Multiscale and Auto-Tuned Semi-Supervised Deep Subspace Clustering and Its Application in Brain Tumor Clustering

In this paper,we introduce a novel Multi-scale and Auto-tuned Semi-supervised Deep Subspace Clustering(MAS-DSC)algorithm,aimed at addressing the challenges of deep subspace clustering in high-dimensional real-world data,particularly in the field of medical imaging.Traditional deep subspace clustering algorithms,which are mostly unsupervised,are limited in their ability to effectively utilize the inherent prior knowledge in medical images.Our MAS-DSC algorithm incorporates a semi-supervised learning framework that uses a small amount of labeled data to guide the clustering process,thereby enhancing the discriminative power of the feature representations.Additionally,the multi-scale feature extraction mechanism is designed to adapt to the complexity of medical imaging data,resulting in more accurate clustering performance.To address the difficulty of hyperparameter selection in deep subspace clustering,this paper employs a Bayesian optimization algorithm for adaptive tuning of hyperparameters related to subspace clustering,prior knowledge constraints,and model loss weights.Extensive experiments on standard clustering datasets,including ORL,Coil20,and Coil100,validate the effectiveness of the MAS-DSC algorithm.The results show that with its multi-scale network structure and Bayesian hyperparameter optimization,MAS-DSC achieves excellent clustering results on these datasets.Furthermore,tests on a brain tumor dataset demonstrate the robustness of the algorithm and its ability to leverage prior knowledge for efficient feature extraction and enhanced clustering performance within a semi-supervised learning framework.

Contrastive Consistency and Attentive Complementarity for Deep Multi-View Subspace Clustering

Deep multi-view subspace clustering (DMVSC) based on self-expression has attracted increasing attention dueto its outstanding performance and nonlinear application. However, most existing methods neglect that viewprivatemeaningless information or noise may interfere with the learning of self-expression, which may lead to thedegeneration of clustering performance. In this paper, we propose a novel framework of Contrastive Consistencyand Attentive Complementarity (CCAC) for DMVsSC. CCAC aligns all the self-expressions of multiple viewsand fuses them based on their discrimination, so that it can effectively explore consistent and complementaryinformation for achieving precise clustering. Specifically, the view-specific self-expression is learned by a selfexpressionlayer embedded into the auto-encoder network for each view. To guarantee consistency across views andreduce the effect of view-private information or noise, we align all the view-specific self-expressions by contrastivelearning. The aligned self-expressions are assigned adaptive weights by channel attention mechanism according totheir discrimination. Then they are fused by convolution kernel to obtain consensus self-expression withmaximumcomplementarity ofmultiple views. Extensive experimental results on four benchmark datasets and one large-scaledataset of the CCAC method outperformother state-of-the-artmethods, demonstrating its clustering effectiveness.

Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.

Subspace Clustering in High-Dimensional Data Streams:A Systematic Literature Review

Clustering high dimensional data is challenging as data dimensionality increases the distance between data points,resulting in sparse regions that degrade clustering performance.Subspace clustering is a common approach for processing high-dimensional data by finding relevant features for each cluster in the data space.Subspace clustering methods extend traditional clustering to account for the constraints imposed by data streams.Data streams are not only high-dimensional,but also unbounded and evolving.This necessitates the development of subspace clustering algorithms that can handle high dimensionality and adapt to the unique characteristics of data streams.Although many articles have contributed to the literature review on data stream clustering,there is currently no specific review on subspace clustering algorithms in high-dimensional data streams.Therefore,this article aims to systematically review the existing literature on subspace clustering of data streams in high-dimensional streaming environments.The review follows a systematic methodological approach and includes 18 articles for the final analysis.The analysis focused on two research questions related to the general clustering process and dealing with the unbounded and evolving characteristics of data streams.The main findings relate to six elements:clustering process,cluster search,subspace search,synopsis structure,cluster maintenance,and evaluation measures.Most algorithms use a two-phase clustering approach consisting of an initialization stage,a refinement stage,a cluster maintenance stage,and a final clustering stage.The density-based top-down subspace clustering approach is more widely used than the others because it is able to distinguish true clusters and outliers using projected microclusters.Most algorithms implicitly adapt to the evolving nature of the data stream by using a time fading function that is sensitive to outliers.Future work can focus on the clustering framework,parameter optimization,subspace search techniques,memory-efficient synopsis structures,explicit cluster change detection,and intrinsic performance metrics.This article can serve as a guide for researchers interested in high-dimensional subspace clustering methods for data streams.

