A Multi-objective Clustering Ensemble Algorithm with Automatic k-Determination

Typically clustering algorithms provide clustering solutions with prespecified number of clusters. The lack of a priori knowledge on the true number of underlying clusters in the dataset makes it important to have a metric to compare the clustering solutions with different number of clusters. This article quantifies a notion of persistence of clustering solutions that enables comparing solutions with different number of clusters. The persistence relates to the range of dataresolution scales over which a clustering solution persists; it is quantified in terms of the maximum over two-norms of all the associated cluster-covariance matrices. Thus we associate a persistence value for each element in a set of clustering solutions with different number of clusters. We show that the datasets where natural clusters are a priori known, the clustering solutions that identify the natural clusters are most persistent - in this way, this notion can be used to identify solutions with true number of clusters. Detailed experiments on a variety of standard and synthetic datasets demonstrate that the proposed persistence-based indicator outperforms the existing approaches, such as, gap-statistic method, X-means, Gmeans, PG-means, dip-means algorithms and informationtheoretic method, in accurately identifying the clustering solutions with true number of clusters. Interestingly, our method can be explained in terms of the phase-transition phenomenon in the deterministic annealing algorithm, where the number of distinct cluster centers changes (bifurcates) with respect to an annealing parameter.

<p>Clustering is an unsupervised machine learning technique, which involves discovering different clusters (groups) of similar objects in unlabeled data and is generally considered to be a NP hard problem. Clustering methods are widely used in a verity of disciplines for analyzing different types of data, and a small improvement in clustering method can cause a ripple effect in advancing research of multiple fields. Clustering any type of data is challenging and there are many open research questions. The clustering problem is exacerbated in the case of text data because of the additional challenges such as issues in capturing semantics of a document, handling rich features of text data and dealing with the well known problem of the curse of dimensionality. In this thesis, we investigate the limitations of existing text clustering methods and address these limitations by providing five new text clustering methods--Query Sense Clustering (QSC), Dirichlet Weighted K-means (DWKM), Multi-View Multi-Objective Evolutionary Algorithm (MMOEA), Multi-objective Document Clustering (MDC) and Multi-Objective Multi-View Ensemble Clustering (MOMVEC). These five new clustering methods showed that the use of rich features in text clustering methods could outperform the existing state-of-the-art text clustering methods. The first new text clustering method QSC exploits user queries (one of the rich features in text data) to generate better quality clusters and cluster labels. The second text clustering method DWKM uses probability based weighting scheme to formulate a semantically weighted distance measure to improve the clustering results. The third text clustering method MMOEA is based on a multi-objective evolutionary algorithm. MMOEA exploits rich features to generate a diverse set of candidate clustering solutions, and forms a better clustering solution using a cluster-oriented approach. The fourth and the fifth text clustering method MDC and MOMVEC address the limitations of MMOEA. MDC and MOMVEC differ in terms of the implementation of their multi-objective evolutionary approaches. All five methods are compared with existing state-of-the-art methods. The results of the comparisons show that the newly developed text clustering methods out-perform existing methods by achieving up to 16\% improvement for some comparisons. In general, almost all newly developed clustering algorithms showed statistically significant improvements over other existing methods. The key ideas of the thesis highlight that exploiting user queries improves Search Result Clustering(SRC); utilizing rich features in weighting schemes and distance measures improves soft subspace clustering; utilizing multiple views and a multi-objective cluster oriented method improves clustering ensemble methods; and better evolutionary operators and objective functions improve multi-objective evolutionary clustering ensemble methods. The new text clustering methods introduced in this thesis can be widely applied in various domains that involve analysis of text data. The contributions of this thesis which include five new text clustering methods, will not only help researchers in the data mining field but also to help a wide range of researchers in other fields.</p>

A robust adaptive clustering analysis method for automatic identification of clusters

