Dynamic ensemble has significantly greater potential space to improve the classification of imbalanced data compared to static ensemble. However, dynamic ensemble schemes are far less successful than static ensemble methods in the imbalanced learning field. Through an in-depth analysis on the behavior characteristics of dynamic ensemble, we find that there are some important problems that need to be addressed to release the full potential of dynamic ensemble, including but not limited to, correcting the component classifiers’ bias towards the majority classes, increasing the proportions of the positive classifiers (i.e., the component classifiers making correct prediction) for difficult samples, and providing the accurate competence estimations on the hard-to-classify samples w.r.t the classifier pool. Inspired by these, we propose a Dynamic Ensemble Framework for imbalanced data classification (imDEF). imDEF first uses the data generation method OREM$\mathrm{_{G}}$to generate multiple artificial synthetic datasets, which have diverse class distributions by rebalancing the original imbalanced data. Based on each of such synthetic datasets, imDEF then utilizes a Classification Error-aware Self-Paced Sampling Ensemble (SPSE$\mathrm{_{CE}}$) method to gradually focus more on difficult samples, to create a low-biased classifier pool and increase the proportions of the positive classifiers for the difficult samples. Finally, imDEF constructs a referee system to achieve the competence estimations by leveraging an Ensemble Margin-aware Self-Paced Sampling Ensemble (SPSE$\mathrm{_{EM}}$) method. SPSE$\mathrm{_{EM}}$incrementally strengthens the learning of the hard-to-classify samples, so that the competent levels of component classifiers could be estimated accurately. Extensive experiments demonstrate the effectiveness of imDEF. The source codes have been made publicly available on GitHub.

Multiple Kernel Clustering (MKC) has emerged as a prominent research domain in recent decades due to its capacity to exploit diverse information from multiple views by learning an optimal kernel. Despite the successes achieved by various MKC methods, a significant challenge lies in the computational complexity associated with generating a consensus partition from the optimal kernel matrix, typically of size$n \times n$, where$n$represents the number of samples. This computational bottleneck restricts the practical applicability of these methods when confronted with large-scale datasets. Furthermore, certain existing MKC algorithms derive the consensus partition matrix by fusing all base partitions. However, this fusion process may inadvertently overlook critical information embedded in individual base kernels, potentially leading to inferior clustering performance. In light of these challenges, we introduce an innovative and efficient multiple kernel$k$-means approach, denoted as FAMKKM. Notably, FAMKKM incorporates two approximated partition matrices instead of the original individual partition matric for each base kernel. This strategic substitution significantly reduces computational complexity. Additionally, FAMKKM leverages the original kernel information to guide the fusion of all base partitions, thereby enhancing the quality of the resulting consensus partition matrix. Finally, we substantiate the efficacy and efficiency of the proposed FAMKKM through extensive experiments conducted on six benchmark datasets. Our results demonstrate its superiority over state-of-the-art methods. The demo code of this work is publicly available athttps://github.com/WangJun2023/FAMKKM

Multiple kernel clustering (MKC) aims to extract and integrate the clustering information from a set of pre-defined kernels for handling data which cannot be linearly separated well. More precisely, existing MKC methods generally devote to learn the complementary information from a set of kernel partitions, whose feature dimensions are commonly fixed as the upper bound$n$or lower bound$c$, where$n$and$c$represents the number of samples and clusters, respectively. However, the adopting of the lower bound or upper bound generally leads to poor clustering performance caused by the lack or redundancy of clustering information carried by kernel partitions. To tackle this issue, we propose a novel late fusion multiple kernel clustering method, termed as Eigenvalue Ratio Inspired Partition Learning and Fusion for Multiple Kernel Clustering (ERMKC), in this paper. Specifically, we propose an eigenvalue ratio based criterion to guide the kernel partition learning for each single kernel matrix, which ensures more suitable feature dimensions for the learnt kernel partitions. In addition, we also propose a novel late fusion model for fusing the learnt kernel partitions optimally. Furthermore, we conduct extensive experiments on numerous benchmark datasets to evaluate the proposed ERMKC method, whose results verify the effectiveness and advantage of the proposed method compared to the other state-of-the-art methods.

