This paper addresses a multi-objective feature selection problem for early time series classification. Previous research has focused on how many features to consider for a classifier, but has not considered the starting time of classification, which is also important for early classification. Motivated by this, we developed a mathematical model for which the objectives are to maximize classification performance and minimize the starting time and execution time of classification. We designed an efficient genetic algorithm to generate solutions with high probability. In experiment, we compared the proposed algorithm and general genetic algorithm under various experimental settings. From the experiment, we verified that the proposed algorithm can find a better feature set in terms of classification performance, starting time and execution time of classification than feature set found by general genetic algorithm.

Introduction

Time series classification is used to predict the class label of a time series instance by a welltrained classifier (Deng et al., 2013). That is, if a time series instance , ? ? (?) = (? , is given, its label, , is predicted by the classifier as (?) 1 , ? (?) 2 , ⋯, ? (?) ? ) ? (?) ?( ∙ ) ? (?) = ? (? . Time series classification is used to accomplish tasks in many fields, including fault (?) ) detection in the manufacturing field (Lee et al., 2017), disease diagnosis in the medical field (Lacy et al., 2018), and stock trend analysis in the financial field (Moews et al., 2019). Various classifiers such as neural networks (NNs) and support vector machines (SVMs) are employed and modified to classify time series. Ignatov (2018) employed a convolutional neural network (CNN) to recognize human activity from accelerometer data. Kim and Cho (2018) developed a C-LSTM (CNN- Long Short-Term Memory model) NN to detect anomalies in web traffic data. CNNs and LSTMs in the developed model extracted spatial features and temporal characteristics, respectively. Emoto et al. (2018) used NNs to detect low-intensity snoring episodes from a sleeping sound dataset. Cheng and Dong (2019) employed SVM technology to monitor the nanomachining process with respect to the machining performance. Kalantarian et al. (2016) used SVMs to segment streaming timeseries audio signals probabilistically.