Time Series Classification Based on Spectral Analysis

Abstract

For time series data with obvious periodicity (e.g., electric motor systems and cardiac monitor) or vague periodicity (e.g., earthquake and explosion, speech, and stock data), frequency-based techniques using the spectral analysis can usually capture the features of the series. By this approach, we are able not only to reduce the data dimensions into frequency domain but also utilize these frequencies by general classification methods such as linear discriminant analysis (LDA) and k-nearest-neighbor (KNN) to classify the time series. This is a combination of two classical approaches. However, there is a difficulty in using LDA and KNN in frequency domain due to excessive dimensions of data. We overcome the obstacle by using Singular Value Decomposition to select essential frequencies. Two data sets are used to illustrate our approach. The classification error rates of our simple approach are comparable to those of several more complicated methods.

Keywords:

• Classification
• k-nearest-neighbor
• Linear discriminant analysis
• Spectral analysis
• Time series

Mathematics Subject Classification:

• 62M10
• 62M15

Notes

KNN: Using ten-fold cross-validation on training data.

KNN: Using eight-fold cross-validation on training data.

*Povinelli et al. (2004) when the number of mixtures is greater than 16.

*Huang et al. (2004) gave a discriminant statistic using Kullback–Leibler divergence.

**LDA and KNN using eight-fold cross-validation on training data.