Evolutionary multi-objective clustering (EMOC) algorithms have gained popularity recently, as they can obtain a set of clustering solutions in a single run by optimizing multiple objectives. Particularly, in one type of EMOC algorithm, the number of clusters k is taken as one of the multiple objectives to obtain a set of clustering solutions with different k. However, the numbers of clusters k and other objectives are not always in conflict, so it is impossible to obtain the clustering solutions with all different k in a single run. Therefore, evolutionary multi-objective k-clustering (EMO-KC) has recently been proposed to ensure this conflict. However, EMO-KC could not obtain good clustering accuracy on high-dimensional datasets. Moreover, EMO-KC’s validity is not ensured as one of its objectives (SSDexp, which is transformed from the sum of squared distances (SSD)) could not be effectively optimized and it could not avoid invalid solutions in its initialization. In this paper, an improved evolutionary multi-objective clustering algorithm based on autoencoder (AE-IEMOKC) is proposed to improve the accuracy and ensure the validity of EMO-KC. The proposed AE-IEMOKC is established by combining an autoencoder with an improved version of EMO-KC (IEMO-KC) for better accuracy, where IEMO-KC is improved based on EMO-KC by proposing a scaling factor to help effectively optimize the objective of SSDexp and introducing a valid initialization to avoid the invalid solutions. Experimental results on several datasets demonstrate the accuracy and validity of AE-IEMOKC. The results of this paper may provide some useful information for other EMOC algorithms to improve accuracy and convergence.

Evaluation measures for cluster ensembles based on a fuzzy generalized Rand index

Due to their damage to Internet security, malware and phishing website detection has been the Internet security topics that are of great interests. Compared with malware attacks, phishing website fraud is a relatively new Internet crime. However, they share some common properties: 1) both malware samples and phishing websites are created at a rate of thousands per day driven by economic benefits; and 2) phishing websites represented by the term frequencies of the webpage content share similar characteristics with malware samples represented by the instruction frequencies of the program. Over the past few years, many clustering techniques have been employed for automatic malware and phishing website detection. In these techniques, the detection process is generally divided into two steps: 1) feature extraction, where representative features are extracted to capture the characteristics of the file samples or the websites; and 2) categorization, where intelligent techniques are used to automatically group the file samples or websites into different classes based on computational analysis of the feature representations. However, few have been applied in real industry products. In this paper, we develop an automatic categorization system to automatically group phishing websites or malware samples using a cluster ensemble by aggregating the clustering solutions that are generated by different base clustering algorithms. We propose a principled cluster ensemble framework to combine individual clustering solutions that are based on the consensus partition, which can not only be applied for malware categorization, but also for phishing website clustering. In addition, the domain knowledge in the form of sample-level/website-level constraints can be naturally incorporated into the ensemble framework. The case studies on large and real daily phishing websites and malware collection from the Kingsoft Internet Security Laboratory demonstrate the effectiveness and efficiency of our proposed method.

Cluster ensemble is one of the main branches in the ensemble learning area which is an important research focus in recent years. The objective of cluster ensemble is to combine multiple clustering solutions in a suitable way to improve the quality of the clustering result. In this paper, we design a new noise immune cluster ensemble framework named as $AP^{2}CE$ to tackle the challenges raised by noisy datasets. $AP^{2}CE$ not only takes advantage of the affinity propagation algorithm (AP) and the normalized cut algorithm (Ncut), but also possesses the characteristics of cluster ensemble. Compared with traditional cluster ensemble approaches, $AP^{2}CE$ is characterized by several properties. ( $1$ ) It adopts multiple distance functions instead of a single Euclidean distance function to avoid the noise related to the distance function. ( $2$ ) $AP^{2}CE$ applies AP to prune noisy attributes and generate a set of new datasets in the subspaces consists of representative attributes obtained by AP. ( $3$ ) It avoids the explicit specification of the number of clusters. ( $4$ ) $AP^{2}CE$ adopts the normalized cut algorithm as the consensus function to partition the consensus matrix and obtain the final result. In order to improve the performance of $AP^{2}CE$ , the adaptive $AP^{2}CE$ is designed, which makes use of an adaptive process to optimize a newly designed objective function. The experiments on both synthetic and real datasets show that ( $1$ ) $AP^{2}CE$ works well on most of the datasets, in particular the noisy datasets; ( $2$ ) $AP^{2}CE$ is a better choice for most of the datasets when compared with other cluster ensemble approaches; ( $3$ ) $AP^{2}CE$ has the capability to provide more accurate, stable and robust results.

