In the paper "MLCM: Multi-Label Confusion Matrix" a method for computing the confusion matrix for the multi-label classification problem is proposed. Although the authors state that there is no similar work on computing confusion-matrix for multi-label classification problems, we point out that the method for computing multi-label confusion-matrix was previously proposed in the paper "Multi-Label Classifier Performance Evaluation with Confusion Matrix" by Krstinić et al. We will show that both methods are based on the same set of assumptions and scenarios for instances of true and predicted labels, while there are differences in computing the contribution of classification errors to the confusion matrix between these two approaches.

Laser pointers are one of the most widely used interactive and pointing devices in different human-computer interaction systems. Existing approaches to vision-based laser spot tracking are designed for controlled indoor environments with the main assumption that the laser spot is very bright, if not the brightest, spot in images. In this work, we are interested in developing a method for an outdoor, open-space environment, which could be implemented on embedded devices with limited computational resources. Under these circumstances, none of the assumptions of existing methods for laser spot tracking can be applied, yet a novel and fast method with robust performance is required. Throughout the paper, we will propose and evaluate an efficient method based on modified circular Hough transform and Lucas–Kanade motion analysis. Encouraging results on a representative dataset demonstrate the potential of our method in an uncontrolled outdoor environment, while achieving maximal accuracy indoors. Our dataset and ground truth data are made publicly available for further development.

The confusion matrix is the tool commonly used for the evaluation of the performance of a classification algorithm. While the computation of the confusion matrix for multi-class classification follows a well-developed procedure, the common approach for computing the confusion matrix for multi-label classification suffers from the ambiguity related to one-vs-rest strategy and ignores the possibility that predictions could be partially correct, which also leads to inaccuracies of the derived evaluation metric. Only recently, the two approaches dealing with the computation of multi-label confusion matrix have been proposed which take into account the specifics of multi-label classification. In this work, a new method for calculating evaluation metrics for multi-label classification is proposed. The proposed method is based on the calculation of two confusion matrices combined into the confusion tensor. It builds upon the insights into the shortcomings of the two existing approaches for calculating the multi-label confusion matrix. The main drawback of these techniques is their inability to compute precision and recall precisely. The Multi-Label Confusion Tensor was tested on synthetic and real data and compared with existing methods for calculating the multi-label confusion matrix. The source code and the data used to test the methodology are made publicly available.