Cluster features tree

Fig. 4.16 Main workflow used by HTSview. First a similarity matrix is computed based on Feature Tree similarity, Then the Feature Trees are clustered. For selected clusters MTree models are constructed. A QSAR matrix is computed based on the MTree as an align-...

Percolation theory describes [32] the random growth of molecular clusters on a d-dimensional lattice. It was suggested to possibly give a better description of gelation than the classical statistical methods (which in fact are equivalent to percolation on a Bethe lattice or Caley tree, Fig. 7a) since the mean-field assumptions (unlimited mobility and accessibility of all groups) are avoided [16,33]. In contrast, immobility of all clusters is implied, which is unrealistic because of the translational diffusion of small clusters. An important fundamental feature of percolation is the existence of a critical value pc of p (bond formation probability in random bond percolation) beyond which the probability of finding a percolating cluster, i.e. a cluster which spans the whole sample, is non-zero. 

A curious feature of the A -R-B model is that it apparently possesses two critical points. But one of them is in fact physically unrealizable. Now consider an x-meric cluster of the A -R-By model without rings (we are considering the virtual tree molecule). The total number of B FUs within this molecule is (f - g)x, of which the number of reacted FUs amounts to x-1. The extent of reaction within this molecule, thus, may be written... 

The impurity of a cluster can be formulated in a number of ways as we shall see in Section 15.1.9. Here even a simple measure will do, for example the ratio of word-1 over word-2. The stopping criteria usually involves specifying a minimum decrease in impurity. The decision tree gets round the problem of modelling all the feature combinations by effectively clustering certain feature combinations together. This is not always ideal, but it certainly does allow for more accurate modelling than naive Bayes, as we can see that the same feature can appear in different parts of the tree and have a different affect on the outcome. 

We solve this by making use of some of the common properties of phones, and the most common way of doing this is to use the phones distinctive features (see Section 7.4.3). In doing so, we are for instance positing that phones which share the same place of articulation may have more similar acoustic realisations than ones which don t. The most common way of performing this feature based clustering is to use a decision tree the clever thing about this is that while we... 

An important point about the decision tree grown in this way is that it provides a cluster for every feature combination, not just those encountered in the training data. So see this, consider the tree in Figure 15.12. One branch of this has the feature set... 

As well shall see in Sections 15.2.4 and 16.4.1, decision tree clustering is a key component of a number of s mthesis systems. In these, the decision is not seen so much as a clustering algorithm, but rather as a mapping or function from the discrete feature space to the acoustic space. As this is fully defined for every possible feature combination, it provides a general mechanism for generating acoustic representations from linguistic ones. 

The usefulness of the tree is that it provides natural metrics of similarity between all feature combinations, not just those observed. The clever bit is that the tree will always lead us to a cluster even for feature combinations completely missing Ifom the data. As with observed feature combinations, we can just measure the distance between the means of these to give us the value for our target function. 

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