# Retrieval of Similar Evolution Patterns from Satellite Image Time Series +
## 1 Introduction
DTW is able of handling comparisons between sequences characterized by irregular time sampling or missing data issues [7]. In this regard, K-means with DTW as the distance measure the yield land cover and land use maps of SITS [7]. However, performing an unsupervised clustering over an entire multi-spectral SITS data is time-consuming, and the temporal characteristics of the data may be missed. Other versions of DTW include a weighting procedure to mark the seasonality characteristics of temporal evolutions [9, 10]. This weighting procedure works well for cropland mapping, but it may not be helpful for other applications that do not account for a periodicity effect (e.g., construction of buildings). In addition, recently, a tree-based structure formed of multiple K-means clustering algorithms that use the DTW distance measure was developed in [11] for the indexing and classification of SITS. The methodology described in [12] for time series analysis is based on computing change maps between pairs of consecutive images using different similarity measures (e.g., correlation coefficient, first order Kullback-Liebler Divergence, Conditional Information, Normalized Compression Distance). Figure 1: Spectro-temporal signature in a Landsat satellite image time series (SITS). The change maps are transformed into a collection of words through the K-means clustering algorithm. All the words form a dictionary. The transformed change maps are processed afterwards using the Latent Dirichlet Allocation (LDA) model to discover classes (or evolution-topics) based on the latent information from the scene. Thus, the final results of the analysis provide an unsupervised classification of the spatio-temporal evolutions into classes. A study of several general purpose supervised classifiers, like Random Forest and Support Vector Machine (SVM), was presented in [13] as a solution for land cover mapping. The features extracted from the images were spectral features (e.g., color, normalized difference vegetation, water and build-up indexes, brightness, greenness, wetness, brilliance) and temporal features (e.g., statistical values from normalized difference vegetation index profile, phenological parameters marking important events in a season like sowing, threshing, cropping). However, SVM and Random Forest classifiers are known for having large training times, which may last even several days [13]. In this sense, this type of classification system cannot be used for online retrieval of spatio-temporal evolutions, where a fast response is needed. In addition, supervised classifiers need large amounts of training data. This requirement is not easy to fulfill in SITS classification tasks. Frequent sequential pattern analysis was introduced in [14; 15] for unsupervised SITS mining. This approach performs a quantization of the images in the SITS using a fixed number of gray levels (or, labels) and forms a sequence of \(T\) labels for each pixel location, where \(T\) is the number of images in the SITS. In this context, an ordered list of labels is called a frequent sequential pattern if the number of its occurrences in the SITS is greater than a fixed threshold. Inferring spatial connectivity constraints when determining the frequent sequential patterns proved to be efficient in monitoring crop or ground deformations [14]. However, the determination of the frequency of sequential patterns in SITS is sensitive to the number of levels used for image quantization. In addition, the method extracts a large number of patterns which may be difficult to interpret in terms of changes that appear in an area. Moreover, missing data may raise difficulties when interpreting the results for SITS analysis. Apart from the irregular time sampling, missing data, and high data variability in the spatial, temporal, and spectral domains that were mentioned above, another difficult challenge that is met in SITS analysis is the assignment of semantic meaning to patterns of spatio-temporal evolution.