Agent-Based Subspace Clustering

High dimensional data is a phenomenon in real-world data mining applications. Text data is a typical example. In text mining, a text document is viewed as a vector of terms whose dimension is equal to the total number of unique terms in a data set, which is usually in thousands. High dimensional data occurs in business as well. In retails, for example, to effectively manage supplier relationship, suppliers are often categorized according to their business behaviors (Zhang, Huang, Qian, Xu, & Jing, 2006). The supplier’s behavior data is high dimensional, which contains thousands of attributes to describe the supplier’s behaviors, including product items, ordered amounts, order frequencies, product quality and so forth. One more example is DNA microarray data. Clustering high-dimensional data requires special treatment (Swanson, 1990; Jain, Murty, & Flynn, 1999; Cai, He, & Han, 2005; Kontaki, Papadopoulos & Manolopoulos., 2007), although various methods for clustering are available (Jain & Dubes, 1988). One type of clustering methods for high dimensional data is referred to as subspace clustering, aiming at finding clusters from subspaces instead of the entire data space. In a subspace clustering, each cluster is a set of objects identified by a subset of dimensions and different clusters are represented in different subsets of dimensions. Soft subspace clustering considers that different dimensions make different contributions to the identification of objects in a cluster. It represents the importance of a dimension as a weight that can be treated as the degree of the dimension in contribution to the cluster. Soft subspace clustering can find the cluster memberships of objects and identify the subspace of each cluster in the same clustering process.

Subspace clustering has important and wide applications in computer vision and pattern recognition. It is a challenging task to learn low-dimensional subspace structures due to the possible errors (e.g., noise and corruptions) existing in high-dimensional data. Recent subspace clustering methods usually assume a sparse representation of corrupted errors and correct the errors iteratively. However large corruptions in real-world applications can not be well addressed by these methods. A novel optimization model for robust subspace clustering is proposed in this paper. The objective function of our model mainly includes two parts. The first part aims to achieve a sparse representation of each high-dimensional data point with other data points. The second part aims to maximize the correntropy between a given data point and its low-dimensional representation with other points. Correntropy is a robust measure so that the influence of large corruptions on subspace clustering can be greatly suppressed. An extension of our method with explicit introduction of representation error terms into the model is also proposed. Half-quadratic minimization is provided as an efficient solution to the proposed robust subspace clustering formulations. Experimental results on Hopkins 155 dataset and Extended Yale Database B demonstrate that our method outperforms state-of-the-art subspace clustering methods.

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.

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

Recently, many data mining techniques were revisited to cope with the new big data challenges. Nearly all of these algorithms considered the efficiency of the mining algorithm to survive the increasing size of the data. However, as the dimensionality of the data increases, not only the efficiency but also the effectiveness of traditional mining algorithms is compromised. For instance, clusters hidden in some subspaces are hard to be detected using traditional clustering algorithms, as the dimensionality of the data increases. In this paper, we consider both the huge size, and the high dimensionality of big data by providing a novel solution that presents a three-phase model for subspace stream clustering algorithms. Our novel model, overcomes the huge size of the big data in its first phase, by continuously applying a streaming concept over the huge data objects, and summarizing them into micro-clusters. Then, after each certain batch of data, or after upon a user request, the second phase is applied over the data summarized in micro-clusters, to reconstruct the current distribution of the data out of the current summaries. In the third phase, a subspace clustering algorithm is applied to overcome the high dimensionality of the data, and to find hidden clusters within some subspace. An extensive evaluation study over different scenarios that follow our model over a big data set is performed.KeywordsSubspace stream clusteringStreaming big dataReal-time streaming analysis of big data

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

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.

Clustering in high dimensional data is an important task. Subspace clustering has emerged as a possible solution to the challenges associated with high dimensional clustering. A subspace cluster is a subset of points together with a subset of attributes, such that some category of value of cluster points has great aggregation in these attributes. This paper proposes a subspace clustering algorithm which follows the bottom-up strategy, evaluating each dimension separately and then using only those dimensions with great aggregation in further steps. Experimental results on synthetic data show that presented algorithm scales linearly with the number of the attributes and has good scalability as the size of the data objects is increased.

Advances made to the traditional clustering algorithms solves the various problems such as curse of dimensionality and sparsity of data for multiple attributes. The traditional H-K clustering algorithm can solve the randomness and apriority of the initial centers of K-means clustering algorithm. But when we apply it to high dimensional data it causes the dimensional disaster problem due to high computational complexity. All the advanced clustering algorithms like subspace and ensemble clustering algorithms improve the performance for clustering high dimension dataset from different aspects in different extent. Still these algorithms will improve the performance form a single perspective. The objective of the proposed model is to improve the performance of traditional H-K clustering and overcome the limitations such as high computational complexity and poor accuracy for high dimensional data by combining the three different approaches of clustering algorithm as subspace clustering algorithm and ensemble clustering algorithm with H-K clustering algorithm.

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

Block-diagonal structure learning for subspace clustering

Video co-segmentation refers to the task of jointly segmenting common objects appearing in a given group of videos. In practice, high-dimensional data such as videos can be conceptually thought as being drawn from a union of subspaces corresponding to categories rather than from a smooth manifold. Therefore, segmenting data into respective subspaces --- subspace clustering --- finds widespread applications in computer vision, including co-segmentation. State-of-the-art methods via subspace clustering seek to solve the problem in two steps: First, an affinity matrix is built from data, with appearance features or motion patterns. Second, the data are segmented by applying spectral clustering to the affinity matrix. However, this process is insufficient to obtain an optimal solution since it does not take into account the {\em interdependence} of the affinity matrix with the segmentation. In this work, we present a novel unified video co-segmentation framework inspired by the recent Structured Sparse Subspace Clustering ($\mathrm{S^{3}C}$) based on the {\em self-expressiveness} model. Our method yields more consistent segmentation results. In order to improve the detectability of motion features with missing trajectories due to occlusion or tracked points moving out of frames, we add an extra-dimensional signature to the motion trajectories. Moreover, we reformulate the $\mathrm{S^{3}C}$ algorithm by adding the affine subspace constraint in order to make it more suitable to segment rigid motions lying in affine subspaces of dimension at most $3$. Our experiments on MOViCS dataset show that our framework achieves the highest overall performance among baseline algorithms and demonstrate its robustness to heavy noise.

Subspace clustering by directly solving Discriminative K-means

Nonlinear subspace clustering by functional link neural networks

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.