At the heart of unsupervised clustering and semi-supervised clustering is the calculation of matrix eigenvalues(eigenvectors) or matrix inversion. In generally, its complexity is O(N). By using Krylov Subspace Methods and Fast Methods, we improve the performance to O(NlogN). We also make a thorough evaluation of errors introduced by the fast algorithm.

Face recognition is a typical problem of pattern recognition and machine learning. Among these approaches to the problem of face recognition, subspace analysis gives the most promising results, and becomes one of the most popular methods. This paper researches typical subspace analysis approaches, based on the introduction of main approaches of linear subspace analysis, such as Principal Compon...

Yi = f(xi) + εi = g(Θ >xi) + εi, i = 1, . . . , n, is addressed. In the general setup we are interested in, the covariates xi ∈ R, Θ is a d×m orthogonal matrix (ΘΘ = Im∗) and g : R ∗ → R is an unknown function. To be able to estimate Π consistently, we assume that S = Im(Θ) is the smallest subspace satisfying f(xi) = f(ΠSxi), ∀i = 1, . . . , n, where ΠS stands for the orthogonal projector in R ...

Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [25] to cluster noisy data, and develops some novel theory demonstrating its correctness. In particular, the theory uses ideas from geometric functional analysi...

We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the optimal semiparametric efficiency bound...

It is well-known that traditional clustering methods considering all dimensions of the feature space usually fail in terms of efficiency and effectivity when applied to high-dimensional data. This poor behavior is based on the fact that clusters may not be found in the high-dimensional feature space, although clusters exist in subspaces of the feature space. To overcome these limitations of tra...

The ESPRIT algorithm is suitable for parametric channel estimation of slow varying channel of OFDM system. In this algorithm, the subspace decomposition technology is usually first used to estimate the multipath delay information of the channel, and then the channel is reconstructed through the estimate of the multipath delay information. This paper focuses on fast subspace tracking technology,...