An Improved Soft Subspace Clustering Algorithm for Brain MR Image Segmentation

In recent years,the soft subspace clustering algorithm has shown good results for high-dimensional data,which can assign different weights to each cluster class and use weights to measure the contribution of each dimension in various features.The enhanced soft subspace clustering algorithm combines interclass separation and intraclass tightness information,which has strong results for image segmentation,but the clustering algorithm is vulnerable to noisy data and dependence on the initialized clustering center.However,the clustering algorithmis susceptible to the influence of noisydata and reliance on initializedclustering centers andfalls into a local optimum;the clustering effect is poor for brain MR images with unclear boundaries and noise effects.To address these problems,a soft subspace clustering algorithm for brain MR images based on genetic algorithm optimization is proposed,which combines the generalized noise technique,relaxes the equational weight constraint in the objective function as the boundary constraint,and uses a genetic algorithm as a method to optimize the initialized clustering center.The genetic algorithm finds the best clustering center and reduces the algorithm’s dependence on the initial clustering center.The experiment verifies the robustness of the algorithm,as well as the noise immunity in various ways and shows good results on the common dataset and the brain MR images provided by the Changshu First People’s Hospital with specific high accuracy for clinical medicine.

Evaluating Partitioning Based Clustering Methods for Extended Non-negative Matrix Factorization (NMF)

Data is humongous today because of the extensive use of World WideWeb, Social Media and Intelligent Systems. This data can be very important anduseful if it is harnessed carefully and correctly. Useful information can beextracted from this massive data using the Data Mining process. The informationextracted can be used to make vital decisions in various industries. Clustering is avery popular Data Mining method which divides the data points into differentgroups such that all similar data points form a part of the same group. Clusteringmethods are of various types. Many parameters and indexes exist for the evaluationand comparison of these methods. In this paper, we have compared partitioningbased methods K-Means, Fuzzy C-Means (FCM), Partitioning AroundMedoids (PAM) and Clustering Large Application (CLARA) on secure perturbeddata. Comparison and identification has been done for the method which performsbetter for analyzing the data perturbed using Extended NMF on the basis of thevalues of various indexes like Dunn Index, Silhouette Index, Xie-Beni Indexand Davies-Bouldin Index.

CSFW-SC: Cuckoo Search Fuzzy-Weighting Algorithm for Subspace Clustering Applying to High-Dimensional Clustering

Aimed at the issue that traditional clustering methods are not appropriate to high-dimensional data, a cuckoo search fuzzy-weighting algorithm for subspace clustering is presented on the basis of the exited soft subspace clustering algorithm. In the proposed algorithm, a novel objective function is firstly designed by considering the fuzzy weighting within-cluster compactness and the between-cluster separation, and loosening the constraints of dimension weight matrix. Then gradual membership and improved Cuckoo search, a global search strategy, are introduced to optimize the objective function and search subspace clusters, giving novel learning rules for clustering. At last, the performance of the proposed algorithm on the clustering analysis of various low and high dimensional datasets is experimentally compared with that of several competitive subspace clustering algorithms. Experimental studies demonstrate that the proposed algorithm can obtain better performance than most of the existing soft subspace clustering algorithms.

