Certainty of outlier and boundary points processing in data mining

Data certainty is one of the issues in the real-world applications which is caused by unwanted noise in data. Recently, more attentions have been paid to overcome this problem. We proposed a new method based on neutrosophic set (NS) theory to detect boundary and outlier points as challenging points in clustering methods. Generally, firstly, a certainty value is assigned to data points based on the proposed definition in NS. Then, certainty set is presented for the proposed cost function in NS domain by considering a set of main clusters and noise cluster. After that, the proposed cost function is minimized by gradient descent method. Data points are clustered based on their membership degrees. Outlier points are assigned to noise cluster and boundary points are assigned to main clusters with almost same membership degrees. To show the effectiveness of the proposed method, two types of datasets including 3 datasets in Scatter type and 4 datasets in UCI type are used. Results demonstrate that the proposed cost function handles boundary and outlier points with more accurate membership degrees and outperforms existing state of the art clustering methods.Comment: Conference Paper, 6 page

Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies

In motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data, in order to describe motion patterns in a compact way, and to discriminate between them. In an unsupervised context, i.e., no prior model of the moving object(s) is available, such a structure has to be learned from the data in a bottom-up fashion. In recent times, volumetric approaches in which the motion is captured from a number of cameras and a voxel-set representation of the body is built from the camera views, have gained ground due to attractive features such as inherent view-invariance and robustness to occlusions. Automatic, unsupervised segmentation of moving bodies along entire sequences, in a temporally-coherent and robust way, has the potential to provide a means of constructing a bottom-up model of the moving body, and track motion cues that may be later exploited for motion classification. Spectral methods such as locally linear embedding (LLE) can be useful in this context, as they preserve "protrusions", i.e., high-curvature regions of the 3D volume, of articulated shapes, while improving their separation in a lower dimensional space, making them in this way easier to cluster. In this paper we therefore propose a spectral approach to unsupervised and temporally-coherent body-protrusion segmentation along time sequences. Volumetric shapes are clustered in an embedding space, clusters are propagated in time to ensure coherence, and merged or split to accommodate changes in the body's topology. Experiments on both synthetic and real sequences of dense voxel-set data are shown. This supports the ability of the proposed method to cluster body-parts consistently over time in a totally unsupervised fashion, its robustness to sampling density and shape quality, and its potential for bottom-up model constructionComment: 31 pages, 26 figure

Automatic Image Segmentation by Dynamic Region Merging

This paper addresses the automatic image segmentation problem in a region merging style. With an initially over-segmented image, in which the many regions (or super-pixels) with homogeneous color are detected, image segmentation is performed by iteratively merging the regions according to a statistical test. There are two essential issues in a region merging algorithm: order of merging and the stopping criterion. In the proposed algorithm, these two issues are solved by a novel predicate, which is defined by the sequential probability ratio test (SPRT) and the maximum likelihood criterion. Starting from an over-segmented image, neighboring regions are progressively merged if there is an evidence for merging according to this predicate. We show that the merging order follows the principle of dynamic programming. This formulates image segmentation as an inference problem, where the final segmentation is established based on the observed image. We also prove that the produced segmentation satisfies certain global properties. In addition, a faster algorithm is developed to accelerate the region merging process, which maintains a nearest neighbor graph in each iteration. Experiments on real natural images are conducted to demonstrate the performance of the proposed dynamic region merging algorithm.Comment: 28 pages. This paper is under review in IEEE TI