Consensus clustering is an aggregation of base clusterings into an ensemble clustering which is better than the individual base clusterings. It is beneficial to determine the clusters from heterogeneous data. This paper presents a new approach that generates a set of good quality base clusterings and finds a single by aggregation of base clusterings into one clustering solution. The new approach consists of two phases. In the first phase, we present a new tree-based $k$ -means algorithm to build different base clusterings. It builds a cluster-tree which gives us one base clustering. The tree generation process uses two stopping criteria which base on the underlying data distribution of a data set. We change the value of the input parameter of the tree generation algorithm to produce multiple cluster-trees where each tree gives a base clustering with a variable number of clusters. In the second phase, we propose a new nonnegative matrix factorization-based consensus method to ensemble base clusterings into final clustering. We investigated the quality and diversity of base clusterings, which often have a large influence on the performances of consensus clustering. Experimental results on various real-world and synthetic data sets have demonstrated that the proposed algorithm was dominant over the well-known algorithms in term of clustering accuracy.

目的 随着实际应用场景中海量数据采集技术的发展和数据标注成本的不断增加，自监督学习成为海量数据分析的一个重要策略。然而，如何从海量数据中抽取有用的监督信息，并该监督信息下开展有效的学习仍然是制约该方向发展的研究难点。为此，提出了一个基于共识图学习的自监督集成聚类框架。方法 框架主要包括3个功能模块。首先，利用集成学习中多个基学习器构建共识图；其次，利用图神经网络分析共识图，捕获节点优化表示和节点的聚类结构，并从聚类中挑选高置信度的节点子集及对应的类标签生成监督信息；再次，在此标签监督下，联合其他无标注样本更新集成成员基学习器。交替迭代上述功能块，最终提高无监督聚类的性能。结果 为验证该框架的有效性，在标准数据集（包括图像和文本数据）上设计了一系列实验。实验结果表明，所提方法在性能上一致优于现有聚类方法。尤其是在MNIST-Test （modified national institute of standards and technology database）上，本文方法实现了97.78%的准确率，比已有最佳方法高出3.85%。结论 该方法旨在利用图表示学习提升自监督学习中监督信息捕获的能力，监督信息的有效获取进一步强化了集成学习中成员构建的能力，最终提升了无监督海量数据本质结构的挖掘性能。;Objective Clustering is focused on machine learning-related data segmentation for multiple datasets. Its applications are in relevant to such domains like image segmentation and anomaly detection. In addition，to simplify complex tasks optimize its performance，clustering is used in data preprocessing tasks of those are data sub-blocks segmentation， pseudo-labels generation，and abnormal points-removal. Self-supervised learning has become an essential technique for massive data analysis. However，it is challenged to extract effective supervision information and analyze the input data. Method A consensus graph learning based self-supervised ensemble clustering（CGL-SEC）framework is developed. It consists of three main modules：1）to construct the consensus graph based on several ensemble components（i. e. ，the basic clustering methods）. 2）to extract the supervision information by learning the consensus graph representation，and 3）its node clustering results，where the subset of nodes with the high-confidence are selected as labeled samples. To optimize the ensemble components and the corresponding consensus graph，t basic clustering methods are re-trained in related the option of samples-labeled and other samples-unlabeled. The final clustering results can be optimized iteratively until the learning process converges. Result A series of experiments are carried out on benchmarks，including both image and textual datasets. Especially，CGL-SEC is 3. 85% over baseline in terms of clustering evaluation metric on themodified national institute of standards and technology database（MNIST-Test）. First，to optimize data representation and cluster assignment at the same time，deep embedding clustering can be focused on data itself as the supervision information and auto-encoder with the reconstruction loss is pre-trained. The soft cluster assignment of features-embedded is then calculated，and the KL（Kullback-Leibler）divergence is minimized between the soft cluster assignment and the auxiliary target distribution. To improve the performance of the model further，following deep clustering network（DCN）can use hard clustering instead of soft allocation，and local constraints are applied by improved deep embedding clustering（IDEC）. The pseudo-label strategy is implemented as a self-supervised learning method that uses the prediction results of the neural network as the label to simulate the supervision information compared to using data itself as the supervision information. Deepcluster-based K-means clustering is used to generate pseudo-labels to guide the training of convolutional networks. However，the generated pseudo-labels have lower confidence and are prone to trivial solutions in the initial stage of network training. Deep embedding clustering with data augmentation（DEC-DA）and MixMatch-based prediction of data-enhanced samples are used as the supervision information of the original data，which improves the accuracy of the supervision information to a certain extent，but this method is difficult to extend to text and other fields. Deep adaptive clustering-based high-confidence pseudo-label subsets-selected are iteratively trained the network in the prediction results，but lowconfidence samples-involved data distribution information is ignored. Pseudo-semi-supervised clustering votes are used to select a subset of high-confidence pseudo-labels，and all samples are used to train semi-supervised neural network. Although the ensemble strategy can improve the confidence of the pseudo-label，the voting strategy is concerned of category representation only without the feature representation of the sample itself，which can reduce the clustering performance in some cases. The ensemble learning is regarded as a representative machine learning method that reflects the ability of group intelligence，whereas a learning method can improve the overall prediction performance via multiple base learners training and their coordinated prediction results. In pseudo-label-based clustering tasks，it can coordinate multiple base learners to obtain high-confidence pseudo-labels. However，the effectiveness of the supervision information acquisition is still to be resolved. The category information of the sample is considered for current pseudo-label-based ensemble clustering method only when the label is captured and some effective information are ignored like the feature representation of the sample itself and the clustering structure between samples. Conclusion Graph neural network is composed of content information of nodes and the structural information between nodes at the same time. To design a self-supervised ensemble clustering method based on consensus graph representation learning，it is required to make full use of sample features and relationships between samples in ensemble learning. To obtain higher confidence pseudo-labels as supervised information and improve the performance of self-supervised clustering，it is necessary to mine global and local information at the same time. We illustrate a learnable data ensemble representation through graph neural network. The confidence of pseudo-labels is improved，and the entire model is trained in self-supervision iteratively. To be summarized：1）Commonly-used consensus graph learning-integrated clustering framework is developed，which can use multi-level information like clusteringintegrated sample characteristics and category structure. 2）Self-supervision method is proposed，which uses graph neural network to mine the global and local information of the consensus graph，and high-confidence pseudo-labels are obtained as supervised information. 3）Experiments are demonstrated that the consensus graph learning ensemble clustering method has its potentials on image and text datasets.

