Data Mining: The Textbook

Meteorological data: Quantifications of important weather characteristics, such as the temperature and pressure, are typically measured at different geographical locations. These can be analyzed to discover interesting events in the underlying data.

2. 
   Mobile objects: Moving objects typically create trajectories. Such trajectories can be analyzed for a wide variety of insights, such as characteristic trends, or anomalous paths of objects.
   

3. 
   Earth science data: The land cover types at different spatial locations may be rep-resented as behavioral attributes. Anomalies in such patterns provide insights about anomalous trends in human activity, such as deforestation or other anomalous vege-tation trends.
   

4. 
   Disease outbreak data: Data about disease outbreaks are often aggregated by spatial locations such as ZIP code and county. The analysis of trends in such data can provide information about the causality of the outbreaks.
   

5. 
   Medical diagnostics: Magnetic resonance imaging (MRI) and positron emission tomog-raphy (PET) scans are spatial data in 2 or 3 dimensions. The detection of unusual
   

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532 CHAPTER 16. MINING SPATIAL DATA

localized regions in such data can help in detecting diseases such as brain tumors, the onset of Alzheimer disease, and multiple sclerosis lesions. In general, any form of image data may be considered spatial data. The analysis of shapes in such data is of considerable importance in a variety of applications.

6. 
   Demographic data: Demographic (behavioral) attributes such as age, sex, race, and salary can be combined with spatial (contextual) attributes to provide insights about the demographic patterns in distributions. Such information can be useful for target-marketing applications.
   

Most forms of spatial data may be classified as a contextual data type, in which the attributes are partitioned into contextual attributes and behavioral attributes. This parti-tioning is similar to that in time series and discrete sequence data:

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  Contextual attribute(s): These represent the attributes that provide the context in which the measurements are made. In other words, the contextual attributes provide the reference points at which the behavioral values are measured. In most cases, the contextual attributes contain the spatial coordinates of a data point. In some cases, the contextual attribute might be a logical location, such as a building or a state. In the case of spatiotemporal data, the contextual attributes may include time. For example, in an application in which the sea surface temperatures are measured at sensors at specific locations, the contextual attributes may include both the position of the sensor, and the time at which the measurement is made.
  

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  Behavioral attribute(s): These represent the behavioral values at the reference points. For example, in the aforementioned sea surface temperature application, these corre-spond to the temperature attribute values.
  

In most forms of spatial data, the spatial attributes are contextual, and may optionally include temporal attributes. An exception is the case of trajectory data, in which the spatial attributes are behavioral, and time is the only contextual attribute. In fact, trajectory data can be considered equivalent to multivariate time series data. This equivalence is discussed in greater detail in Sect. 16.3.

This chapter separately studies cases where the spatial attributes are contextual, and those in which the spatial attributes are behavioral. The latter case typically corresponds to trajectory data, in which the contextual attribute corresponds to time. Thus, trajectory data is a form of spatiotemporal data. In other forms of spatiotemporal data, both spatial and temporal attributes are contextual.

This chapter is organized as follows. Section 16.2 addresses data mining scenarios in which the spatial attributes are contextual. In this context, the chapter studies several important problems, such as pattern mining, clustering, outlier detection, and classification. Section 16.3 discusses algorithms for mining trajectory data. Section 16.4 discusses the summary.

16.2 Mining with Contextual Spatial Attributes

In many forms of meteorological data, a variety of (behavioral) attributes, such as temper-ature, pressure, and humidity, are measured at different spatial locations. In these cases, the spatial attributes are contextual. An example of sea surface temperature contour charts