Soft Subspace Clustering for High-Dimensional Data

Fuzzy partition based soft subspace clustering and its applications in high dimensional data

In this paper, two novel soft subspace clustering algorithms, namely fuzzy weighting subspace clustering with competitive agglomeration (FWSCA) and entropy weighting subspace clustering with competitive agglomeration (EWSCA), are proposed to overcome the problems of the unknown number of clusters and the initialization of prototypes for soft subspace clustering. The main advantage of FWSCA and EWSCA lies in the fact that they effectively integrate the merits of soft subspace clustering and the good properties of fuzzy clustering with competitive agglomeration. This makes it possible to obtain the appropriate number of clusters during the clustering progress. Moreover, FWSCA and EWSCA algorithms can converge regardless of the initial number of clusters and initialization. Substantial experimental results on both synthetic and real data sets demonstrate the effectiveness of FWSCA and EWSCA in addressing the two problems.

While the Euclidean distance metric is commonly utilized in most soft subspace clustering algorithms, some robust distance metrics can also be considered for soft subspace clustering. In this study, a novel soft subspace clustering algorithm called Alternative Soft Subspace Clustering (ASSC) is proposed by incorporating the alternative distance metric into the framework of entropy weighting subspace clustering. The properties of ASSC are investigated and a theoretical analysis on robustness is established accordingly. Experiments on UCI data are conducted and the experimental results show the effectiveness of the proposed algorithm.

High-dimensional data clustering is of great importance in the big data era. Multi-objective evolutionary soft subspace clustering (SSC) algorithms have shown promise in handling such datasets, but the objective functions and local search strategies used have not yet been well investigated. To consider these issues, this paper proposes an improved multiobjective evolutionary approach with new objective function and local search operator for clustering high-dimensional data. First, a new objective function is provided, which optimizes the clustering validity indexes and additional item simultaneously to overcome the difficulty of coefficient settings in the objective functions of existing SSC approaches. Second, an improved local search operator is introduced, which updates the weights of features by considering both the within-class compactness and between-class separation to capture a more comprehensive data structure. An experimental study with comparison with state-of-the-art SSC methods demonstrates the efficiency of the proposed approach.

Soft subspace clustering (SSC), which analyzes high-dimensional data and applies various weights to each cluster class to assess the membership degree of each cluster to the space, has shown promising results in recent years. This method of clustering assigns distinct weights to each cluster class. By introducing spatial information, enhanced SSC algorithms improve the degree to which intraclass compactness and interclass separation are achieved. However, these algorithms are sensitive to noisy data and have a tendency to fall into local optima. In addition, the segmentation accuracy is poor because of the influence of noisy data. In this study, an SSC approach that is based on particle swarm optimization is suggested with the intention of reducing the interference caused by noisy data. The particle swarm optimization method is used to locate the best possible clustering center. Second, increasing the amount of geographical membership makes it possible to utilize the spatial information to quantify the link between different clusters in a more precise manner. In conclusion, the extended noise clustering method is implemented in order to maximize the weight. Additionally, the constraint condition of the weight is changed from the equality constraint to the boundary constraint in order to reduce the impact of noise. The methodology presented in this research works to reduce the amount of sensitivity the SSC algorithm has to noisy data. It is possible to demonstrate the efficacy of this algorithm by using photos with noise already present or by introducing noise to existing photographs. The revised SSC approach based on particle swarm optimization (PSO) is demonstrated to have superior segmentation accuracy through a number of trials; as a result, this work gives a novel method for the segmentation of noisy images.

Self-organizing subspace clustering for high-dimensional and multi-view data

Subspace clustering by directly solving Discriminative K-means

High dimensional data clustering is a difficult task due to the curse of dimensionality. Traditional clustering methods usually fail to produce meaningful results for high dimensional data. Hypergraph partition is believed to be a promising method for dealing with this challenge. In this work, a new high dimensional clustering method called Merging Dense SubGraphs (MDSG) is proposed. A graph G is first constructed from the data by defining an adjacency relationship between the data points using Shared k Nearest Neighbors (SNN). Then a hypergraph is created from the graph G by defining the hyperedges to be all the maximal cliques in the graph. After the hypergraph is produced, an improved hypergraph partitioning method is used to produce the final clustering results. The proposed MDSG method is evaluated on several real high dimensional handwritten datasets, and the experimental results show that the proposed method is superior to the traditional clustering method and other hypergraph partition methods for high dimensional handwritten data clustering.

