cluster analysis because it represents clusters of feature vectors by non-zero coefficients that are concentrated in blocks. However, recovering a block diagonal affinity matrix is challenging in real-world applications, in which the data may be subject to outliers and heavy-tailed noise that obscure the hidden cluster structure. To address this issue, we first analyze the effect of different fundamental outlier types in graph-based cluster analysis. A key idea that simplifies the analysis is to introduce a vector that represents a block diagonal matrix as a piece-wise linear function of the similarity coefficients that form the affinity matrix. We reformulate the problem as a robust piece-wise linear fitting problem and propose a Fast and Robust Sparsity-Aware Block Diagonal Representation (FRS-BDR) method, which jointly estimates cluster memberships and the number of blocks. Comprehensive experiments on a variety of real-world applications demonstrate the effectiveness of FRS-BDR in terms of clustering accuracy, robustness against corrupted features, computation time and cluster enumeration performance.

Unimodality, pivotal in statistical analysis, offers insights into dataset structures and drives sophisticated analytical procedures. While unimodality's confirmation is straightforward for one-dimensional data using methods like Silverman's approach and Hartigans' dip statistic, its generalization to higher dimensions remains challenging. By extrapolating one-dimensional unimodality principles to multi-dimensional spaces through linear random projections and leveraging point-to-point distancing, our method, rooted in $\alpha$-unimodality assumptions, presents a novel multivariate unimodality test named mud-pod. Both theoretical and empirical studies confirm the efficacy of our method in unimodality assessment of multidimensional datasets as well as in estimating the number of clusters.

When visualizing a high-dimensional dataset, dimension reduction techniques are commonly employed which provide a single 2 dimensional view of the data. We describe ENS-t-SNE: an algorithm for Embedding Neighborhoods Simultaneously that generalizes the t-Stochastic Neighborhood Embedding approach. By using different viewpoints in ENS-t-SNE's 3D embedding, one can visualize different types of clusters within the same high-dimensional dataset. This enables the viewer to see and keep track of the different types of clusters, which is harder to do when providing multiple 2D embeddings, where corresponding points cannot be easily identified. We illustrate the utility of ENS-t-SNE with real-world applications and provide an extensive quantitative evaluation with datasets of different types and sizes.

The software for clustering students according to their educational achievements using fuzzy logic was developed in Python using the Google Colab cloud service. In the process of analyzing educational data, the problems of Data Mining are solved, since only some characteristics of the educational process are obtained from a large sample of data. Data clustering was performed using the classic K-Means method, which is characterized by simplicity and high speed. Cluster analysis was performed in the space of two features using the machine learning library scikit-learn (Python). The obtained clusters are described by fuzzy triangular membership functions, which allowed to correctly determine the membership of each student to a certain cluster. Creation of fuzzy membership functions is done using the scikit-fuzzy library. The development of fuzzy functions of objects belonging to clusters is also useful for educational purposes, as it allows a better understanding of the principles of using fuzzy logic. As a result of processing test educational data using the developed software, correct results were obtained. It is shown that the use of fuzzy membership functions makes it possible to correctly determine the belonging of students to certain clusters, even if such clusters are not clearly separated. Due to this, it is possible to more accurately determine the recommended level of difficulty of tasks for each student, depending on his previous evaluations.

When users in a digital library read or browse online resources, it generates an immense amount of data. If the underlying system can recommend items, such as books and journals, to the users, it will help them to find the related items. In this research analyzes a digital library's usage data to recommend items to its users, and it uses different clustering algorithms to design the recommender system. We have used content-based clustering, including hierarchical, expectation maximization (EM), K-mean, FarthestFirst and density-based clustering algorithms, and user access pattern-based clustering, which uses a hypergraph-based approach to generate the clusters. This research shows that the recommender system designed using the hypergraph algorithm generates the most accurate recommendation model compared to those designed using the content-based clustering approaches.

Unsupervised relation extraction (URE) aims to extract relations between named entities from raw text without requiring manual annotations or pre-existing knowledge bases. In recent studies of URE, researchers put a notable emphasis on contrastive learning strategies for acquiring relation representations. However, these studies often overlook two important aspects: the inclusion of diverse positive pairs for contrastive learning and the exploration of appropriate loss functions. In this paper, we propose AugURE with both within-sentence pairs augmentation and augmentation through cross-sentence pairs extraction to increase the diversity of positive pairs and strengthen the discriminative power of contrastive learning. We also identify the limitation of noise-contrastive estimation (NCE) loss for relation representation learning and propose to apply margin loss for sentence pairs. Experiments on NYT-FB and TACRED datasets demonstrate that the proposed relation representation learning and a simple K-Means clustering achieves state-of-the-art performance.

Human mobility demonstrates a high degree of regularity, which facilitates the discovery of lifestyle profiles. Existing research has yet to fully utilize the regularities embedded in high-order features extracted from human mobility records in such profiling. This study proposes a progressive feature extraction strategy that mines high-order mobility features from users' moving trajectory records from the spatial, temporal, and semantic dimensions. Specific features are extracted such as travel motifs, rhythms decomposed by discrete Fourier transform (DFT) of mobility time series, and vectorized place semantics by word2vec, respectively to the three dimensions, and they are further clustered to reveal the users' lifestyle characteristics. An experiment using a trajectory dataset of over 500k users in Shenzhen, China yields seven user clusters with different lifestyle profiles that can be well interpreted by common sense. The results suggest the possibility of fine-grained user profiling through cross-order trajectory feature engineering and clustering.