基于正則化的半監(jiān)督等距映射數(shù)據(jù)降維方法
doi: 10.11999/JEIT150694
基金項(xiàng)目:
浙江省自然科學(xué)基金(LZ14F030001, LY14F030009)
Data Dimensionality Reduction Method of Semi-supervised Isometric Mapping Based on Regularization
Funds:
Zhejiang Provincial Natural Science Foundation (LZ14F030001, LY14F030009)
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摘要: 針對(duì)等距映射(ISOMAP)算法無監(jiān)督，不能生成顯式映射函數(shù)等局限性，該文提出一種正則化的半監(jiān)督等距映射(Reg-SS-ISOMAP)算法。該算法首先利用訓(xùn)練樣本的標(biāo)簽樣本構(gòu)建K聯(lián)通圖(K-CG)，得到近似樣本間測(cè)地線距離，并作為矢量特征代替原始數(shù)據(jù)點(diǎn)；然后通過測(cè)地線距離計(jì)算核矩陣，用半監(jiān)督正則化方法代替多維尺度分析(MDS)算法處理矢量特征；最后利用正則化回歸模型構(gòu)建目標(biāo)函數(shù)，得到低維表示的顯式映射。算法在多個(gè)數(shù)據(jù)集上進(jìn)行了比較實(shí)驗(yàn)，結(jié)果表明，文中提出的算法降維效果穩(wěn)定，識(shí)別率高，顯示了算法的有效性。
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關(guān)鍵詞:
- 數(shù)據(jù)降維 /
- 流形學(xué)習(xí) /
- 半監(jiān)督學(xué)習(xí) /
- 正則化
Abstract: This paper proposes Regularized Semi-Supervised ISOmetric MAPping (Reg-SS-ISOMAP) algorithm to solve the problem that ISOmetric MAPping (ISOMAP) algorithm is unsupervised and can not generate explicit mapping function. At first, this algorithm creates K-Connectivity Graph (K-CG) by labeled samples in training samples to get geodesic distance between approximate samples and takes it as feature vector substituting for original data. Then, it takes the geodesic distance as kernel and processes feature vector through semi-supervised regularization not MultiDimensional Scaling (MDS) algorithm. At last, it constructs objective function by regularization regression model which is low dimension and explicit mapping. The algorithm is simulated on different data sets, results show that it is stable in dimension reduction and high recognition rate. -
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