- freely available
ISPRS Int. J. Geo-Inf. 2016, 5(11), 205; https://doi.org/10.3390/ijgi5110205
2. Methods for Time Series Clustering
2.1. Measurement of Similarity between Objects
2.2. A New Adaptive Strategy for Time Series Clustering
3. The DTSC Algorithm
3.1. Construction of Spatial Proximity Relationships
3.2. Clustering Objects with Similar Time Series Attributes
- Spatial neighbors: Objects connected by edges in the modified Delaunay triangulation.
- Attribute directly reachable: Objects with similar time series attribute values and attribute trends are considered as attribute directly reachable. The object and are attribute directly reachable, if
- and ; and
- Attribute reachable: Attribute reachable measures the similarity between an object and its neighboring objects. For a set of objects S, its neighboring object is considered attribute reachable from S if the attribute distance between and the mean value of S is less than TS.
- Density indicator: Density indicator represents the density of objects with similar attributes in the spatial domain. For an object , the density indicator is calculated with the following equation:
3.3. Accuracy Evaluation of Clustering Results
4.1. Validation of DTSC Algorithm on Simulated Datasets
4.1.1. Validation of DTSC Algorithm Based on Simulated Dataset
- and contain 759 and 806 objects, respectively,
- The time dimensionality is 20 and the neighboring time intervals are equal,
- Nine predefined clusters labeled as to in (in Figure 4) and five predefined clusters labeled as to in (in Figure 6) exist. These clusters possess arbitrary geometrical shapes and different densities. The non-spatial attributes of the cluster at every time point are randomly distributed under one range, and the mean value of attributes in every cluster are shown in Figure 5 and Figure 7,
- To maintain consistency with the real applications, noises are set in the simulated datasets and are classified into five types. Type 1 comprises the spatial noises that have a meaning similar to that of spatial outliers whose spatial attribute values are significantly different from those of other objects in their spatial neighborhood; these are labeled as (such as ). The non-spatial attributes of spatial noises are similar to the nearest clusters in dataset . Types 2 and 3 are the non-spatial attribute noises and non-spatial attribute trend noises, respectively, which are labeled as (such as to ) and (such as to ), respectively. The attributes of these types of noises are significantly different from those of their neighboring objects. Type 4 comprises noises whose attribute values and attribute trends are both significantly different from those of neighboring objects; these noises are labeled as (such as to ). Type 5 comprises gradually changing noises, whose attribute values change in a descending or ascending fashion along the spatial position although their attribute trends are similar. For example, the temperature decreases as the altitude increases, and the temperature trend is similar at different altitudes with seasonal variations. These gradually changing noises are labeled as (such as ).
4.1.2. Comparison between DTSC and Typical Algorithms
4.1.3. Comparison of the DTSC Algorithm with Optimal and Non-Optimal Parameters in the Spatial Domain
4.1.4. Comparison of the DTSC Algorithm with Proposed Similarity Measurements and Typical Similarity Measurements in the Non-Spatial Domain
4.2. A Case Study of DTSC on Rainfall Data
5. Discussion and Further Work
Conflicts of Interest
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|Clustering Results||Simulated Dataset||Accuracy Values||Computation Cost|
|Results of DTSC||√||1||1||1||5|
|Results of density-based time series clustering algorithm||√||0.95||0.95||1||4|
|Results of DTSC||√||1||1||1||4|
|Results of density-based time series clustering algorithm||√||0.65||0.55||0.44||3|
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