Neural networks-based approach to the acquisition of acceleration from noisy velocity signal
In this paper, we propose a neural networks-based approach to acquire the angular acceleration from a noisy velocity signal. Our scheme consists of two cascaded neural networks: Neural Network I and II. Neural Network I attenuates the measurement noise from the velocity signal. Neural Network II further reduces the residual noise level, and calculates the final angular acceleration estimate. As an illustrative example, we discuss the application of our scheme in the elevator velocity and acceleration signal acquisition. Two different kinds of neural network models are employed: the back-propagation neural network (BP) and the adaptive-network-based fuzzy inference system (ANFIS). We compare the performances of these two neural networks by illustrative simulation experiments.
We study the problem of learning a kernel matrix from an apriori kernel and training data. An unconstrained convex optimization formulation is proposed, with an arbitrary convex smooth loss function on kernel entries and a LogDet divergence for regularization. Since the number of variables is of order O(n), standard Newton and quasi-Newton methods are too time-consuming. An operator form Hessian is used to develop an O(n) trust-region inexact Newton method, where the Newton direction is computed using several conjugate gradient steps on the Hessian operator equation. On the uspst dataset, our algorithm can handle 2 million optimization variables within one hour. Experiments are shown for both linear (Mahalanobis) metric learning and for kernel learning. The convergence rate, speed and performance of several loss functions and algorithms are discussed.