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Discriminant Subspace Analysis: An Adaptive Approach for Image Classification

机译：判别子空间分析：一种自适应的图像分类方法

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Linear discriminant analysis (LDA) and biased discriminant analysis (BDA) are two effective techniques for dimension reduction, which pay attention to different roles of the positive and negative samples in finding discriminating subspace. However, the drawbacks of these two methods are obvious: LDA has limited efficiency in classifying sample data from subclasses with different distributions, and BDA does not account for the underlying distribution of negative samples. In order to effectively exploit favorable attributes of both BDA and LDA and avoid their unfavorable ones, we propose a novel adaptive discriminant analysis (ADA) for image classification. ADA can find an optimal discriminative subspace with adaptation to different sample distributions. In addition, three novel variants and extensions of ADA are further proposed: 1) integrated boosting (i.Boosting), which enhances and combines a set of ADA classifiers into a more powerful one. i.Boosting integrates feature re-weighting, relevance feedback, and AdaBoost into one framework. With affordable computational cost, i.Boosting can provide a unified and stable solution to ADA prediction result. 2) Fast adaptive discriminant analysis (FADA). Instead of searching parameters, FADA can directly find a close-to-optimal projection very fast based on different sample distributions. 3) Two-dimensional adaptive discriminant analysis (2DADA). As opposed to ADA, 2DADA is based on 2-D image matrix representation rather than 1-D vector. So it is simpler, more straightforward, and has lower time complexity to use for image feature extraction. Extensive experiments on synthetic data, UCI benchmark data sets, hand-digit data set, four facial image data sets, and COREL color image data sets show the superior performance of our proposed approaches.
机译：线性判别分析（LDA）和有偏判别分析（BDA）是两种有效的降维技术，它们在寻找辨别子空间时要注意正样本和负样本的不同作用。但是，这两种方法的缺点是显而易见的：LDA在对具有不同分布的子类的样本数据进行分类的效率有限，并且BDA不能解释负样本的基本分布。为了有效地利用BDA和LDA的有利属性并避免它们的不利属性，我们提出了一种用于图像分类的新型自适应判别分析（ADA）。 ADA可以找到适应不同样本分布的最佳判别子空间。此外，还提出了ADA的三个新颖变体和扩展：1）集成增强（i.Boosting），它将一组ADA分类器增强和组合为一个功能更强大的分类器。 i.Boosting将功能重新加权，相关性反馈和AdaBoost集成到一个框架中。 i.Boosting以合理的计算成本为ADA预测结果提供了统一而稳定的解决方案。 2）快速自适应判别分析（FADA）。不用搜索参数，FADA可以基于不同的样本分布直接非常快速地找到接近最佳的投影。 3）二维自适应判别分析（2DADA）。与ADA相反，2DADA基于2D图像矩阵表示而不是1D向量。因此，它更简单，更直接，并且用于图像特征提取的时间复杂度更低。在合成数据，UCI基准数据集，手手指数据集，四个面部图像数据集和COREL彩色图像数据集上的大量实验表明，我们提出的方法具有优越的性能。

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