Clustering ensembles combine multiple partitions of data into a single clustering solution. It is an effective technique for improving the quality of clustering results. Current clustering ensemble algorithms are usually built on the pairwise agreements between clusterings that focus on the similarity via consensus functions, between data objects that induce similarity measures from partitions and re-cluster objects, and between clusters that collapse groups of clusters into meta-clusters. In most of those models, there is a strong assumption on IIDness (i.e., independent and identical distribution), which states that base clusterings perform independently of one another and all objects are also independent. In the real world, however, objects are generally likely related to each other through features that are either explicit or even implicit. There is also latent but definite relationship among intermediate base clusterings because they are derived from the same set of data. All these demand a further investigation of clustering ensembles that explores the interdependence characteristics of data. To solve this problem, a new coupled clustering ensemble (CCE) framework that works on the interdependence nature of objects and intermediate base clusterings is proposed in this article. The main idea is to model the coupling relationship between objects by aggregating the similarity of base clusterings, and the interactive relationship among objects by addressing their neighborhood domains. Once these interdependence relationships are discovered, they will act as critical supplements to clustering ensembles. We verified our proposed framework by using three types of consensus function: clustering-based, object-based, and cluster-based. Substantial experiments on multiple synthetic and real-life benchmark datasets indicate thatCCEcan effectively capture the implicit interdependence relationships among base clusterings and among objects with higher clustering accuracy, stability, and robustness compared to 14 state-of-the-art techniques, supported by statistical analysis. In addition, we show that the final clustering quality is dependent on the data characteristics (e.g., quality and consistency) of base clusterings in terms of sensitivity analysis. Finally, the applications in document clustering, as well as on the datasets with much larger size and dimensionality, further demonstrate the effectiveness, efficiency, and scalability of our proposed models.

