Time-Constrained Fashion Sales Forecasting by Extended Random Vector Functional Link Model

Introduction

Forecasting is about predicting the future based on the past historical data. It is important in all kinds of applications. It is especially important in industries such as fashion retailing because of the ever changing market needs and fashion trends. However, it is usually a tremendously difficult task as the future is truly unknown in many situations (Sztandera et al., 2004). Many statistical (Abraham & Ledolter, 1983) and mathematical (Frank et al., 2002) models are applicable for the purpose of forecasting. Techniques such as averaging over a horizon, moving average, Bayesian approach, and exponential smoothing (Hanke & Wichern, 2009) are all well-studied in the literature. Many of these statistical models are still being actively used in everyday’s application and are proven to be useful and fast. The Artificial Neural Network (ANN) is originated from the mathematical model that simulates the structure and functions of biological neural networks. ANN has demonstrated superior performance in optical character recognition, speech recognition, signal filtering in communication networks and so on (Hansen & Nelson, 1997; Bhagat, 2005; Masters, 1994). ANN is also powerful in making prediction about future events or processes (Cortez et al., 1995; Zhang et al., 1998), including sales forecasting (Yu et al., 2010a). Essentially, ANN has been used as a non-linear data-modeling tool based on its capability of learning and finding sophisticated patterns from historical data. The typical ANN models apply gradient learning mechanisms and have to repeatedly run and fine-tune their parameters so as to learn the patterns from data well (Hertz, 1990). While the ANN models are capable of modeling both linear and non-linear models, they are often much slower compared to the traditional statistical models. There have been many efforts devoted to improving the efficiency of ANN, and many of them concentrate on the learning algorithm (MacKay, 2003). For instance, a new learning algorithm has been proposed recently based on neuron-by-neuron computation methods for the gradient vector and the Jacobian matrix (Wilamowski, 2008). The algorithm can handle ANN with arbitrarily neurons, and its training speed is much faster than the other algorithms. Although the neuron-by-neuron computation method is faster, it suffers a major limitation on its convergence ability. To be specific, there is a significant probability that the algorithm will fail to converge the global minima, so that the algorithm has to repeat from the very beginning. Although there are solutions for this, the algorithm is not as fast as it can be.