*6.2. Bandwidth Calibration*

To achieve a good prediction, we must first find an optimal bandwidth. In other words, the parameter *h*, which appears in the Equation (1) via the kernel function, must be adjusted in order to eliminate bad behavior of our classification procedure. With the above assumptions in mind, this requires a tradeoff between bias and variance. A value of *h* close to 0 will give a good estimate of the regression function in the learning database. Otherwise, large values of *h* will eventually affect the overall error. The optimal bandwidth ˆ *h* realized this task: This is a good compromise between a low error term and a good capability of prediction. For this purpose, we used a leave-one-out cross validation procedure to estimate the bandwidth. The training set is made of 126 images: 9 deal with person 0. The optimal bandwidth is calculated as *<sup>h</sup>* <sup>=</sup> *argmin <sup>n</sup> i*=1 *Yi* − *Y*ˆ(*i*) 2 , where *Y*ˆ(*i*) is the

prediction for person i calculated without the i-th observation. We find that the optimal bandwidth ˆ *h* is 1.06. Now that the optimal bandwidth ˆ *h* is found, we can use the classification algorithm by fixing the value of ˆ *h* into Equation (1).
