We introduce the Neural Collaborative Subspace Clustering, a neural model that discovers clusters of data points drawn from a union of low-dimensional subspaces. In contrast to previous attempts, our model runs without the aid of spectral clustering. This makes our algorithm one of the kinds that can gracefully scale to large datasets. At its heart, our neural model benefits from a classifier which determines whether a pair of points lies on the same subspace or not. Essential to our model is the construction of two affinity matrices, one from the classifier and the other from a notion of subspace self-expressiveness, to supervise training in a collaborative scheme. We thoroughly assess and contrast the performance of our model against various state-of-the-art clustering algorithms including deep subspace-based ones.
In learning theory, distinguishing outliers and noisy samples from clean ones to facilitate training is an active research topic. For example, Random Sample Consensus (RANSAC) @cite_40 is a classical and well-received algorithm for fitting a model to a cloud of points corrupted by noise. Employing RANSAC on subspaces @cite_55 in large-scale problems does not seem to be the right practice, as RANSAC requires a large number of iterations to achieve an acceptable fit.
@cite_55 @cite_40
2085261163 2314497771 2168104347 2207085776
A new paradigm, Random Sample Consensus (RANSAC), for fitting a model to experimental data is introduced. RANSAC is capable of interpreting smoothing data containing a significant percentage of gross errors, and is thus ideally suited for applications in automated image analysis where interpretation is based on the data provided by error-prone feature detectors. A major portion of this paper describes the application of RANSAC to the Location Determination Problem (LDP): Given an image depicting a set of landmarks with known locations, determine that point in space from which the image was obtained. In response to a RANSAC requirement, new results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form. These results provide the basis for an automatic system that can solve the LDP under difficult viewing This paper presents a novel improved RANSAC algorithm based on probability and DS evidence theory to deal with the robust pose estimation in robot 3D map building. In this proposed RANSAC algorithm, a parameter model is estimated by using a random sampling test set. Based on this estimated model, all points are tested to evaluate the fitness of current parameter model and their probabilities are updated by using a total probability formula during the iterations. The maximum size of inlier set containing the test point is taken into account to get a more reliable evaluation for test points by using DS evidence theory. Furthermore, the theories of forgetting are utilized to filter out the unstable inliers and improve the stability of the proposed algorithm. In order to boost a high performance, an inverse mapping sampling strategy is adopted based on the updated probabilities of points. Both the simulations and real experimental results demonstrate the feasibility and effectiveness of the proposed algorithm. The Random Sample Consensus (RANSAC) algorithm is a popular tool for robust estimation problems in computer vision, primarily due to its ability to tolerate a tremendous fraction of outliers. There have been a number of recent efforts that aim to increase the efficiency of the standard RANSAC algorithm. Relatively fewer efforts, however, have been directed towards formulating RANSAC in a manner that is suitable for real-time implementation. The contributions of this work are two-fold: First, we provide a comparative analysis of the state-of-the-art RANSAC algorithms and categorize the various approaches. Second, we develop a powerful new framework for real-time robust estimation. The technique we develop is capable of efficiently adapting to the constraints presented by a fixed time budget, while at the same time providing accurate estimation over a wide range of inlier ratios. The method shows significant improvements in accuracy and speed over existing techniques. Robust estimation of model parameters in the presence of outliers is a key problem in computer vision. RANSAC inspired techniques are widely used in this context, although their application might be limited due to the need of a priori knowledge on the inlier noise level. We propose a new approach for jointly optimizing over model parameters and the inlier noise level based on the likelihood ratio test. This allows control over the type I error incurred. We also propose an early bailout strategy for efficiency. Tests on both synthetic and real data show that our method outperforms the state-of-the-art in a fraction of the time.