Abstract
Data fitting is the main method of functional data analysis, and it is widely used in the fields of economy, social science, engineering technology and so on. Least square method is the main method of data fitting, but the least square method is not convergent, no memory property, big fitting error and it is easy to over fitting. Based on the orthogonal trigonometric function system, this paper presents a data forward stepwise fitting algorithm. This algorithm takes forward stepwise fitting strategy, each time using the nearest base function to fit the residual error generated by the previous base function fitting, which makes the residual mean square error minimum. In this paper, we theoretically prove the convergence, the memory property and the fitting error diminishing character for the algorithm. Experimental results show that the proposed algorithm is effective, and the fitting performance is better than that of the least square method and the forward stepwise fitting algorithm based on the non-orthogonal function system.
Highlights
Data fitting or data approximation is an important and common technique in data mining [1]
Least squares method (LSM) has the following drawbacks: the solution may not exist; the number of parameters to be far less than the number of data, otherwise prone to over fitting; not successive approximation algorithm, the fitting error does not decrease with increasing complexity; do not have memory property, when increasing the base function, need to retraining parameters
The original data sequence is matched with the key points of the data sequence, which is used to compress the original sequence in order to get smaller storage and computation cost
Summary
Data fitting or data approximation is an important and common technique in data mining [1]. The paper [2-5] puts forward the method of piecewise linear fitting. In this method, the original data sequence is matched with the key points of the data sequence, which is used to compress the original sequence in order to get smaller storage and computation cost. Based on the popular method of surface rendering, the paper [9] applies a complete orthogonal function system to fit the point cloud data. Because of the excellent properties of orthogonal function system, this paper adopts the linear combination of complete orthogonal trigonometric function on L2 [0, 1] to fit the original data. The algorithm proposed in this paper has some excellent properties, such as convergence, memory property, and gradual approximation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
