While neural network binary classifiers are often evaluated on metrics such as Accuracy and $F_1$-Score, they are commonly trained with a cross-entropy objective. How can this training-evaluation gap be addressed? While specific techniques have been adopted to optimize certain confusion matrix based metrics, it is challenging or impossible in some cases to generalize the techniques to other metrics. Adversarial learning approaches have also been proposed to optimize networks via confusion matrix based metrics, but they tend to be much slower than common training methods. In this work, we propose a unifying approach to training neural network binary classifiers that combines a differentiable approximation of the Heaviside function with a probabilistic view of the typical confusion matrix values using soft sets. Our theoretical analysis shows the benefit of using our method to optimize for a given evaluation metric, such as $F_1$-Score, with soft sets, and our extensive experiments show the effectiveness of our approach in several domains.

We present a non-rigid object matching algorithm based on hyper graph method. Previous work has achieved good performance for rigid object matching. However, because of deformation and wrinkle, existing algorithms cannot solve non-rigid object matching problem effectively. This paper mainly focuses on matching patterns on cloth which often deforms greatly. First, we extract stable regions from the given image. Second, we combine several features in region as bundled feature. In addition, we describe the characteristic of region based on bundled feature and the relationship among regions based on star topology. Finally, we establish the problem model and get the matching result by mathematical programming technique and refinement. Experimental results on both synthetic data and real image show the good performance of our algorithm.