In recent year, stock investor in Indonesia increased rapidly, so it is required to do analysis about the stock that helps the investor in their investment plan. Clustering is beneficial to select the appropriate stock for investors. Unfortunately, stock prices keep varying from time to time. Consequently, it is not an easy work to select the stock for investment. In addition, stock price time series data are high dimensional data that influenced by many factors. In this study, high dimensional data are obtained by the time frame of each factor. Therefore, it is important to use a suitable technique to cluster high dimensional data. This paper presents High Dimensional Data Clustering (HDDC), a model-based clustering based on Gaussian Mixture Model, using the Expectation-Maximization (EM) algorithm. HDDC via EM algorithm gives a more robust result, and it possible to make an additional assumption. Moreover, this paper combines a high-dimensional clustering technique HDDC via EM algorithm and the most popular feature extraction technique Principal Component Analysis (PCA). This paper comparing methods of clustering technique HDDC and the combination between HDDC and PCA to know the most effective method which gives better result in clustering high-dimensional time series data. The 155 data features are reduced to 7 principal components using PCA analysis. Despite PCA has increased the time efficiency of building the model, clustering technique HDDC via EM algorithm enables to handle the high-dimensional data better than the combination with PCA.

Multiple imputation (MI) is a well-established method for dealing with missing data. MI is computationally intensive when imputing missing covariates with high-dimensional outcome data (e.g., DNA methylation data in epigenome-wide association studies (EWAS)), because every outcome variable must be included in the imputation model to avoid biasing associations towards the null. Instead, EWAS analyses are reduced to only complete cases, limiting statistical power and potentially causing bias. We used simulations to compare 5 MI methods for high-dimensional data under 2 missingness mechanisms. All imputation methods had increased power over complete-case (C-C) analyses. Imputing missing values separately for each variable was computationally inefficient, but dividing sites at random into evenly sized bins improved efficiency and gave low bias. Methods imputing solely using subsets of sites identified by the C-C analysis suffered from bias towards the null. However, if these subsets were added into random bins of sites, this bias was reduced. The optimal methods were applied to an EWAS with missingness in covariates. All methods identified additional sites over the C-C analysis, and many of these sites had been replicated in other studies. These methods are also applicable to other high-dimensional data sets, including the rapidly expanding area of “-omics” studies.

Conventional clustering algorithms are not so efficient on higher dimensional data due to the problem of dimensionality curse. To address this issue searching for clusters in appropriate subspaces is performed. But searching all possible subspaces is exhaustive. In this paper we propose an efficient approach to effectively find the relevant subspaces in high dimensional data and apply clustering in those subspaces. Experiments are conducted on real and synthetic data sets and compared with other approaches and our approach is able to return good clustering results.

Fusion of evolvable genome structure and multi-objective optimization for subspace clustering

This paper presents an agent-based algorithm for discovering subspace clusters in high dimensional data. Each data object is represented by an agent, and the agents move from one local environment to another to find optimal clusters in subspaces. Heuristic rules and objective functions are defined to guide the movements of agents, so that similar agents(data objects) go to one group. The experimental results show that our proposed agent-based subspace clustering algorithm performs better than existing subspace clustering methods on both F1 measure and Entropy. The running time of our algorithm is scalable with the size and dimensionality of data. Furthermore, an application in stock market surveillance demonstrates its effectiveness in real world applications.

Data clustering is an important research topic in data mining and signal processing communications. In all the data clustering methods, the subspace spectral clustering methods based on self expression model, e.g., the Sparse Subspace Clustering (SSC) and the Low Rank Representation (LRR) methods, have attracted a lot of attention and shown good performance. The key step of SSC and LRR is to construct a proper affinity or similarity matrix of data for spectral clustering. Recently, Laplacian graph constraint was introduced into the basic SSC and LRR and obtained considerable improvement. However, the current graph construction methods do not well exploit and reveal the non-linear properties of the clustering data, which is common for high dimensional data. In this paper, we introduce the classic manifold learning method, the Local Linear Embedding (LLE), to learn the non-linear structure underlying the data and use the learned local geometry of manifold as a regularization for SSC and LRR, which results the proposed LLE-SSC and LLE-LRR clustering methods. Additionally, to solve the complex optimization problem involved in the proposed models, an efficient algorithm is also proposed. We test the proposed data clustering methods on several types of public databases. The experimental results show that our methods outperform typical subspace clustering methods with Laplacian graph constraint.

High dimension and complexity of network high-dimensional data lead to poor feature selection effect network high-dimensional data. To effectively solve this problem, feature selection algorithms for high-dimensional network data based on supervised discriminant projection (SDP) have been designed. The sparse representation problem of high-dimensional network data is transformed into an Lp norm optimization problem, and the sparse subspace clustering method is used to cluster high-dimensional network data. Dimensionless processing is carried out for the clustering processing results. Based on the linear projection matrix and the best transformation matrix, the dimensionless processing results are reduced by combining the SDP. The sparse constraint method is used to achieve feature selection of high-dimensional data in the network, and the relevant feature selection results are obtained. The experimental findings demonstrate that the suggested algorithm can effectively cluster seven different types of data and converges when the number of iterations approaches 24. The F1 value, recall, and precision are all kept at high levels. High-dimensional network data feature selection accuracy on average is 96.9%, and feature selection time on average is 65.1 milliseconds. The selection effect for network high-dimensional data features is good.