基于L1-范數(shù)的二維線性判別分析
doi: 10.11999/JEIT141093
基金項(xiàng)目:
國(guó)家自然科學(xué)基金(61202228)和安徽省高校自然科學(xué)研究重點(diǎn)項(xiàng)目(KJ2012A004)資助課題
L1-norm Based Two-dimensional Linear Discriminant Analysis
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摘要: 為了避免圖像數(shù)據(jù)向量化后的維數(shù)災(zāi)難問(wèn)題,以及增強(qiáng)對(duì)野值(outliers)及噪聲的魯棒性,該文提出一種基于L1-范數(shù)的2維線性判別分析(L1-norm-based Two-Dimensional Linear Discriminant Analysis, 2DLDA-L1)降維方法。它充分利用L1-范數(shù)對(duì)野值及噪聲的強(qiáng)魯棒性,并且直接在圖像矩陣上進(jìn)行投影降維。該文還提出一種快速迭代優(yōu)化算法,并給出了其單調(diào)收斂到局部最優(yōu)的證明。在多個(gè)圖像數(shù)據(jù)庫(kù)上的實(shí)驗(yàn)驗(yàn)證了該方法的魯棒性與高效性。
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關(guān)鍵詞:
- 圖像處理 /
- L1-范數(shù) /
- 2維線性判別分析 /
- 線性投影 /
- 降維
Abstract: To overcome the curse of dimensionality caused by vectorization of image matrices, and to increase robustness to outliers, L1-norm based Two-Dimensional Linear Discriminant Analysis (2DLDA-L1) is proposed for dimensionality reduction. It makes full use of strong robustness of L1-norm to outliers and noises. Furthermore, it performs dimensionality reduction directly on image matrices. A rapid iterative optimization algorithm, with its proof of monotonic convergence to local optimum, is given. Experiments on several public image databases verify the robustness and the effectiveness of the proposed method. -
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