An Improved Algorithm for Subspace Clustering Applied to Image Segmentation

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.

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.

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.

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.

Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, end-user comprehensibility of the results, non-presumption of any canonical data distribution, and insensitivity to the order of input records. We present CLIQUE, a clustering algorithm that satisfies each of these requirements. CLIQUE identifies dense clusters in subspaces of maximum dimensionality. It generates cluster descriptions in the form of DNF expressions that are minimized for ease of comprehension. It produces identical results irrespective of the order in which input records are presented and does not presume any specific mathematical form for data distribution. Through experiments, we show that CLIQUE efficiently finds accurate cluster in large high dimensional datasets.

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

The sparsity and the problem of the curse of dimensionality of high-dimensional data, which make the most of the traditional clustering algorithm, lose action in high-dimensional space. Therefore, clustering of data in high-dimensional space is becoming the hot research areas. By utilizing the subtractive clustering as initialized method, and combine with the revised clustering validation indices, this paper offers a subspace clustering algorithm for automatically determining the optimal number of clusters on high dimensional data. The experiment results show that the proposed clustering algorithm can get better cluster validation performance than that of conventional indices.

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

Dense community detection in multi-valued attributed networks

This paper proposes an outlier robust geodesic K-mean algorithm for high dimensional data. The proposed algorithm features three novel contributions. First, it employs a shared nearest neighbour (SNN) based distance metric to construct the nearest neighbour data model. Second, it combines the notion of geodesic distance to the well-known local outlier factor (LOF) model to distinguish outliers from inlier data. Third, it introduces a new ad-hoc strategy to integrate outlier scores into geodesic distances. Numerical experiments with synthetic and real world remote sensing spectral data show the efficiency of the proposed algorithm in clustering of high-dimensional data in terms of the overall clustering accuracy and the average precision.

Subspace clustering is the task of grouping objects based on mutual similarity in subspaces of the full-dimensional space.<br/>The INSCY algorithm extends the well-known density-based clustering algorithm DBSCAN. It finds dimensionality-unbiased non-redundant subspace clusters using a tree structure to speed up the processing of subspaces. Still, finding density-based clusters in all subspaces implies an exponential search space in the number of dimensions. Thus, the running time of INSCY is still measured in hours on even small datasets of 2000 points. For larger datasets, it becomes prohibitively expensive.<br/><br/>To benefit from INSCY for real-world sized datasets, we propose a novel GPU-parallel approach that runs on standard graphics cards. To utilize the many cores of the GPU, we need new algorithmic strategies that fit the computational model of the GPU. While the GPU provides a large number of threads, traditional algorithms incur diverging threads and poor memory alignment, both of which lead to idle time and poor runtime performance. In INSCY, extracting subspace regions from the SCY-tree structure and the density-based clustering of regions itself are thus unfit for the GPU. <br/><br/>Our novel GPU-friendly algorithm GPU-INSCY computes the same subspace clustering as INSCY at dramatically reduced runtimes. <br/>To achieve this, we devise a restructured SCY-tree index-structure and associated operations for the GPU, as well as a GPU-parallel density-based subspace clustering.<br/><br/>We experimentally show that GPU-INSCY scales well with the size of the dataset and the number of dimensions, and improves the running time of INSCY by a factor of several thousand for large datasets of high dimensionality.

Dimension reduction has become an important tool for dealing with high dimensional data. Locally linear embedding (LLE) is a nonlinear dimension reduction method which can preserve local configurations of nearest neighbors. However, finding the nearest neighbors requires the definition of a distance measure, which is a critical step in LLE. In this paper, the Rank-order distance measure is used to substitute the traditional Euclidean distance measure in order to find better nearest neighbor candidates for preserving local configurations of the manifolds. The Rank-order distance between the data points is calculated using their neighbors’ ranking orders, and is shown to be able to improve the clustering of high dimensional data. The proposed method is called Rank-order based LLE (RLLE). The RLLE method is evaluated by comparing with the original LLE, ISO-LLE and IED-LLE on two handwritten datasets. It is shown that the effectiveness of a distance measure in the LLE method is closely related to whether it can be used to find good nearest neighbors. The experimental results show that the proposed RLLE method can improve the process of dimension reduction effectively, and C-index is another good candidate for evaluating the dimension reduction results.

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

Fuzzy weighted C-ordered means clustering algorithm

With the rapid development of hardware and software technology, modern industry has produced a large amount of high-dimensional unlabeled data, such as pictures and videos. As clusters of these data sets may exist in some subspaces, traditional algorithms are no longer applicable. The related algorithms based on sparse subspace can find clusters in the subspace, which solves the problem of high data dimension. However, their clustering process based on only one single feature, which results in their performance being particularly sensitive to this single view. Affected by the integrated algorithm, a large number of multi-view methods began to emerge. These methods improve the clustering performance by integrating the subspace expressions of multiple views, but the problem is that the complementary information of multiple views cannot be fully considered. In addition, the problem of non-uniform distribution in clusters also exists in high-dimensional data sets. In this paper, based on the multi-view subspace clustering method, a clustering algorithm based on tensor low rank expression is proposed to solve the clustering problem of high-dimensional datasets. On the one hand, this paper solves the problem of noise and data corruption by combining the method of $\ell _{2,1} $ norms, which transform the optimization problem of solving multi-view subspace expression into a low-rank expression problem of tensor to fully consider the complementarities between views. On the other hand, the proposed scheme solves the problem of non- uniform distribution in clusters in high-dimensional data by combining with the density peak algorithm based on hierarchical strategy. Experiment results show the effectiveness of the algorithm.