一種基于低秩表示的子空間聚類改進(jìn)算法

張濤; 唐振民; 呂建勇

doi:10.11999/JEIT160009

一種基于低秩表示的子空間聚類改進(jìn)算法

doi: 10.11999/JEIT160009

基金項(xiàng)目:

國(guó)家自然科學(xué)基金(61473154)

計(jì)量
- 文章訪問數(shù): 1476
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- 被引次數(shù): 0
出版歷程
- 收稿日期: 2016-01-04
- 修回日期: 2016-05-12
- 刊出日期: 2016-11-19

Improved Algorithm Based on Low Rank Representation for Subspace Clustering

Funds:

The National Natural Science Foundation of China (61473154)

摘要

摘要: 該文針對(duì)現(xiàn)有的基于低秩表示的子空間聚類算法使用核范數(shù)來代替秩函數(shù)，不能有效地估計(jì)矩陣的秩和對(duì)高斯噪聲敏感的缺陷，提出一種改進(jìn)的算法，旨在提高算法準(zhǔn)確率的同時(shí)，保持其在高斯噪聲下的穩(wěn)定性。在構(gòu)建目標(biāo)函數(shù)時(shí)，使用系數(shù)矩陣的核范數(shù)和Forbenius范數(shù)作為正則項(xiàng)，對(duì)系數(shù)矩陣的奇異值進(jìn)行強(qiáng)凸的正則化后，采用非精確的增廣拉格朗日乘子方法求解，最后對(duì)求得的系數(shù)矩陣進(jìn)行后處理得到親和矩陣，并采用經(jīng)典的譜聚類方法進(jìn)行聚類。在人工數(shù)據(jù)集、Extended Yale B數(shù)據(jù)庫和PIE數(shù)據(jù)庫上同流行的子空間聚類算法的實(shí)驗(yàn)對(duì)比證明了所提改進(jìn)算法的有效性和對(duì)高斯噪聲的魯棒性。
- 子空間聚類 /
- 低秩表示 /
- 秩函數(shù) /
- Forbenius范數(shù) /
- 增廣拉格朗日乘子法
Abstract: The nuclear norm is used to replace the rank function in the subspace clustering algorithm based on low rank representation, it can not estimate the rank of the matrix effectively and it is sensitive to Gauss noise. In this paper, a novel algorithm is proposed to improve the accuracy and maintain its stability under the Gauss noise. When building the objective function, the nuclear norm and Forbenius norm of coefficient matrix are used as the regularization terms, after a strong convex regularizer over singular values of coefficient matrix, an inexact augmented Lagrange multiplier method is utilized to solve the problem. Finally, the affinity matrix is acquired by post-processing of coefficient matrix and the classical spectral clustering method is employed to clustering. The experimental comparison results between the state-of-the-art algorithms on synthetic data, Extended Yale B and PIE datasets demonstrate the effectiveness of the proposed improved method and the robustness to Gauss noise.
- Subspace clustering /
- Low rank representation /
- Rank function /
- Forbenius norm /
- Augmented Lagrange multiplier method

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