Maximum Joint Probability With Multiple Representations for Clustering

K-Means Clustering With Natural Density Peaks for Discovering Arbitrary-Shaped Clusters

Due to simplicity, K-means has become a widely used clustering method. However, its clustering result is seriously affected by the initial centers and the allocation strategy makes it hard to identify manifold clusters. Many improved K-means are proposed to accelerate it and improve the quality of initialize cluster centers, but few researchers pay attention to the shortcoming of K-means in discovering arbitrary-shaped clusters. Using graph distance (GD) to measure the dissimilarity between objects is a good way to solve this problem, but computing the GD is time-consuming. Inspired by the idea that granular ball uses a ball to represent the local data, we select representatives from a local neighborhood, called natural density peaks (NDPs). On the basis of NDPs, we propose a novel K-means algorithm for identifying arbitrary-shaped clusters, called NDP-Kmeans. It defines neighbor-based distance between NDPs and takes advantage of the neighbor-based distance to compute the GD between NDPs. Afterward, an improved K-means with high-quality initial centers and GD is used to cluster NDPs. Finally, each remaining object is assigned according to its representative. The experimental results show that our algorithms can not only recognize spherical clusters but also manifold clusters. Therefore, NDP-Kmeans has more advantages in detecting arbitrary-shaped clusters than other excellent algorithms.

Multiview Clustering With Propagating Information Bottleneck

In many practical applications, massive data are observed from multiple sources, each of which contains multiple cohesive views, called hierarchical multiview (HMV) data, such as image-text objects with different types of visual and textual features. Naturally, the inclusion of source and view relationships offers a comprehensive view of the input HMV data and achieves an informative and correct clustering result. However, most existing multiview clustering (MVC) methods can only process single-source data with multiple views or multisource data with single type of feature, failing to consider all the views across multiple sources. Observing the rich closely related multivariate (i.e., source and view) information and the potential dynamic information flow interacting among them, in this article, a general hierarchical information propagation model is first built to address the above challenging problem. It describes the process from optimal feature subspace learning (OFSL) of each source to final clustering structure learning (CSL). Then, a novel self-guided method named propagating information bottleneck (PIB) is proposed to realize the model. It works in a circulating propagation fashion, so that the resulting clustering structure obtained from the last iteration can "self-guide" the OFSL of each source, and the learned subspaces are in turn used to conduct the subsequent CSL. We theoretically analyze the relationship between the cluster structures learned in the CSL phase and the preservation of relevant information propagated from the OFSL phase. Finally, a two-step alternating optimization method is carefully designed for optimization. Experimental results on various datasets show the superiority of the proposed PIB method over several state-of-the-art methods.

Positive-Incentive Noise

Noise is conventionally viewed as a severe problem in diverse fields, e.g., engineering and learning systems. However, this brief aims to investigate whether the conventional proposition always holds. It begins with the definition of task entropy, which extends from the information entropy and measures the complexity of the task. After introducing the task entropy, the noise can be classified into two kinds, positive-incentive noise (Pi-noise or π -noise) and pure noise, according to whether the noise can reduce the complexity of the task. Interestingly, as shown theoretically and empirically, even the simple random noise can be the π -noise that simplifies the task. π -noise offers new explanations for some models and provides a new principle for some fields, such as multitask learning, adversarial training, and so on. Moreover, it reminds us to rethink the investigation of noises.

Design of health information management model for elderly care using an advanced higher-order hybrid clustering algorithm from the perspective of sports and medicine integration

In the context of integrating sports and medicine domains, the urgent resolution of elderly health supervision requires effective data clustering algorithms. This paper introduces a novel higher-order hybrid clustering algorithm that combines density values and the particle swarm optimization (PSO) algorithm. Initially, the traditional PSO algorithm is enhanced by integrating the Global Evolution Dynamic Model (GEDM) into the Distribution Estimation Algorithm (EDA), constructing a weighted covariance matrix-based GEDM. This adapted PSO algorithm dynamically selects between the Global Evolution Dynamic Model and the standard PSO algorithm to update population information, significantly enhancing convergence speed while mitigating the risk of local optima entrapment. Subsequently, the higher-order hybrid clustering algorithm is formulated based on the density value and the refined PSO algorithm. The PSO clustering algorithm is adopted in the initial clustering phase, culminating in class clusters after a finite number of iterations. These clusters then undergo the application of the density peak search algorithm to identify candidate centroids. The final centroids are determined through a fusion of the initial class clusters and the identified candidate centroids. Results showcase remarkable improvements: achieving 99.13%, 82.22%, and 99.22% for F-measure, recall, and precision on dataset S1, and 75.22%, 64.0%, and 64.4% on dataset CMC. Notably, the proposed algorithm yields a 75.22%, 64.4%, and 64.6% rate on dataset S, significantly surpassing the comparative schemes' performance. Moreover, employing the text vector representation of the LDA topic vector model underscores the efficacy of the higher-order hybrid clustering algorithm in efficiently clustering text information. This innovative approach facilitates swift and accurate clustering of elderly health data from the perspective of sports and medicine integration. It enables the identification of patterns and regularities within the data, facilitating the formulation of personalized health management strategies and addressing latent health concerns among the elderly population.

View-Wise Versus Cluster-Wise Weight: Which Is Better for Multi-View Clustering?

Weighted multi-view clustering (MVC) aims to combine the complementary information of multi-view data (such as image data with different types of features) in a weighted manner to obtain a consistent clustering result. However, when the cluster-wise weights across views are vastly different, most existing weighted MVC methods may fail to fully utilize the complementary information, because they are based on view-wise weight learning and can not learn the fine-grained cluster-wise weights. Additionally, extra parameters are needed for most of them to control the weight distribution sparsity or smoothness, which are hard to tune without prior knowledge. To address these issues, in this paper we propose a novel and effective Cluster-weighted mUlti-view infoRmation bottlEneck (CURE) clustering algorithm, which can automatically learn the cluster-wise weights to discover the discriminative clusters across multiple views and thus can enhance the clustering performance by properly exploiting the cluster-level complementary information. To learn the cluster-wise weights, we design a new weight learning scheme by exploring the relation between the mutual information of the joint distribution of a specific cluster (containing a group of data samples) and the weight of this cluster. Finally, a novel draw-and-merge method is presented to solve the optimization problem. Experimental results on various multi-view datasets show the superiority and effectiveness of our cluster-wise weighted CURE over several state-of-the-art methods.

Implicit consensus clustering from multiple graphs

Dealing with relational learning generally relies on tools modeling relational data. An undirected graph can represent these data with vertices depicting entities and edges describing the relationships between the entities. These relationships can be well represented by multiple undirected graphs over the same set of vertices with edges arising from different graphs catching heterogeneous relations. The vertices of those networks are often structured in unknown clusters with varying properties of connectivity. These multiple graphs can be structured as a three-way tensor, where each slice of tensor depicts a graph which is represented by a count data matrix. To extract relevant clusters, we propose an appropriate model-based co-clustering capable of dealing with multiple graphs. The proposed model can be seen as a suitable tensor extension of mixture models of graphs, while the obtained co-clustering can be treated as a consensus clustering of nodes from multiple graphs. Applications on real datasets and comparisons with multi-view clustering and tensor decomposition methods show the interest of our contribution.