## 4 Experiments
### Experimental Setup  
Three main ways have been adopted by gesture recognition literature to report classification results on the Opportunity dataset. First, in [57; 58], the proposed method was tested on the challenging task B2 [58], where performance recognition must be reported on the testing set composed of ADL4 and ADL5 for Subjects 2 and 3. According to the challenge, the authors are free to include any remaining subsets into the training set. Missing values, due to packet-loss, have been replaced by linear interpolation. All on-body sensors have been exploited, resulting in an input space with 113 dimensions. Secondly, [58] also reported gesture recognition performances for each of the four subjects using an identical data preparation provided by the UCI repository. Although datasets have 113 dimensions, the methods used for handling missing data may reduce this number. [PERSON] et al. [59] conducted a similar experimentation, but all types of sensors were included, i.e., 243 dimensions. Finally, in [18], a five-fold cross validation (in \(K\)-fold cross validation), a dataset \(\mathcal{D}\) is split into \(k\) mutually exclusive subsets, where the size of each fold is approximately equal. One of the partition \(\mathcal{D}_{t}\), with \(t\in\{1,2,\ldots,k\}\), is used for testing the classifier performance, and the remaining of the dataset, i.e., \(\mathcal{D}\setminus\mathcal{D}_{t}\), consists of its training dataset. This process has to be repeated \(k\)-times and was performed on the 'drill run' subset of the Opportunity dataset using accelerometers on arms. Based on the same model validation technique, [19] evaluated the proposed methods on the 'drill run' of each subject using a five-fold cross validation. The experiments only employed 17 3D-sensors, and raw signals were down-sampled. In this work and the aforementioned one, there is no mention of methods for handling missing data. In our proposed method, the whole training data stream must be quantized for each solution since the selected dimensions and discretization scheme vary. Due to the humongous Euclidean distance searches induced and limited experiment time requirements, we favour smaller datasets. Hence, for the sake of comparison, we reproduced the experiments of [PERSON] et al. [19] but without down-sampling raw signals. All 51 dimensions were scaled to unit size. We used the default method for handling missing values provided by the UCI repository. For each subject, Table 1 summarizes the number of repetitions (#inst) per gesture and their average length (avg) with standard deviation (SD). It follows that gestures have strong variability, especially 'CleanTable', 'DrinkfromCup', and ToggleSwitch', and the number of instances is inconstant. Additionally, this input dataset noticeably contains a very large portion of 'null classes' (40%). In this paper, we performed a five-fold cross-validation. The proposed framework for building a multi-class gesture recognition system based on LM-WLCSS, however, requires the partitioning of each training dataset, \(\mathcal{Z}=\mathcal{D}\setminus\mathcal{D}_{t}\), into three mutually exclusive subsets, \(\mathcal{Z}_{1}\), \(\mathcal{Z}_{2}\), and \(\mathcal{Z}_{3}\), to avoid biased results. \(\mathcal{Z}_{1}\) represents the training dataset used for all the base-level classifiers and contains 70% of \(\mathcal{Z}\). The remaining data is equally split over \(\mathcal{Z}_{1}\) and \(\mathcal{Z}_{2}\). Performance recognition is maximized over the test set \(\mathcal{Z}_{2}\). Once each binary classifier has been trained, predictions on the stream \(\mathcal{Z}_{3}\) are obtained, transforming all incoming multi-modal samples into a succession of decision vectors. This newly created dataset, \(\mathcal{Z}_{3}\)', allows us to resolve conflicts by training a light-weight classifier. Finally, the final performance of the system is assessed by using the testing dataset \(\mathcal{D}_{t}\).