KPCA-based training of a kernel fuzzy classifier with ellipsoidal regions
KPCA-based training of a kernel fuzzy classifier with ellipsoidal regions
复制标题
DOI：
10.1016/j.ijar.2004.03.001
复制
发表时间：
2004-11
期刊：
影响因子：
--
通讯作者：
K. Kaieda;S. Abe
中科院分区：
文献类型：
--
作者：
K. Kaieda;S. Abe
在具有椭圆体区域的模糊分类器中，为每个类别定义基于马哈拉诺比斯距离的模糊规则。然后调整模糊规则，使得训练数据的识别率最大化。大多数情况下，每一类有一条模糊规则就足以获得较高的泛化能力。但在某些情况下，我们需要对类数据进行分区，以便为每个类定义多个规则。在本文中，我们没有对类数据进行划分，而是将输入空间映射到高维特征空间，然后在特征空间中生成具有椭圆体区域的模糊分类器。我们将该分类器称为具有椭圆体区域的核模糊分类器。为了加速训练，首先我们选择跨越特征空间中的子空间的独立训练数据并计算核主成分。通过这种方法，我们可以避免使用奇异值分解，从而提高训练速度。在特征空间中，训练数据通常是退化的。即，映射的训练数据所跨越的空间是真子空间。因此，如果映射的测试数据位于互补子空间中，则马哈拉诺比斯距离可能会变得错误，从而错误分类的概率变高。为了克服这个问题，我们提出了转导训练：在训练中，我们添加输入空间的基向量作为未标记的数据；在分类中，如果映射的未知数据不在子空间中，我们会扩展子空间以将它们包括在内。我们通过计算机模拟证明了我们方法的有效性。
In a fuzzy classifier with ellipsoidal regions, a fuzzy rule, which is based on the Mahalanobis distance, is defined for each class. Then the fuzzy rules are tuned so that the recognition rate of the training data is maximized. In most cases, one fuzzy rule per one class is enough to obtain high generalization ability. But in some cases, we need to partition the class data to define more than one rule per class. In this paper, instead of partitioning the class data, we map the input space into the high dimensional feature space and then generate a fuzzy classifier with ellipsoidal regions in the feature space. We call this classifier kernel fuzzy classifier with ellipsoidal regions. To speed up training, first we select independent training data that span the subspace in the feature space and calculate the kernel principal components. By this method, we can avoid using singular value decomposition, which leads to training speedup. In the feature space, training data are usually degenerate. Namely, the space spanned by the mapped training data is a proper subspace. Thus, if the mapped test data are in the complementary subspace, the Mahalanobis distance may become erroneous and thus the probability of misclassification becomes high. To overcome this problem, we propose transductive training: in training, we add basis vectors of the input space as unlabelled data; and in classification, if mapped unknown data are not in the subspace we expand the subspace so that they are included. We demonstrate the effectiveness of our method by computer simulations.