Unsupervised clustering problems

The two pattern recognition techniques used In this work are among those usually used for unsupervised learning. The results will be examined for the clusters which arise from the analysis of the data. On the other hand, the number of classes and a rule for assigning compounds to each had already been determined by the requirements of the mixture analysis problem. One might suppose that a supervised approach would be more suitable. In our case, this Is not so because our aim Is not to develop a classifier. Instead, we wish to examine the data base of FTIR spectra and the metric to see If they are adequate to help solve a more difficult problem, that of analyzing complex mixtures by class. 

This technique makes use of the innate human cognition to perform clustering in multidimensional space (Osbourn and Martinez, 1995). It is unsupervised and model-free, therefore requires from the user only the data input. A special mask mathematically defines the visual region of influence. Its shape is based on human visual perception, taking advantage of the human brain to recognize and cluster objects (Fig. 10.10a). Its properties are as follows. Two points in space are clustered only if no other point lies within area of the mask which thus defines the exclusion region. In this way, an n-dimensional problem is reduced to set of n two-dimensional problems. 

There are two different approaches to the protein sequence classification problem. One can use an unsupervised neural network to group proteins if there is no knowledge of the number and composition of final clusters (e.g., Ferran Ferrara, 1992). Or one can use supervised networks to classify sequences into known (existing) protein families (e.g., Wu et al., 1992). 

It is now necessary to measure the effect the various combinations have on E. For instance, let H be the degree of cluster overlap. In this case it is possible to observe how different masks affect E. Of course, it is vital to have decided on which objects belong to a cluster. In other words, the analysis is temporarily turned into a supervised rather than an unsupervised problem which for complex cases can be solved by methods like CART [45] and discriminant PLS [46-48] and Quinlan s C4.5 algorithm [49]. 

Tasks that fall within the paradigm of unsupervised learning are in general estimation problems the applications include clustering and estimating statistical distributions, compression, and filtering. 

In the previous section, the classification problem was considered to be essentially that of learning how to make decisions about assigning cases to known classes. There are, however, different forms of classification problem, which may be tackled by unsupervised learning, or clustering. Unsupervised classification is appropriate when the definitions of the classes, and perhaps even the number of classes, are not known in advance, e.g., market segmentation of customers into similar groups who can then be targeted separately. 

If the class membership of the patterns are known one speaks about supervised learning (learning with a teacheh) More difficult is the problem if no natural classes of patterns are known a priori. In this case an unsupervised learning (learning without a teacher) requires a cluster analysis and a physically meaningful interpretation of the clus- ters. 

If an assignment of classes to patterns is not evident, then unsupervised Learning methods are often helpful. Methods of finding clusters in a multidimensional pattern space are used to find natural classes in a data set. Such methods are not trivial and always contain heuristic and arbitrary elements. Subjective parameters are necessary to control the size, shape and number of clusters for a certain problem. different representations of the data often give different clusters. 

The classical variants of both the pattern recognition categories - supervised and unsupervised learning - will assign the data unambiguously to one class or another to its full degree (see Chemometrics Multivariate View on Chemical Problems). Objects lying at class boundaries are less typical members of each class than those near to the cluster center. These objects may be outliers or they may be hybrids,... 

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