Data Stream Subspace Clustering for Anomalous Network Packet Detection

As the Internet offers increased connectivity between human beings, it has fallen prey to malicious users who exploit its resources to gain illegal access to critical information. In an effort to protect computer networks from external attacks, two common types of Intrusion Detection Systems (IDSs) are often deployed. The first type is signature-based IDSs which can detect intrusions efficiently by scanning network packets and comparing them with human-generated signatures describing previously-observed attacks. The second type is anomaly-based IDSs able to detect new attacks through modeling normal network traffic without the need for a human expert. Despite this advantage, anomaly-based IDSs are limited by a high false-alarm rate and difficulty detecting network attacks attempting to blend in with normal traffic. In this study, we propose a StreamPreDeCon anomaly-based IDS. StreamPreDeCon is an extension of the preference subspace clustering algorithm PreDeCon designed to resolve some of the challenges associated with anomalous packet detection. Using network packets extracted from the first week of the DARPA '99 intrusion detection evaluation dataset combined with Generic Http, Shellcode and CLET attacks, our IDS achieved 94.4% sensitivity and 0.726% false positives in a best case scenario. To measure the overall effectiveness of the IDS, the average sensitivity and false positive rates were calculated for both the maximum sensitivity and the minimum false positive rate. With the maximum sensitivity, the IDS had 80% sensitivity and 9% false positives on average. The IDS also averaged 63% sensitivity with a 0.4% false positive rate when the minimal number of false positives is needed. These rates are an improvement on results found in a previous study as the sensitivity rate in general increased while the false positive rate decreased.

Forest-Fire Recognition by Sparse and Collaborative Subspace Clustering

Traditional forest-fire recognition based on the characteristics of smoke, temperature and light fails to accurately detect and respond to early fires. By analyzing the characteristics of flame, the methods based on aerial image recognition have been widely used, such as RGB-based and HIS-based methods. However, these methods are susceptible to background factors causing interference and false detection. To alleviate these problems, we investigate two subspace clustering methods based on sparse and collaborative representation, respectively, to detect and locate forest fires. Firstly, subspace clustering segments flame from the whole image. Afterwards, sparse or collaborative representation is employed to represent most of the flame information in a dictionary with l1-regularization or l2-regularization term, which results in fewer reconstruction errors. Experimental results show that the proposed SSC and CSC substantially outperform the state-of-the art methods.

Clustering Student Discussion Messages on Online Forumby Visualization and Non-Negative Matrix Factorization

The use of online discussion forum can?effectively engage students in their studies. As the number of messages posted on the forum is increasing, it is more difficult for instructors to read and respond to them in a prompt way. In this paper, we apply non-negative matrix factorization and visualization to clustering message data, in order to provide a summary view of messages that disclose their deep semantic relationships. In particular, the NMF is able to find the underlying issues hidden in the messages about which most of the students are concerned. Visualization is employed to estimate the initial number of clusters, showing the relation communities. The experiments and comparison on a real dataset have been reported to demonstrate the effectiveness of the approaches.

A Data Stream Subspace Clustering Algorithm

The main aim of data stream subspace clustering is to find clusters in subspace in rational time accurately. The existing data stream subspace clustering algorithms are greatly influenced by parameters. Due to the flaws of traditional data stream subspace clustering algorithms, we propose SCRP, a new data stream subspace clustering algorithm. SCRP has the advantages of fast clustering and being insensitive to outliers. When data stream changes, the changes will be recorded by the data structure named Region-tree, and the corresponding statistics information will be updated. Further SCRP can regulate clustering results in time when data stream changes. According to the experiments on real datasets and synthetic datasets, SCRP is superior to the existing data stream subspace clustering algorithms on both clustering precision and clustering speed, and it has good scalability to the number of clusters and dimensions.

