摘要:
依据最大间距判别准则(Maximum margin criterion, MMC)的基本原理,并结合模糊技术和张量理论, 提出一种矩阵模式的模糊最大间距判别准则(Matrix model fuzzy maximum margin criterion, MFMMC),并在此基础上形成具有模糊聚类功能的双向二维无监督特征提取方法(Two-directional two-dimensional unsupervised feature extraction method with fuzzy clustering ability, (2D)2UFFCA). 该方法不但能直接实现矩阵模式数据的模糊聚类,而且还可以对矩阵模式数据进行双向二维特征提取,实现特征降维. 同时我们还从几何的直观含义出发,合理地设定矩阵模式的模糊最大间距判别准则中的调节参数γ并从理论上证明其合理性.为了提高特征提取的效率,还提出一种能有效计算矩阵模式数据的投影变换矩阵的方法.实验结果表明该方法具有上述优势.
Abstract:
In this paper, based on the principles of the maximum margin criterion (MMC) and by introducing the fuzzy method and the tensor theory into it, a novel matrix model fuzzy maximum margin criterion (MFMMC) is proposed. Also, on the basis of it, a two-directional two-dimensional unsupervised feature extraction method with fuzzy clustering ability ((2D)2UFFCA) is constructed. This method can directly realize fuzzy clustering of matrix model data. And it can also achieve the two-directional two-dimensional feature extraction of them, that is, the realization of dimension reduction. At the same time, the adjusting parameter γ in the matrix model fuzzy maximum margin criterion is defined reasonably from the respect of geometry intuition, which is proved theoretically. In order to improve the efficiency of feature extraction, an effective method which can find out the projection matrices of matrix model data is presented. The results of tests show the above advantages of the method.
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