Existing Subspace Clustering Algorithms Research Articles

Hyperspectral Image Processing in Internet of Things model using Clustering Algorithm

With the advent of technology, several domains have b on Internet of Things (IoT). The hyper spectral sensors present in earth observation system sends hyper spectral images (HSIs) to the cloud for further processing. Artificial intelligence (AI) models are used to analyse data in edge servers, resulting in a faster response time and reduced cost. Hyperspectral images and other high-dimensional image data may be analysed by using a core AI model called subspace clustering. The existing subspace clustering algorithms are easily affected by noise since they are constructed based on a single model. The representation coefficient matrix connectivity and sparsity is hardly balanced. In this paper, connectivity and sparsity factors are considered while proposing the subspace clustering algorithm with post-process strategy. A non-dominated sorting algorithm is used for that selection of close neighbours that are defined as neighbours with high coefficient and common neighbours. Further, pruning of useless, incorrect or reserved connections based on the coefficients between the close and sample neighbours are performed. Lastly, inter and intra subspace connections are reserved by the post-process strategy. In the field of IoT and image recognition, the conventional techniques are compared with the proposed post-processing strategies to verify its effectiveness and universality. The clustering accuracy may be improved in the IoT environment while processing the noise data using the proposed strategy as observed in the experimental results.

A meta-heuristic density-based subspace clustering algorithm for high-dimensional data

Subspace clustering is one of the efficient techniques for determining the clusters in different subsets of dimensions. Ideally, these techniques should find all possible non-redundant clusters in which the data point participates. Unfortunately, existing hard subspace clustering algorithms fail to satisfy this property. Additionally, with the increase in dimensions of data, classical subspace algorithms become inefficient. This work presents a new density-based subspace clustering algorithm (S_FAD) to overcome the drawbacks of classical algorithms. S_FAD is based on a bottom-up approach and finds subspace clusters of varied density using different parameters of the DBSCAN algorithm. The algorithm optimizes parameters of the DBCAN algorithm through a hybrid meta-heuristic algorithm and uses hashing concepts to discover all non-redundant subspace clusters. The efficacy of S_FAD is evaluated against various existing subspace clustering algorithms on artificial and real datasets in terms of F_Score and rand_index. Performance is assessed based on three parameters: average ranking, SRR ranking, and scalability on varied dimensions. Statistical analysis is performed through the Wilcoxon signed-rank test. Results reveal that S_FAD performs considerably better on the majority of the datasets and scales well up to 6400 dimensions on the actual dataset.

Subspace Clustering by Integrating Sparseness and Spatial-Closeness Priors

How to construct an effective sample affinity matrix is an important problem for subspace clustering, and most existing subspace clustering algorithms pursue the affinity matrix in a single space. In this paper, we propose a novel computational framework for subspace clustering, called Complementary Subspace Clustering (CSC) at first, where the affinity matrix is constructed in a pair of complementary spaces which provide different and complementary constraints on the affinity matrix. Many existing structural priors on self representation and dimensionality reduction can be seamlessly integrated into the CSC framework. Then under this framework, we explore a simple and effective subspace clustering algorithm by respectively introducing two basic priors - sparse representation and spatial closeness - into the referred pair of spaces. Moreover, a kernel variant of the proposed clustering algorithm is present. Extensive experimental results demonstrate that although only basic priors are involved, the explored algorithms from the CSC framework can improve the clustering performances significantly when the number of the sample classes is relatively big.

A Scalable Framework for Data-Driven Subspace Representation and Clustering

This paper considers the problem of subspace clustering which segments data samples into their underlying subspaces. While existing subspace clustering algorithms have been successfully applied to various problems, they are not applicable for large-scale or streaming data due to their expensive computational cost. As a remedy, we propose a unified scalable pipeline to reduce the complexity of all sub-tasks in subspace clustering. We first present a robust incremental summary representation, assuming that a subspace can be represented by sparse factors. Based on the summary representation, we propose a fully scalable learning pipeline by integrating the affinity learning task with post-processing and spectral clustering, such that the overall time complexity is linear in the number of samples. Moreover, the proposed framework is integrated with kernel methods for nonlinear subspace clustering. An extensive set of experimental studies demonstrate that the proposed framework gives an order-of-magnitude speed-up over existing subspace clustering baselines with competitive clustering performance.

Subspace Clustering via Good Neighbors.

Finding the informative subspaces of high-dimensional datasets is at the core of numerous applications in computer vision, where spectral-based subspace clustering is arguably the most widely studied method due to its strong empirical performance. Such algorithms first compute an affinity matrix to construct a self-representation for each sample using other samples as a dictionary. Sparsity and connectivity of the self-representation play important roles in effective subspace clustering. However, simultaneous optimization of both factors is difficult due to their conflicting nature, and most existing methods are designed to address only one factor. In this paper, we propose a post-processing technique to optimize both sparsity and connectivity by finding good neighbors. Good neighbors induce key connections among samples within a subspace and not only have large affinity coefficients but are also strongly connected to each other. We reassign the coefficients of the good neighbors and eliminate other entries to generate a new coefficient matrix. We show that the few good neighbors can effectively recover the subspace, and the proposed post-processing step of finding good neighbors is complementary to most existing subspace clustering algorithms. Experiments on five benchmark datasets show that the proposed algorithm performs favorably against the state-of-the-art methods with negligible additional computation cost.