Subspace Distribution Clustering HMM for Chinese Digit Speech Recognition

As a kind of statistical method, the technique of Hidden Markov Model （HMM） is widely used for speech recognition. In order to train the HMM to be more effective with much less amount of data, the Subspace Distribution Clustering Hidden Markov Model （SDCHMM）, derived from the Continuous Density Hidden Markov Model （CDHMM）, is introduced. With parameter tying, a new method to train SDCHMMs is described. Compared with the conventional training method, an SDCHMM recognizer trained by means of the new method achieves higher accuracy and speed. Experiment results show that the SDCHMM recognizer outperforms the CDHMM recognizer on speech recognition of Chinese digits.

Mining maximal pattern-based subspace clusters in high dimensional space

The problem of pattern-based subspace clustering, a special type of subspace clustering that uses pattern similarity as a measure of similarity, is studied. Unlike most traditional clustering algorithms that group the close values of objects in all the dimensions or a set of dimensions, clustering by pattern similarity shows an interesting pattern, where objects exhibit a coherent pattern of rise and fall in subspaces. A novel approach, named EMaPle to mine the maximal pattern-based subspace clusters, is designed. The EMaPle searches clusters only in the attribute enumeration spaces which are relatively few compared to the large number of row combinations in the typical datasets, and it exploits novel pruning techniques. EMaPle can find the clusters satisfying coherent constraints, size constraints and sign constraints neglected in MaPle. Both synthetic data sets and real data sets are used to evaluate EMaPle and demonstrate that it is more effective and scalable than MaPle.

Graph Regularized L_p Smooth Non-negative Matrix Factorization for Data Representation

This paper proposes a Graph regularized Lpsmooth non-negative matrix factorization(GSNMF) method by incorporating graph regularization and L_p smoothing constraint, which considers the intrinsic geometric information of a data set and produces smooth and stable solutions. The main contributions are as follows: first, graph regularization is added into NMF to discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. Second,the Lpsmoothing constraint is incorporated into NMF to combine the merits of isotropic(L_2-norm) and anisotropic(L_1-norm)diffusion smoothing, and produces a smooth and more accurate solution to the optimization problem. Finally, the update rules and proof of convergence of GSNMF are given. Experiments on several data sets show that the proposed method outperforms related state-of-the-art methods.

Total Variation Constrained Non-Negative Matrix Factorization for Medical Image Registration

This paper presents a novel medical image registration algorithm named total variation constrained graphregularization for non-negative matrix factorization(TV-GNMF).The method utilizes non-negative matrix factorization by total variation constraint and graph regularization.The main contributions of our work are the following.First,total variation is incorporated into NMF to control the diffusion speed.The purpose is to denoise in smooth regions and preserve features or details of the data in edge regions by using a diffusion coefficient based on gradient information.Second,we add graph regularization into NMF to reveal intrinsic geometry and structure information of features to enhance the discrimination power.Third,the multiplicative update rules and proof of convergence of the TV-GNMF algorithm are given.Experiments conducted on datasets show that the proposed TV-GNMF method outperforms other state-of-the-art algorithms.

Linear manifold clustering for high dimensional data based on line manifold searching and fusing

High dimensional data clustering,with the inherent sparsity of data and the existence of noise,is a serious challenge for clustering algorithms.A new linear manifold clustering method was proposed to address this problem.The basic idea was to search the line manifold clusters hidden in datasets,and then fuse some of the line manifold clusters to construct higher dimensional manifold clusters.The orthogonal distance and the tangent distance were considered together as the linear manifold distance metrics. Spatial neighbor information was fully utilized to construct the original line manifold and optimize line manifolds during the line manifold cluster searching procedure.The results obtained from experiments over real and synthetic data sets demonstrate the superiority of the proposed method over some competing clustering methods in terms of accuracy and computation time.The proposed method is able to obtain high clustering accuracy for various data sets with different sizes,manifold dimensions and noise ratios,which confirms the anti-noise capability and high clustering accuracy of the proposed method for high dimensional data.