Multiview clustering (MVC) collects complementary and abundant information, which draws much attention in machine learning and data mining community. Existing MVC methods usually hold the assumption that all the views are complete. However, multiple source data are often incomplete in real-world applications, and so on sensor failure or unfinished collection process, which gives rise to incomplete multiview clustering (IMVC). Although enormous efforts have been devoted in IMVC, there still are some urgent issues that need to be solved: (i) The locality among multiple views has not been utilized in the existing mechanism; (ii) Existing methods inappropriately force all the views to share consensus representation while ignoring specific structures. In this paper, we propose a novel method termed partial MVC with locality graph regularization to address these issues. First, followed the traditional IMVC approaches, we construct weighted semi-nonnegative matrix factorization models to handle incomplete multiview data. Then, upon the consensus representation matrix, the locality graph is constructed for regularizing the shared feature matrix. Moreover, we add the coefficient regression term to constraint the various base matrices among views. We incorporate the three aforementioned processes into a unified framework, whereas they can negotiate with each other serving for learning tasks. An effective iterative algorithm is proposed to solve the resultant optimization problem with theoretically guaranteed convergence. The comprehensive experiment results on several benchmarks demonstrate the effectiveness of the proposed method.

Deep clustering gains superior performance than conventional clustering by jointly performing feature learning and cluster assignment. Although numerous deep clustering algorithms have emerged in various applications, most of them fail to learn robust cluster-oriented features which in turn hurts the final clustering performance. To solve this problem, we propose a two-stage deep clustering algorithm by incorporating data augmentation and self-paced learning. Specifically, in the first stage, we learn robust features by training an autoencoder with examples that are augmented by random shifting and rotating the given clean examples. Then, in the second stage, we encourage the learned features to be cluster-oriented by alternatively finetuning the encoder with the augmented examples and updating the cluster assignments of the clean examples. During finetuning the encoder, the target of each augmented example in the loss function is the center of the cluster to which the clean example is assigned. The targets may be computed incorrectly, and the examples with incorrect targets could mislead the encoder network. To stabilize the network training, we select most confident examples in each iteration by utilizing the adaptive self-paced learning. Extensive experiments validate that our algorithm outperforms the state of the arts on four image datasets.

Feature extraction and feature selection have been regarded as two independent dimensionality reduction methods in most of the existing literature. In this paper, we propose to integrate both approaches into a unified framework and design an unsupervised linear feature selective projection (FSP) for feature extraction with low-rank embedding and dual Laplacian regularization, with the aim to exploit the intrinsic relationship among data and suppress the impact of noise. Specifically, a projection matrix with an l2,1-norm regularization is introduced to project original high dimensional data points into a new subspace with lower dimension, where the l2,1-norm regularization can endow the projection with good interpretability. We deploy a coefficient matrix with low rank constraint to reconstruct the data points and the l2,1-norm is imposed to regularize the data reconstruction errors in the low-dimensional subspace and make FSP robust to noise. Furthermore, a dual graph Laplacian regularization term is imposed on the low dimensional data and data reconstruction matrix for preserving the local manifold geometrical structure of data. Finally, an alternatively iterative algorithm is carefully designed for solving the proposed optimization model. Theoretical convergence and computational complexity analysis of the algorithm are also provided. Comprehensive experiments on various benchmark datasets have been carried out to evaluate the performance of the proposed FSP. As indicated, our algorithm significantly outperforms other state-of-the-art methods for feature extraction.

Recently, network lasso has dawn much attention due to its remarkable performance on simultaneous clustering and optimization. However, it usually suffers from the imperfect data (noise, missing values, etc.), and yields sub-optimal solutions. The reason is that it finds the similar instances according to their features directly, which is usually impacted by the imperfect data, and thus returns sub-optimal results. In this paper, we propose triangle lasso to avoid its disadvantage for graph datasets. In a graph dataset, each instance is represented by a vertex. If two instances have many common adjacent vertices, they tend to become similar. Although some instances are profiled by the imperfect data, it is still able to find the similar counterparts. Furthermore, we develop an efficient algorithm based on Alternating Direction Method of Multipliers (ADMM) to obtain a moderately accurate solution. In addition, we present a dual method to obtain the accurate solution with the low additional time consumption. We demonstrate through extensive numerical experiments that triangle lasso is robust to the imperfect data. It usually yields a better performance than the state-of-the-art method when performing data analysis tasks in practical scenarios.