Large-Scale Manifold Learning by Semidefinite Facial Reduction
نویسنده
چکیده
The problem of nonlinear dimensionality reduction is often formulated as a semidefinite programming (SDP) problem. However, only SDP problems of limited size can be directly solved directly using current SDP solvers. To overcome this difficulty, we propose a novel SDP formulation for dimensionality reduction based on semidefinite facial reduction that significantly reduces the number of variables and constraints of the SDP problem, allowing us to solve very large manifold learning problems. Moreover, our reduction is exact, so we obtain high quality solutions without the need for post-processing by local gradient descent search methods, as is often required by other SDP-based methods for manifold learning.
منابع مشابه
بهبود مدل تفکیککننده منیفلدهای غیرخطی بهمنظور بازشناسی چهره با یک تصویر از هر فرد
Manifold learning is a dimension reduction method for extracting nonlinear structures of high-dimensional data. Many methods have been introduced for this purpose. Most of these methods usually extract a global manifold for data. However, in many real-world problems, there is not only one global manifold, but also additional information about the objects is shared by a large number of manifolds...
متن کاملBILGO: Bilateral greedy optimization for large scale semidefinite programming
Many machine learning tasks (e.g. metric and manifold learning problems) can be formulated as convex semidefinite programs. To enable the application of these tasks on a large-scale, scalability and computational efficiency are considered desirable properties for a practical semidefinite programming algorithm. In this paper, we theoretically analyse a new bilateral greedy optimization(denoted B...
متن کاملAlgorithms for manifold learning
Manifold learning is a popular recent approach to nonlinear dimensionality reduction. Algorithms for this task are based on the idea that the dimensionality of many data sets is only artificially high; though each data point consists of perhaps thousands of features, it may be described as a function of only a few underlying parameters. That is, the data points are actually samples from a low-d...
متن کاملVideo Subject Inpainting: A Posture-Based Method
Despite recent advances in video inpainting techniques, reconstructing large missing regions of a moving subject while its scale changes remains an elusive goal. In this paper, we have introduced a scale-change invariant method for large missing regions to tackle this problem. Using this framework, first the moving foreground is separated from the background and its scale is equalized. Then, a ...
متن کاملMaximum Covariance Unfolding : Manifold Learning for Bimodal Data
We propose maximum covariance unfolding (MCU), a manifold learning algorithm for simultaneous dimensionality reduction of data from different input modalities. Given high dimensional inputs from two different but naturally aligned sources, MCU computes a common low dimensional embedding that maximizes the cross-modal (inter-source) correlations while preserving the local (intra-source) distance...
متن کامل