PMSSC:Parallelizable multi-subset based self-expressive model for subspace clustering

Subspace clustering methods which embrace a self-expressive model that represents each data point as a linear combination of other data points in the dataset provide powerful unsupervised learning techniques.However,when dealing with large datasets,representation of each data point by referring to all data points via a dictionary suffers from high computational complexity.To alleviate this issue,we introduce a parallelizable multi-subset based self-expressive model(PMS)which represents each data point by combining multiple subsets,with each consisting of only a small proportion of the samples.The adoption of PMS in subspace clustering(PMSSC)leads to computational advantages because the optimization problems decomposed over each subset are small,and can be solved efficiently in parallel.Furthermore,PMSSC is able to combine multiple self-expressive coefficient vectors obtained from subsets,which contributes to an improvement in self-expressiveness.Extensive experiments on synthetic and real-world datasets show the efficiency and effectiveness of our approach in comparison to other methods.

基于二部图的联合谱嵌入多视图聚类算法

多视图聚类在图像处理、数据挖掘和机器学习等领域引起了越来越多的关注.现有的多视图聚类算法存在两个不足,一是在图构造过程中只考虑每个视图数据之间的成对关系生成亲和矩阵,而缺乏邻域关系的刻画;二是现有的方法将多视图信息融合和聚类的过程相分离,从而降低了算法的聚类性能.为此,提出一种更为准确和鲁棒的基于二部图的联合谱嵌入多视图聚类算法.首先,基于多视图子空间聚类的思想构造二部图进而产生相似图,接着利用相似图的谱嵌入矩阵进行图融合,其次,在融合过程中考虑每个视图的重要性进行权重约束,进而引入聚类指示矩阵得到最终的聚类结果.提出的模型将二部图、嵌入矩阵与聚类指示矩阵约束在一个框架下进行优化.此外,提供一种求解该模型的快速优化策略,该策略将优化问题分解成小规模子问题,并通过迭代步骤高效解决.提出算法和已有的多视图聚类算法在真实数据集上进行实验分析.实验结果表明,相比已有方法,提出算法在处理多视图聚类问题上是更加有效和鲁棒的.

基于滑窗OPTICS算法和DATA-SSI算法的桥梁模态参数智能化识别

针对现有基于数据驱动的随机子空间(data-driven stochastic subspace identification,DATA-SSI)算法存在的不足,无法实现稳定图中真假模态的智能化筛选,提出了一种新的模态参数智能化识别算法。首先通过引入滑窗技术来实现对输入信号的合理划分,以避免虚假模态和模态遗漏现象的出现;其次通过引入OPTICS(ordering points to identify the clustering structure)密度聚类算法实现稳定图中真实模态的智能化筛选,最后将所提算法运用于某实际大型斜拉桥主梁结构的频率和模态振型识别过程中。结果表明,所提改进算法识别的频率值结果与理论值(MIDAS有限元结果)以及实际值(现场动力特性实测结果)间的误差均在5%以内,且识别的模态振型图与理论模态振型图具有很高的相似性。

基于子空间的I-nice聚类算法

高维数据的子空间聚类是无监督学习领域的热点研究问题,其难点在于寻找恰当的子空间以及其中的数据簇。大多数现有的子空间聚类算法均存在计算复杂度高和参数选择难的缺陷,这是因为在高维数据中子空间的组合数量很大,算法的执行时间非常长,且不同数据集和应用场景需要不同的参数设定。为此,提出了基于子空间的I-nice(简记为sub-I-nice)聚类算法用于识别高维数据中子空间内数据簇的个数。首先,该算法将原始数据维度随机划分成多个维度组,根据维度组生成子空间样本;接着,使用最新的I-niceMO算法对每个子空间数据进行聚类;最后,采用新设计的球模型对所有子空间的基聚类结果进行集成。在含有噪声的高维仿真数据集上对所提出的sub-I-nice算法进行了详细的性能验证,实验结果表明sub-I-nice算法相比其他3种代表性聚类算法有更好的准确性和鲁棒性,从而证实了其合理性和有效性。