2. Preliminaries/nature of time series data

Univariate and multivariate time series data. Time series inputs can be categorized into: (i) Univariate Time series which have only a single variable observed at each time and thus resulting in one channel per time series input, and (ii) Multivariate Time series which have two or more variables observed at each time, ending up with multiple channels per time series input. Most time series analysis methods focus on univariate data as it is the simplest to work with. Multivariate time series analysis considers simultaneously multiple time series, which, in general is much more complicated than univariate time series analysis as it is harder to model and often many of the classical methods do not perform well.

Raw data or extracted signals. A raw time series is a series of data points indexed in time order i.e., a sequence of discrete-time data taken at successive equally spaced points in time. In time series classification tasks, some authors choose to evaluate the performance of their approaches using raw time series data taken from a specific field/domain while some others prefer to use public datasets in which the raw time series is already segmented and converted into a set of fixed-length signals. Indeed, several research papers using CNNs [17–19, 22, 24, 26, 27] build their experimental studies on the UCR time series classification archive [28] which

consists of extracted short signals. Nonetheless, this benchmark is composed of relatively small datasets (with a small number of instances), which makes the CNN less efficient knowing that CNNs require large training sets for training. Furthermore, in most of the cases, fixed-length signals cannot be further encoded into new representations (which are discussed in Section 3.1), as opposed to raw time series. These issues have led authors of [3–6, 15, 25, 29, 30] to use raw time series data instead.

3.1.2 Other pre-processing methods

CNN Approaches for Time Series Classification DOI: http://dx.doi.org/10.5772/intechopen.81170

from time series inputs.

3.2 Stockwell transform

are analyzed.

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3.2.1 Methodology

inputs for the CNN training process.

can further improve the CNN performance.

Several research papers have focused mainly on applying some pre-processing to raw time series before being fed into the CNN. In this subsection, we present some important contributions which demonstrated that applying changes to the signals

Several attempts have been made in order to encode raw time series as a matrix representation (e.g., 2D images) such as the Gramian Angular Field (GAF) [15], the Markov Transition Field (MTF) [15], Recurrence Plots (RP) [27], and stacked time series signals [29, 31], multivariate time series are treated as a 2D time-space input

Another type of data pre-processing based on applying transformation to data is performed in order to augment the data, thereby ensuring a better CNN training and thus a higher performance. For instance, the window slicing method [24] trains the CNN using slices of the time series input, then at test time classifies each slice of

Knowing that random noise and high-frequency perturbations present in the time series data can interfere tremendously with the learning process and that it is hard to capture useful features with the presence of noise in raw time series data, some works [5, 30] proposed to apply the Fast Fourier transform (FFT) and convert the raw time series into a set of frequency domain signals which serve as

Instead of employing the FFT which is restricted to a predefined fixed window

The advantage of the ST over the FFT is its ability to adaptively capture spectral changes over time without windowing of data, resulting in a better time-frequency

h l½�¼ h lð Þ ∙T , l ¼ 0, 1, …, N � 1, be the samples of the continuous signal h tð Þ, where T is the sampling interval (i.e., the sampling interval of our sensor or measuring

> N�1 l¼0 h l½ �e �i2πml

<sup>N</sup> (1)

length, we choose to adopt the Stockwell transform (ST) as our preprocessing method for CNN training [3, 4]. In this section, the ST method is defined, its implementation on real world applications is detailed, and its experimental results

resolution for non-stationary signals [32]. To illustrate the ST method, let

H m½ �¼ ∑

device). The discrete Fourier transform (DFT) can be written as,

signals with one dimension denoting discrete time flows and the other corresponding to different channels of the multivariate time series.

the test time series using CNN, and performs majority voting to output the predicted label. The window warping method [24] consists of warping a randomly selected slice of a time series by speeding it up or down, producing a transformed raw time series. Then, this latter is further converted into fixed-length input signals/instances via window slicing. Another attempt of augmenting time series is suggested in [3] where either small noise or smoothing is applied to the raw time series. Other transformations were also considered in [17] such as down-sampling to generate versions of a time series at different time scales, and spectral transformations in the frequency domain by adopting low frequency to remove noise
