# Effective Behavioural Dynamic Coupling through Echo State Networks
## 1 Introduction
In this context, three are the main aspects that require attention: (i) the recognition model should be able to accommodate input patterns of different lengths; (ii) it should be trained and able to adapt to different users needs and preferences in a short time, so that the user does not disengage; (iii) the recognition should be implemented with a low complexity of computation [3]. Adaptive methodologies that present useful features like the ones above have only started to appear, most of them working under a classification paradigm [4; 5]. In this context, the challenges presented are mainly two: (a) detecting that a sequence is actually present in the data stream received from the input and (b) correctly classifying it. Most research features these two aspects with independent mechanisms [6; 7; 8; 9; 10], however, having a unified mechanism for the two tasks, saves computational resources overall and, at the same time, the recognition process becomes faster. Moreover, the task of dynamic sequence recognition becomes especially complicated when working with real and continuous streams of data and the complexity increases when the sequences have different lengths. Methods used for the classification span from distance measures (e.g., Dynamic Time Warping) [11; 12] and statistical models (e.g., Hidden Markov Models) [13; 14], to artificial neural architectures (e.g., Recurrent Neural Networks) [15; 16; 17; 18; 19] and hybrid solutions [20]. These methods vary in complexity and adaptability, with Recurrent Neural Networks being one of the most promising direction in the field [21]. Adaptation of RNNs though, is known to have high computational complexity. In addition, the training procedure is shown to have difficulties in finding good solutions, usually referred to as a gradient vanish problem [22; 23; 24]. Given the inner complexity of the recognition task itself, working in real world environments is particularly difficult and demanding for adaptive models. Performance degrades rapidly when working directly with noisy user data taken from real input devices, making most methods not applicable in real world situations. Cleaning and pre-processing input data, as it is often required for model to work, is not a viable option when the fundamental demand is for a method that should be readily available to the user and work reliably in real-time. The task becomes even more difficult when the input is sampled in real time and is treated continuously. Not having the ability to segment the input data, i.e., not having a starting and stopping point, makes the usage of recurrent methods necessary, as they can integrate the signal continuously in time. On the other hand, training such models requires clean data to perform well, making them difficult to train with data obtained from real users. A potential solution in this case is a computational model that is able to capture the internal dynamics of a behaviour, such as an action performed by the user on a given input device, and thus provide a robust recognition [3]. A recurrent architecture that is shown to work well with noisy data under the restrictions mentioned above is the Echo State Network approach. ESNs seems to perform surprisingly well with noisy data directly taken from a user actions and can also adapt rapidly, making their usage for user oriented systems particularly appealing [19; 25; 26; 27; 28; 29]. In the present paper, since we are interested in behaviour recognition, data comes directly from the user manipulations of an input device. Data can be noisy and the user repetition is not always perfect, resulting to training sets of data with high degrees of noise and variation between samples (e.g., gestures, behaviours). The ESN approach followed here provides a stable and robust mapping of the input commands for user behaviour recognition. For the investigation and validation of the method, we have followed a methodology that encompasses three stages.