Prediction of Major Earthquakes as Rare Events Using RF-Typed Polynomial Neural Networks

Introduction

In the history of mankind, earthquakes inflicted greatest loss of life surpassing the events of world wars and plagues, devastation to civilization, and huge loss in economy of a nation. Unfortunately, as of now, there exists no best method in accurate and reliable earthquake prediction. In general there are three schools of thoughts pertaining to earthquake prediction: one being optimistic that earthquake could be predicted accurately one day given sufficient external data (Jordan, 2011); the other felt that certain trending may be possible by assuming and abstracting all the factors behind – the historical results as earthquakes that happened have already embraced all the environmental factors which contributed to the events. So similar to trend-following strategies in stock markets (Fong, 2012), by observing just the tending data from the earthquake time-series it is possible to forecast the forthcoming events. The last group of researchers disbelieves the possibility and reliability of such forecasts as the variations of earthquakes are seemed to be too high (Wang, 2006). They are nothing more than a random process.

Technically earthquake data when viewed as a time series over a long time, exhibits a complex pattern that is composed of a mix of statistical features. The magnitude variation is high, the occurrence of extreme values is sporadic; hence the white noise component is dominating backed by the fact that many minor earthquakes are occurring in almost every minute somewhere around the world. This characterizes a situation of rare-event prediction whose difficulty has been well recognized in data mining and statistics research communities.

In this article, we explore the outlook of applying a highly non-linear prediction model, namely Polynomial Neural Network (PNN) as an alternative to traditional time-series forecasting algorithm (TTF), on major earthquake prediction. In particular, major earthquakes are treated as rare-events. Thus we opt to select only the major earthquakes, converting the univariate time-series to multivariate dataset with relevant extra inputs. Providing relevant multivariate inputs to PNN is important because the strength of neural network is on predicting outcomes from multivariate data. PNN, as its name indicates, is a well-known ensemble type of prediction method that is capable of modeling highly non-linear relations, and achieving an optimal accuracy by inducing through all possible structures of polynomial forecasting models.

In TTF, the prediction models are usually based on the input of univariate time series. PNN is extended with residual-feedback (RF) and Hurst factors; hence, the name RF-typed PNN. We investigate the qualities of different prediction models by TTF and PNN and search for prediction results that offer the lowest error of curve fitting. This article contributes a step forward in finding an accurate prediction model from the perspective of rare-event forecasting.