Outlier detection using optimal B-spline smoothing with application to data compression of digital-ink with pen-slip

This paper considers a problem of optimally constructing smoothing spline curves for a given set of data. The curve is constituted by employing normalized uniform B-splines as basis functions. In particular, considering the case when a set of given data includes some outliers, we develop an algorithm for detecting such outliers so that L2 smoothing splines can be robustly constructed with the optimal estimate of the so-called smoothing parameter. Such an algorithm is developed by utilizing the difference between sensitivities of optimal L₁ and L₂ smoothing splines to outliers. Moreover, we apply the method to a problem on data compression of “Digital-Ink” which is a sequence of data sampled from the traced curve at some sampling rate. It is shown that our method can be used effectively for excluding the influence due to the pen slips. We demonstrate the effectiveness by some experimental studies.