AdaBoost with different costs for misclassification and its applications to contextual image classification

Consider a confusion matrix obtained by a classifier of land-cover categories. Usually, misclassification rates are not uniformly distributed in off-diagonal elements of the matrix. Some categories are easily classified from the others, and some are not. The loss function used by AdaBoost ignores the difference. If we derive a classifier which is efficient to classify categories close to the remaining categories, the overall accuracy may be improved. In this paper, the exponential loss function with different costs for misclassification is proposed in multiclass problems. Costs due to misclassification should be pre-assigned. Then, we obtain an emprical cost risk function to be minimized, and the minimizing procedure is established (Cost AdaBoost). Similar treatments for logit loss functions are discussed. Also, Spatial Cost AdaBoost is proposed. Out purpose is originally to minimize the expected cost. If we can define costs appropriately, the costs are useful for reducing error rates. A simple numerical example shows that the proposed method is useful for reducing error rates.