Multiple Flat Projections for Cross-Manifold Clustering
ABSTARCT :
Cross-manifold clustering is an extreme challenge learning problem. Since the low-density hypothesis is not satisfied in cross-manifold problems, many traditional clustering methods failed to discover the cross-manifold structures. In this article, we propose multiple flat projections clustering (MFPC) for cross-manifold clustering. In our MFPC, the given samples are projected into multiple localized flats to discover the global structures of implicit manifolds. Thus, the intersected clusters are distinguished in various projection flats. In MFPC, a series of nonconvex matrix optimization problems is solved by a proposed recursive algorithm. Furthermore, a nonlinear version of MFPC is extended via kernel tricks to deal with a more complex cross-manifold learning situation. The synthetic tests show that our MFPC works on the cross-manifold structures well. Moreover, experimental results on the benchmark datasets and object tracking videos show excellent performance of our MFPC compared with some state-of-the-art manifold clustering methods.
EXISTING SYSTEM :
? It should be noted, that, unlike tensor voting, local PCA cannot be used to refine these estimates or take advantage of existing orientation estimates that may be available at the inputs.
? The main assumption is that some form of smoothness exists in the data and unobserved outputs can be predicted from previously observed outputs for similar inputs.
? The distinction between low and high-dimensional spaces is necessary, since highly specialized methods for low-dimensional cases exist in the literature.
? Our approach is local, nonparametric and has a weak prior model of smoothness, which is implemented in the form of votes that communicate a point’s preferred orientation to its neighbors.
DISADVANTAGE :
? In this paper, we proposed a novel flat-type method named Multiple Flat Projections Clustering (MFPC) for crossmanifold problems.
? The non-convex matrix optimization problems in our MFPC are decomposed into several non-convex vector optimization problems by a recursive algorithm, and the latter problems are solved by a proposed iterative algorithm of which the convergence is also given.
? To further investigate the ability to handle cross-manifold problem, we tested these methods on a nonlinear cross-manifold “Sine2” dataset, where the samples were from two sine functions and they intersected with each other.
? The above tests illustrate the ability of our MFPC to handle some cross-manifold problems.
PROPOSED SYSTEM :
• The major contribution of this approach is that it proposes a global, isometric method, which, unlike Isomap, can be applied to non-convex data sets.
• Linear patches, areas of curvature and noise can be distinguished using the proposed measure.
• One could find multiple nearest neighbors, run the proposed algorithm starting from each of them and produce a multi-valued answer with a probability associated with each potential output value.
• One can view the proposed approach as learning data from a single class, which can serve as the groundwork for an approach for pattern recognition, data mining, supervised and unsupervised classification.
ADVANTAGE :
? Some synthetic and benchmark datasets show the amazing performance of our MFPC compared with some state-of-the art clustering methods.
? We analyze the performance of our MFPC compared with kmeans, SMMC, kPC, kPPC, LkPPC, TWSVC, kFC and LkFC on some synthetic and benchmark datasets.
? However, on the other six datasets, one should carefully select the parameters to achieve the best performance.
? Thus, an appropriate feature space, which actually improve the performance of nonlinear MFPC, has the precedence in parameter selection.
? In these methods, some subtle techniques were used to distinguish the different manifold s from the intersections.
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