Partial Sum Minimization of Singular Values Representation on Grassmann Manifolds

Clustering is one of the fundamental topics in data mining and pattern recognition. As a prospective clustering method, the subspace clustering has made considerable progress in recent researches, e.g., sparse subspace clustering (SSC) and low rank representation (LRR). However, most existing subspace clustering algorithms are designed for vectorial data from linear spaces, thus not suitable for high-dimensional data with intrinsic non-linear manifold structure. For high-dimensional or manifold data, few research pays attention to clustering problems. The purpose of clustering on manifolds tends to cluster manifold-valued data into several groups according to the mainfold-based similarity metric. This article proposes an extended LRR model for manifold-valued Grassmann data that incorporates prior knowledge by minimizing partial sum of singular values instead of the nuclear norm, namely Partial Sum minimization of Singular Values Representation (GPSSVR). The new model not only enforces the global structure of data in low rank, but also retains important information by minimizing only smaller singular values. To further maintain the local structures among Grassmann points, we also integrate the Laplacian penalty with GPSSVR. The proposed model and algorithms are assessed on a public human face dataset, some widely used human action video datasets and a real scenery dataset. The experimental results show that the proposed methods obviously outperform other state-of-the-art methods.

Summarisation of subspace clusters based on similarity connectedness

Subspace clustering is an emerging area which explores clusters of objects in various subspaces. The existing subspace clustering algorithms are computationally expensive as they generate a large number of possibly redundant subspace clusters limiting the interpretability of the results. The problem gets even worse with the increase in data's dimensionality. So, this demands for efficient summarisation framework that generates limited number of interesting subspace clusters. A novel algorithm, Similarity Connectedness Based clustering on subspace clusters (SCoC) is proposed to form natural grouping of lower-dimensional subspace clusters. The concept of similarity connectedness is introduced to group and merge the subspace clusters formed in different lower-dimensional subspaces leaping through the lattice of dimensions. The resulted compact and summarised high-dimensional subspace clusters would easily be interpreted for making sound decisions. The SCoC algorithm is thoroughly tested on various benchmark datasets and found that it outperforms PCoC and SUBCLU both in cluster quality and execution time.

Summarisation of subspace clusters based on similarity connectedness

Subspace clustering is an emerging area which explores clusters of objects in various subspaces. The existing subspace clustering algorithms are computationally expensive as they generate a large number of possibly redundant subspace clusters limiting the interpretability of the results. The problem gets even worse with the increase in data's dimensionality. So, this demands for efficient summarisation framework that generates limited number of interesting subspace clusters. A novel algorithm, Similarity Connectedness Based clustering on subspace clusters (SCoC) is proposed to form natural grouping of lower-dimensional subspace clusters. The concept of similarity connectedness is introduced to group and merge the subspace clusters formed in different lower-dimensional subspaces leaping through the lattice of dimensions. The resulted compact and summarised high-dimensional subspace clusters would easily be interpreted for making sound decisions. The SCoC algorithm is thoroughly tested on various benchmark datasets and found that it outperforms PCoC and SUBCLU both in cluster quality and execution time.

Subspace clustering based on latent low rank representation with Frobenius norm minimization

Abstract The problem of subspace clustering which refers to segmenting a collection of data samples approximately drawn from a union of linear subspaces is considered in this paper. Among existing subspace clustering algorithms, low rank representation (LRR) based subspace clustering is a very powerful method and has demonstrated that its performance is good. Latent low rank representation (LLRR) subspace clustering algorithm is an improvement of the original LRR algorithm when the observed data samples are insufficient. The clustering accuracy of LLRR is higher than that of LRR. Recently, Frobenius norm minimization based LRR algorithm has been proposed and its clustering accuracy is higher than that of LRR demonstrating the effectiveness of Frobenius norm as another convex surrogate of the rank function. Combining LLRR and Frobenius norm, a new low rank representation subspace clustering algorithm is proposed in this paper. The nuclear norm in the LLRR algorithm is replaced by the Frobenius norm. The resulting optimization problem is solved via alternating direction method of multipliers (ADMM). Experimental results show that compared with LRR, LLRR and several other state-of-the-art subspace clustering algorithms, the proposed algorithm can get higher clustering accuracy. Compared with LLRR, the running time of the proposed algorithm is reduced significantly.

VISA

To gain insight into today's large data resources, data mining extracts interesting patterns. To generate knowledge from patterns and benefit from human cognitive abilities, meaningful visualization of patterns are crucial. Clustering is a data mining technique that aims at grouping data to patterns based on mutual (dis)similarity. For high dimensional data, subspace clustering searches patterns in any subspace of the attributes as patterns are typically obscured by many irrelevant attributes in the full space. For visual analysis of subspace clusters, their comparability has to be ensured. Existing subspace clustering approaches, however, lack interactive visualization and show bias with respect to the dimensionality of subspaces. In this work, dimensionality unbiased subspace clustering and a novel distance function for subspace clusters are proposed. We suggest two visualization techniques that allow users to browse the entire subspace clustering, to zoom into individual objects, and to analyze subspace cluster characteristics in-depth. Bracketing of different parameter settings enable users to immediately see the effect of parameters on their data and hence to choose the best clustering result for further analysis. Usage of user analysis for feedback to the subspace clustering algorithm directly improves the subspace clustering. We demonstrate our visualization techniques on real world data and confirm results through additional accuracy measurements and comparison with existing subspace clustering algorithms.

Subspace clustering for high dimensional categorical data

Data clustering has been discussed extensively, but almost all known conventional clustering algorithms tend to break down in high dimensional spaces because of the inherent sparsity of the data points. Existing subspace clustering algorithms for handling high-dimensional data focus on numerical dimensions. In this paper, we designed an iterative algorithm called SUBCAD for clustering high dimensional categorical data sets, based on the minimization of an objective function for clustering. We deduced some cluster memberships changing rules using the objective function. We also designed an objective function to determine the subspace associated with each cluster. We proved various properties of this objective function that are essential for us to design a fast algorithm to find the subspace associated with each cluster. Finally, we carried out some experiments to show the effectiveness of the proposed method and the algorithm.