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Instead of finding clusters in the full feature space, subspace clustering is an emergent task which aims at detecting clusters embedded in subspaces. Most of previous works in the literature are density-based approaches, where a cluster is regarded as a high-density region in a subspace. However, the identification of dense regions in previous works lacks of considering a critical problem, called "the density divergence problem" in this paper, which refers to the phenomenon that the region densities vary in different subspace cardinalities. Without considering this problem, previous works utilize a density threshold to discover the dense regions in all subspaces, which incurs the serious loss of clustering accuracy (either recall or precision of the resulting clusters) in different subspace cardinalities. To tackle the density divergence problem, in this paper, we devise a novel subspace clustering model to discover the clusters based on the relative region densities in the subspaces, where the clusters are regarded as regions whose densities are relatively high as compared to the region densities in a subspace. Based on this idea, different density thresholds are adaptively determined to discover the clusters in different subspace cardinalities. Due to the infeasibility of applying previous techniques in this novel clustering model, we also devise an innovative algorithm, referred to as DENCOS (DENsity COnscious Subspace clustering), to adopt a divide-and-conquer scheme to efficiently discover clusters satisfying different density thresholds in different subspace cardinalities. As validated by our extensive experiments on various data sets, DENCOS can discover the clusters in all subspaces with high quality, and the efficiency of DENCOS outperformes previous works. [ABSTRACT FROM AUTHOR]

In this paper, we first study an important but unsolved dilemma in the literature of subspace clustering, which is referred to as "information overlapping-data coverage" challenge. Current solutions of subspace clustering usually invoke a grid-based Apriori-like procedure to identify dense regions and construct subspace clusters afterward. Due to the nature of monotonicity property in Apriori- like procedures, it is inherent that if a region is identified as dense, all its projected regions are also identified as dense, causing overlapping/redundant clustering information to be inevitably reported to users when generating clusters from such highly correlated regions. However, naive methods to filter redundant clusters will incur a challenging problem in the other side of the dilemma, called the "data coverage" issue. Note that two clusters may have highly correlated dense regions but their data members could be highly different to each other. Arbitrarily removing one of them may lose the coverage of data with clustering information, thus likely reporting an incomplete and biased clustering result. In this paper, therefore, we further propose an innovative algorithm, called "NOnRedundant Subspace Cluster mining" (NORSC), to efficiently discover a succinct collection of subspace clusters while also maintaining the required degree of data coverage. NORSC not only avoids generating the redundant clusters with most of the contained data covered by higher dimensional clusters to resolve the information overlapping problem but also limits the information loss to cope with the data coverage problem. As shown by our experimental results, NORSC is very effective in identifying a concise and small set of subspace clusters, while incurring time complexity in orders of magnitude better than that of previous works. [ABSTRACT FROM AUTHOR]

Automatic extraction of vertebra regions from a spinal magnetic resonance (MR) image is normally required as the first step to an intelligent spinal MR image diagnosis system. In this work, we develop a fully automatic vertebra detection and segmentation system, which consists of three stages; namely, AdaBoost-based vertebra detection, detection refinement via robust curve fitting, and vertebra segmentation by an iterative normalized cut algorithm. In order to produce an efficient and effective vertebra detector, a statistical learning approach based on an improved AdaBoost algorithm is proposed. A robust estimation procedure is applied on the detected vertebra locations to fit a spine curve, thus refining the above vertebra detection results. This refinement process involves removing the false detections and recovering the miss-detected vertebrae. Finally, an iterative normalized-cut segmentation algorithm is proposed to segment the precise vertebra regions from the detected vertebra locations. In our implementation, the proposed AdaBoost-based detector is trained from 22 spinal MR volume images. The experimental results show that the proposed vertebra detection and segmentation system can achieve nearly 98% vertebra detection rate and 96% segmentation accuracy on a variety of testing spinal MR images. Our experiments also show the vertebra detection and segmentation accuracies by using the proposed algorithm are superior to those of the previous representative methods. The proposed vertebra detection and segmentation system is proved to be robust and accurate so that it can be used for advanced research and application on spinal MR images. [ABSTRACT FROM AUTHOR]