# Time Series Classification with Shapelet and Canonical Features
## 2 Related Work
### Other Types of Classification Methods  
Classification methods based on intervals assume that local features depend on where they appear and are generally more efficient. Typical methods include time series forest (TSF) [14], random interval spectrum integration (RISE) [21], and typical interval forest (CIF) [3]. TSF randomly selects a set of intervals in the time series to perform transformations over three time domains (mean, variance, and slope, respectively), and trains an integrated classifier based on a decision tree with new feature representations [14]. Unlike TSF, RISE performs four frequency domain transitions for each set of randomly selected intervals, including autocorrelation functions, partial autocorrelation functions, autoregressive models, and power spectra [21]. CIF adds the 22 features in Catch22 [15] to TSF, significantly exceeding TSF and RISE in accuracy [3]. Classification methods based on dictionaries convert time series into a bag of patterns, distinguishing between different categories by the relative frequency with which patterns appear. Representative algorithms include Pattern Package (BoP) [22], SAX-VSM [23], BOSS [24], and WINCL [25]. Among them, BoP and SAX-VSM use symbolic aggregation approximation (SAX) [20] techniques to convert subsequences into words, building feature vectors based on word frequency [23]. BOSS is the most commonly used dictionary-based classification method [21], which constructs words using symbolic Fourier approximation (SFA) [26] techniques and constructs an integrated classifier [24] based on nearest neighbor and specially tailored distance metrics. WEASEL uses a \"supervised\" symbolic Fourier approximation technique to screen words with chi-square tests and ultimately train a logistic regression classifier [25]. In terms of accuracy, WEASEL represents an advanced level of lexicography-based classification methods [3; 18]. However, researchers generally point out that the spatial complexity of WEASEL is extremely high, mainly due to the large characteristic space [5; 27]. Classification methods based on distance usually use elastic distance measurements (i.e., distance measurement methods that can cope with phenomena such as local shifts or distortions of time series to some extent [28; 29; 30]) to quantify the distance between time series and classify them according to the distance between test instances and training instances. In order to improve the accuracy, [PERSON] et al. [30] proposed an elastic integration algorithm consisting of 11 nearest neighbor classification algorithms based on different elastic distance measurements. The training and classification complexity of this method are high, at \(O(n^{2}\cdot l^{2})\) and \(O(n\cdot l^{2})\), respectively. [PERSON] et al. [5] proposed the Proximity Forest algorithm to improve the accuracy and efficiency of the elastic integration algorithm. A neighboring forest is an integration of multiple neighboring trees, where the data on each node are split according to the distance from a randomly selected time series in each class, and the distance measurement and its required parameters are also randomly selected. The time series classification methods introduced earlier, including STC [17], BOSS [24], elastic integration [31], neighboring forests [5], etc., are all integrated methods, but they are all homogeneous integrations, or integrations based on a single representation of time series. The meta-ensemble method [21; 32] is an integration method based on several homogeneous integration methods, that is, integrated integration. HIVE-COTE [21] is the most accurate and representative meta-integration method available, and is an improved version of FLATCOTE [31] that integrates elastic integration [31], STC [17], BOSS [24], time series forest [14], and random interval spectrum integration [21]. HIVE-COTE achieves the highest accuracy on UCR time series datasets [7], but is extremely complex [5; 21], making it difficult to apply to large-scale datasets.