Discriminant analysis of spatial data based on fusion of Markov random fields and machine learning

研究的目的如下：(A)基于类别的空间分布的机器学习对多光谱图像分类的改进；(B)机器学习方法的选择方法的推导和马尔可夫随机场模型的选择；(C)通过实际卫星图像将所提出的方法与常规方法进行比较。因此，我们的目标是得到一种基于统计和机器学习的融合分类方法。Nishii和Eguchi(2004)提出了Space AdaBoost，它通过以下步骤实现：(1)获得训练数据的后验概率。(2)计算每个像素邻域的对数后验均值，并将其作为分类函数。(3)通过使指数风险按顺序最小化来调整对数后方的权重。(4)利用对数后验概率的凸组合对测试数据进行分类，并通过模拟和真实数据集对该方法进行了检验，结果表明该方法具有很高的速度，且性能与基于马尔可夫随机场的分类器相当。在某些情况下，该方法有时会给后验对数一个负权重，因为指数损失会对错误分类的数据造成巨大的惩罚。此外，我们还研究了图像分析和机器学习的相关问题，如稳健损失函数和性质；几何和地形效应的校正；形态纹理分析；字符识别中旋转不变矩的推导。

Aims of the research were as follows : (a)Improvement of multispectral image classification due to machine learning based on spatial distributions of categories, (b)Derivation of selection method of machine learning approaches and model selection of Markov random fields, (c)Comparison of the proposed and the ordinary methods through actual satellite images. Hence the aims were to derive a fused classification method based on statistics and machine learning in short. Nishii and Eguchi (2004) proposed Spatial AdaBoost, which achieved the aims.Spatial AdaBoost is carried out in the following steps, (1)Obtain the posterior probabilities of the training data. (2)Calculate averages of log posteriors in neighborhoods of each pixels, and regard them as classification functions. (3)Tune the weights for the log posteriors by minimizing the exponential risk sequentially. (4)Classify test data by the convex combination of log posteriors.The proposed method is examined through simulated and real data sets, and it is seen that the method is very fast and shows a similar performance to MRF-based classifier. The method sometimes gives a negative weight for the log posterior for some case because the exponential loss puts a huge penalty for outlying misclassified data. Hence, Spatial AdaBoost based on robust loss functions is under investigation, and we obtain a partial answer.Further, we studied issues related to image analysis and machine learning, for example, robust loss functions and properties ; corrections of geometric and topographic effects ; morphological texture analysis ; and derivation of rotation invariant moments for character recognition.