# Interval Feature Transformation for Time Series Classification Using Perceptually Important Points
## 3 Interval Feature Transformation  
### Perceptually Important Points (PIPs)  
For long time sequences, it is more appropriate to measure the similarity by looking for features in specific discriminative time intervals, rather than point-to-point, local comparisons. In the time series mining system, the interesting and frequently appearing patterns usually can be abstractly represented by a few critical points. These points have perceptually important influences in the human vision [28]. By identifying the perceptually important points (PIPs) from the time domain, the time series can be segmented flexibly and effectively according to the needs of the users and the applications. [PERSON] et al. [29] used PIPs to dynamically segment price series into subsequences and used dynamic time warping (DTW) to find similar historical subsequences. [PERSON] et al. [30] used the perceptually important points (PIP) process to represent and index each time series of each station and used the rule set to classify the stations. [PERSON] et al. [31] proposed a framework for mining emerging patterns from time series data, which transformed the time series data into a symbolic representation based on the SAX and PIPs algorithms. The previous studies have shown that the intuitive pattern matching can be carried out effectively by comparing time series segments of different lengths. In this study, we use perceptually important points to segment the series dynamically into subsequences of unequal length. Now, we present the algorithm of constructing PIPs for time series segmentation. A univariate time series is a sequence of data that is typically recorded in temporal order at fixed intervals. The number of real values is the length of the time series. A data set \(T=\{T_{1},T_{2},T_{3},\cdots T_{n}\}\) has \(n\) time series. Each time series \(T_{i}\) has m real-valued ordered data \(\langle t_{1},t_{2},t_{3},\cdots t_{m}\rangle\) and a class label \(l_{i}\), then \(T_{i}=\{t_{1},t_{2},t_{3},\cdots t_{m},l_{i}\}\). For a given time series \(T_{i}\), all the data points, \(t_{1},t_{2},t_{3},\cdots t_{m}\) in \(T_{i}\) will go through the PIPs identification algorithm. The algorithm starts by characterizing the first value \(t_{1}\) and the last value \(t_{m}\) as the first two PIPs. Supposing we want to divide the time series into \(\omega\) segments, we need to obtain \(\omega-1\) PIPs. Firstly, the algorithm calculates the distance between all remaining data points and the two initial PIPs, and also signifies as the third PIP the one with the maximum distance. Subsequently, the fourth PIP will be the point in \(T_{i}\) with the greatest distance to its two adjacent PIPs, either between the first and second PIPs or between the second and the last PIPs. The process of locating the PIPs continues until \(\omega-1\) PIPs are identified, as shown in Figure 1.  
Several importance evaluation methods have been proposed in this work. We chose vertical distance (VD) to evaluate the importance of the PIPs in a time series. In this paper, we introduce a new parameter \(\tau\) to make the PIPs well-distributed. The parameter \(\tau\) is a threshold for selecting important points that represents the minimum interval between adjacent PIPs. Once the interval between the new picked point with the biggest distance and the adjacent PIPs is less than this threshold, the point will be discarded and replaced with the point with the next biggest distance. These two parameters, \(\omega\) and \(\tau\), need be specified by the users manually. There are two ways to select the parameter \(\omega\). If we observe the sequence diagram, the waveform has obvious segmentation, we can directly specify the \(\omega\) value. If not, we take 5 as the initial value and 5 as the step size. Through the test, the best parameter \(\omega\) can be found. Figure 2 shows the influence of parameter \(\tau\) selection for data set OliveOil. When the parameter \(\tau\) is increased to 50, the extremum point which is circled in (c) can be captured very well.