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
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We study the problem of estimating a mixed geometric model of multiple subspaces in the presence of a significant amount of outliers. The estimation of multiple subspaces is an important problem in computer vision, particularly for segmenting multiple motions in an image sequence. We first provide a comprehensive survey of robust statistical techniques in the literature, and identify three main approaches for detecting and rejecting outliers. Through a careful examination of these approaches, we propose and investigate three principled methods for robustly estimating mixed subspace models: random sample consensus, the influence function, and multivariate trimming. Using a benchmark synthetic experiment and a set of real image sequences, we conduct a thorough comparison of the three methods 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