# Time Series Clustering Model based on DTW for Classifying Car Parks
## 1 Introduction
[10] proposed the augmentation of fully convolutional networks with long short term memory recurrent neural network sub-modules for time series classification. Time series mining involves many aspects, such as time series classification, prediction, clustering, etc. The main processes of time series clustering are distance measurement [11] and clustering [12; 13]. In the process of distance measurement, there are many different distance measurement methods for time series mining, including Hausdorff distance [14], Minkowski [15], hidden Markov model-based distance [16], Euclidean distance [17], and dynamic time warping [18], and the most commonly used ones for time series clustering are Euclidean distance (ED) and dynamic time warping (DTW) [19]. For instance, [PERSON] et al. [20] evaluated nine distance measures and several variants thereof, and found that ED is the most efficient measure with a reasonably high accuracy while DTW often performs well. DTW is able to overcome the defect of ED point-to-point, and measure time series data with unequal length by warping time to achieve one-to-many matching of data points, which means that it has strong robustness to time deviation and amplitude change [21]. [PERSON] et al. [22] realized the initial clustering by DTW and hierarchical clustering, and then put the clustering results into hidden Markov model (HMM) for iterative optimization. [PERSON] et al. [23] proposed an analysis framework for classifying the average technology based on DTW. [PERSON] et al. [24] applied a DTW distance based \(k\)-medoids method to group buildings with similar social media activities into functional areas. It is necessary to adopt the DTW to calculate the distance of occupancy rate of car parks. For clustering, we can obtain a lot of experiences and knowledge from the existing literature. [PERSON] et al. [25] combined fuzzy \(c\)-means and fuzzy \(c\)-medoids to deal with time series clustering. In order to effectively utilize the inherent subspace information of time series data set and improve clustering performance, [PERSON] et al. [26] proposed a time series \(k\)-means (TSkmeans). The \(k\)-means clustering method is sensitive to outliers of the data. To solve this problem, [PERSON] et al. [27] introduced a \(k\)-medoids clustering approach to identify the minimum number of sequences necessary to represent each coding sequence in the final probe set. [PERSON] et al. [28] proposed a cohort selection method called \(k\)-medoids cohort selection (KMCS) to select a reference set of non-matched templates which are almost appropriate to the respective subjects. There are many random factors during the process of \(k\)-medoids algorithm, so it is essential to avoid the randomness of clustering process. Therefore, a time series clustering framework is developed for classifying car parks, which contains four aspects, including data preprocessing, distance measurement, clustering, and evaluation. The rest of this paper is organized as follows. In Section 2, the dataset is presented and the framework for classifying car parks is described. The results of clustering are given and discussed in Section 3. Finally, we conclude the paper in Section 4.