标题: | 基于互相干性考量于杂讯干扰下以匹配追求群分稀疏子空间 之效能保证 Coherence-Based Performance Guarantees for Noisy Sparse Subspace Clustering using Matching Pursuit |
作者: | 林晏平 吴卓谕 Lin, Yen-Ping Wu, Jwo-Ywh 电信工程研究所 |
关键字: | 稀疏性表示;群分稀疏子空间;脸部辨识;谱分群;(正交)匹配追求;sparse representation;spectral clustering;(orthogonal) matching pursuit;sparse subspace clustering;face recognition |
公开日期: | 2017 |
摘要: | 本硕士论文是压缩式感测(Compressive Sensing, CS)的概念与演算法应用于群分稀疏子空间(Sparse Subspace)上的一个研究,让每笔资料与其他少量资料建立关联性,并藉此关联性达成分群之目的,且已有相当多研究发现此关联性具有某种程度上的稀疏性时,可以有一定程度的分群效果。 在本硕士论文中,我们讨论归一化的资料落在某些子空间之联集上并且加上有界之杂讯,希望在子空间的资讯全然未知的情形下,可以同时把资料妥善分群并且让每群资料大致上落在其中一个子空间附近,我们考虑以匹配追求(Matching Pursuit, MP)与正交匹配追求(Orthogonal Matching Pursuit, OMP)取代运算复杂度较高的 最小化重建方法来建构资料间的关联性,透过这些数值化的关联性,可以由谱分群(Spectral Clustering)来分离出每群比较可能落在相同子空间的资料。 基于一些几何的基础,我们进行演算法的分析且得到基于互相干性考量下的效能保证,而从模拟中亦可观察到这两种演算法皆有一定程度的稳健度,并且应用于脸部辨识时也会有不错的表现。 High-dimensional signal processing is ubiquitous in many areas of applications. Often, high-dimensional data lie close to some low-dimensional structures corresponding to several classes or categories. In this paper, we consider noisy data points lie close to union of some unknown low-dimensional subspaces. Following the MP and OMP based sparse subspaces clustering proposed by Tschannen and Bölcskei, we construct sparse representation for each data under bounded noise assumption. Then spectral clustering can be used to separate the data that each group is likely to fall on the same subspace. Based on some geometric structures, we analyze the algorithms and obtain coherence-based performance guarantees. Simulations show that these two algorithms not only have certain degree of robustness but also have nice performance in face recognition. |
URI: | http://etd.lib.nctu.edu.tw/cdrfb3/record/nctu/#GT070460218 http://hdl.handle.net/11536/142738 |
显示于类别: | Thesis |