Data Mining - Mehmed Kantardzic [210]
In Figure 12.32, an example of distributed DBSCAN for εglobal = 2εlocal is depicted. In Figure 12.32a the independently detected clusters on site 1, 2, and 3 are represented. The cluster on site 1 is represented using K-means by two representatives, R1 and R2, whereas the clusters on site 2 and site 3 are only represented by one representative as shown in Figure 12.32b. Figure 12.32c illustrates that all four local clusters from the different sites are merged together in one large cluster. This integration is obtained by using an εglobal parameter equal to 2εlocal. Figure 12.32c also makes clear that an εglobal = εlocal is insufficient to detect this global cluster. When the final global model is obtained, the model is distributed to local sites. This model makes corrections comparing previously found local models. For example, in the local clustering some points may be left as outliers, but with the global model they may be integrated into modified clusters.
12.5 CORRELATION DOES NOT IMPLY CAUSALITY
An associational concept is any relationship that can be defined in terms of a frequency-based joint distribution of observed variables, while a causal concept is any relationship that cannot be defined from the distribution alone. Even simple examples show that the associational criterion is neither necessary nor sufficient for causality confirmation. For example, data mining might determine that males with income between $50,000 and $65,000 who subscribe to certain magazines are likely purchasers of a product you want to sell. While you can take advantage of this pattern, say by aiming your marketing at people who fit the pattern, you should not assume that any of these factors (income, type of magazine) cause them to buy your product. The predictive relationships found via data mining are not necessarily causes of an action or behavior.
The research questions that motivate many studies in the health, social, and behavioral sciences are not statistical but causal in nature. For example, what is the efficacy of a given drug in a given population, or what fraction of past crimes could have been avoided by a given policy? The central target of such studies is to determine cause–effect relationships among variables of interests, for example, treatments–diseases or policies–crime, as precondition–outcome relationships. In order to express causal assumptions mathematically, certain extensions are required in the standard mathematical language of statistics, and these extensions are not generally emphasized in the mainstream literature and education.
The aim of standard statistical analysis, typified by regression and other estimation techniques, is to infer parameters of a distribution from samples drawn from that distribution. With the help of such parameters, one can infer associations among variables, or estimate the likelihood of past and future events. These tasks are managed well by standard statistical analysis so long as experimental conditions remain the same. Causal analysis goes one step further; its aim is to infer aspects of the data-generation process. Associations characterize static conditions, while causal analysis deals with changing conditions. There is nothing in the joint distribution of symptoms and diseases to tell us that curing the former would or would not cure the latter.
Drawing analogy to visual perception, the information contained in a probability function is analogous to a geometrical description of a three-dimensional object; it is sufficient for predicting how that object