Thesis - Instituto de Telecomunicações

5.2. USER TUNED FEATURE SELECTION 99the set of features that best separates a genuine user from an impostor, determining afeature subset for each user. Class tuned feature selection has been used previously forbiometric application for example in [119].The overall time to run the algorithm increases with the number of users, but classificationperformance improvement justifies the increased computational cost. To reduce thecomputational burden, we studied the time complexity of the classification system and createdfaster versions of the employed methods. This is described in the following subsections.5.2.2 Computational Improvements on Feature SelectionThe overall learning and classification process proved to be highly computationally demanding.We evaluated the time complexity of the several steps involved in the system, and madesome algorithmic improvements in order to devise strategies to decrease the required timeto obtain the results. We describe the weight of each of the blocks in the time complexity.Figure 5.3 shows a diagram of the steps involved in the classification system, indicating thecorresponding time complexity order.Figure 5.3: Blocks of the classification system with their respective time complexity order.The feature extraction block, when run in batch mode for all the acquired data, requiresan amount of time proportional to the amount of data to process. Considering the featureextraction operation, the processing time linearly increases with the number of users (n c )and with the number of features to extract (n f ), thus leading to a O(n f n c ) time complexity.We verified experimentally that the extraction of all the features was always faster thanthe data acquisition time for the signals studied in the present work (our research team’sslowest computer, operating at 2.0 GHz, performed well in this task).The parametric model learning may require some optimization steps. In the learning foreach feature parameters we assumed conditional independence between features, resultingin linear complexity with the number of features and users (O(n f n c ) time complexity).