Data Mining Mehmed Kantardzic (good english books to read .txt) 📖

of the residual error vector ε are then assumed to be generated from independent and identical standard normal distributions. As in the case of classical regression, the proposed equation has to be transformed via the logistic function for binary dependent variables, and we refer to this equation as the SAR model. Notice that when ρ = 0, this equation collapses to the classical regression model. If the spatial autocorrelation coefficient is statistically significant, then SAR will quantify the presence of spatial autocorrelation in the classification model. It will indicate the extent to which variations in the dependent variable (y) are influenced by the average of neighboring observation values.

2. A spatial outlier is a spatially referenced object whose nonspatial attribute values differ significantly from those of other spatially referenced objects in its spatial neighborhood. This kind of outlier shows a local instability in values of nonspatial attributes. It represents spatially referenced objects whose nonspatial attributes are extreme relative to its neighbors, even though the attributes may not be significantly different from the entire population. For example, a new house in an old neighborhood of a growing metropolitan area is a spatial outlier based on the nonspatial attribute house age.

A variogram-cloud technique displays data points related by neighborhood relationships. For each pair of samples, the square-root of the absolute difference between attribute values at the locations versus the Euclidean distance between the locations is plotted. In data sets exhibiting strong spatial dependence, the variance in the attribute differences will increase with increasing distance between locations. Locations that are near to one another, but with large attribute differences, might indicate a spatial outlier, even though the values at both locations may appear to be reasonable when examining the dataset nonspatially. For example, the spatial data set is represented with six five-dimensional samples given in Figure 12.28a. Traditional nonspatial analysis will not discover any outliers especially because the number of samples is relatively small. However, after applying a variogram-cloud technique, assuming that the first two attributes are X-Y spatial coordinates, and the other three are characteristics of samples, the conclusion could be significantly changed. Figure 12.29 shows the variogram-cloud for this data set. This plot has some pairs of points that are out of main dense region of common distances.

Figure 12.28. An example of a variogram-cloud graph. (a) Spatial data set; (b) a critical sample’s relations in a variogram-cloud.

Figure 12.29. A variogram-cloud technique discovers an outlier.

Computation of spatial distances and distances of samples, as a part of a variogram technique, shows that there is a sample spatially relatively close to a group of other samples (small space distances) but with very high distances in other nonspatial attributes. This is the sample S3, which is spatially close to samples S1, S5, and S6. Coordinates of these samples and corresponding distances are given in Figure 12.28b, selecting S3 as a candidate for an outlier. Visualization of these and other relations between samples through a variogram shows the same results.

12.4 DISTRIBUTED DATA MINING (DDM)

The emergence of tremendous data sets creates a growing need for analyzing them across geographical lines using distributed systems. These developments have created unprecedented opportunities for a large-scale data-driven knowledge discovery, as well as the potential for fundamental gains in scientific and business understanding. Implementations of data-mining techniques on high-performance distributed computing platforms are moving away from centralized computing models for both technical and organizational reasons. In some cases, centralization is hard because it requires these multi-terabyte data sets to be transmitted over very long distances. In others, centralization violates privacy legislation, exposes business secrets, or poses other social challenges. Common examples of such challenges arise in medicine, where relevant data might be spread among multiple parties, in commercial organizations such as drug companies or hospitals, government bodies such as the U.S. Food and Drug Administration, and nongovernment organizations such as charities and public-health organizations. Each organization is bound by regulatory restrictions, such as privacy legislation, or corporate requirements on proprietary information that could give competitors a commercial advantage. Consequently, a need exists for developing algorithms, tools, services, and infrastructure that let us mine data distributed across organizations while preserving privacy.

This shift toward intrinsically distributed, complex environments has prompted a range of new data-mining challenges. The added dimension of distributed data significantly increases the complexity of the data-mining process. Advances in computing and communication over wired and wireless networks have resulted in many pervasive distributed computing environments. Many of these environments deal with different distributed sources of voluminous data, multiple compute nodes, and distributed user community. Analyzing and monitoring these distributed data sources require a new data-mining technology designed for distributed applications. The field of DDM deals with these problems—mining distributed data by paying careful attention to the distributed resources. In addition to data being distributed, the advent of the Internet has led to increasingly complex data, including natural-language text, images, time series, sensor data, and multi-relational and object data types. To further complicate matters, systems with distributed streaming data need incremental or online mining tools that require a complete process whenever a change is made to the underlying data. Data-mining techniques involved in such a complex environment must encounter great dynamics due to changes in the system, and it can affect the overall performance of the system. Providing support for all these features in DDM systems requires novel solutions.

The Web architecture, with layered protocols and services, provides a sound framework for supporting DDM. The new framework embraces the growing trend of merging computation with communication. DDM accepts the fact that data may be inherently distributed among different loosely coupled sites, often with heterogeneous data, and connected by a network. It offers techniques to discover new knowledge through distributed data analysis and modeling using minimal communication of data. Also, interactions in a distributed system need to be implemented in a reliable, stable, and scalable way. Ultimately, systems must be able to hide this technological complexity from users.

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