Healthcare question answering (HQA) system plays a vital role in encouraging patients to inquire for professional consultation. However, there are some challenging factors in learning and representing the question corpus of HQA datasets, such as high dimensionality, sparseness, noise, nonprofessional expression, etc. To address these issues, we propose an inception convolutional autoencoder model for Chinese healthcare question clustering (ICAHC). First, we select a set of kernels with different sizes using convolutional autoencoder networks to explore both the diversity and quality in the clustering ensemble. Thus, these kernels encourage to capture diverse representations. Second, we design four ensemble operators to merge representations based on whether they are independent, and input them into the encoder using different skip connections. Third, it maps features from the encoder into a lower-dimensional space, followed by clustering. We conduct comparative experiments against other clustering algorithms on a Chinese healthcare dataset. Experimental results show the effectiveness of ICAHC in discovering better clustering solutions. The results can be used in the prediction of patients' conditions and the development of an automatic HQA system.

DNA microarray technology monitors gene activity in real-time in living organisms. It creates a large amount of data that helps scientists learn about how genes work. Clustering this data helps understand gene interactions and uncover important biological processes. However, the traditional clustering techniques have difficulties due to the enormous dimensionality of gene expression data and the intricacy of biological networks. Although ensemble clustering is a viable strategy, such high-dimensional data may not lend itself well to traditional approaches. This study introduces a novel technique for gene expression data clustering called incremental ensemble clustering for gene expression data (IECG). There are two steps in the IECG. A technique for grouping gene expression data into windows is presented in the first step, producing a tree of clusters. This procedure is carried out again for succeeding windows that have distinct feature sets. The base clusterings of two consecutive windows are ensembled using a new goal function to form a new clustering solution. By repeating this step-by-step method for further windows, reliable patterns that are beneficial for medical applications can be extracted. The results from both biological and non-biological data demonstrate that the proposed algorithm outperformed the state-of-the-art algorithms. Additionally, the running time of the proposed algorithm has been examined.

There are some general procedures to generate the clusterings in clustering ensembles. One can apply different algorithms to create different clusterings of the data. Some clustering algorithms like k-means require initialization of parameters. Different initializations can lead to different clustering results. The parameters of a clustering algorithm, such as the number of clusters, can be altered to create different data clusterings. Different versions of the data can also be used as the input to the clustering algorithm, leading to different partitions. In this paper, we propose a new scheme for constructing multiple independent clusterings using additional artificially generated data. Then, we compare our new method with seven general clustering ensemble constructing methods. The experiments show that our approach can achieve higher or comparable performance than the other methods.

Fuzzy C-means (FCM) clustering method has been widely used in image segmentation that plays an important role in a variety of applications in image processing and computer vision systems, but the performance of FCM heavily relies on the initial cluster centers which are difficult to determine. To solve the problem, the paper proposes a new hybrid method for image segmentation, which first randomly generates a population of initial clustering solutions and then uses an evolutionary algorithm to search for better clustering solutions; at each iteration, the FCM method is applied on each initial clustering solution to produce its segmentation result. Among a set of popular evolutionary algorithms, we find that the biogeography-based optimization (BBO) metaheuristic exhibits good performance on the considered problem. Besides the basic BBO, we have also proposed a set of improved BBO versions in their combination with FCM for image segmentation. Computational experiments on a set of test images show that the proposed method has significant advantage over the basic FCM algorithm and those hybrid algorithms combining FCM with other evolutionary algorithms such as artificial bee colony and particle swarm optimization.

A vast amount of time-series data is generated from multiple fields. Mining these data can uncover hidden patterns and behavior characteristics. The analysis of such data is complex because they are voluminous and have high dimensions. Clustering can provide a preprocessing step to extract insights. However, clustering such data poses challenges, as many existing algorithms are not efficient enough to handle them. In addition, many traditional and modern clustering algorithms need help with parameter-tuning problems. Ensemble clustering, an amalgamation of clustering algorithms, has emerged as a promising method for improving the accuracy, stability, and robustness of clustering solutions. This study presents Ensemble clustering using Affinity Propagation (ECAP). AP is efficient because it does not require the number of clusters to be specified a priori, allowing the data to reveal its structure. When used in an ensemble framework, the inherent strengths of AP are amplified by integrating multiple clustering results. This aggregation mitigates the influence of any single, potentially suboptimal clustering outcome, leading to more stable and reliable clusters. Extensive experiments were performed on four real-world datasets for rand index, homogeneity, completeness, and V-measure to determine the efficacy of the proposed approach. The results show that the proposed method outperforms AP, Kmeans, and spectral clustering.