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On one hand, the understanding of compact clusters in subsets of dimensions is challenging itself.
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Therefore, it becomes imperative to find the clusters in the relevant subsets of dimensions of the data (called subspaces).
The most well-known subspace analysis technique is subspace clustering which is illustrated in Fig. 2. Subspace clustering algorithms search for clusters not in the whole data space, but within different subsets of dimensions (called subspaces) in which discriminating clusters can be found [14].
Open image in new window Fig. 1 Effects in high-dimensional data: some objects are only similar in a subset of dimensions (=subspace), e.g., (rec_1,,rec_2,,rec_3) in the first three and (rec_3,,rec_{n-1},rec_nn) in the last three dimensions.
We assume the following reasons: (1) patients are typically similar to each other only in a subset of dimensions; (2) a similarity in one dimension can be countered by a dissimilarity in another dimension; and (3) the concentration effect [3] affects the similarity computation in high-dimensional spaces.
As a consequence, we rather search for local clusters in a subset of patients and, more importantly, in a subset of dimensions.
Data group together differently under different subsets of dimensions, called subspaces.
MCA produces a new multidimensional space so that the accumulated variance of the coordinates of every probe in a subset of dimensions is optimal.
We then compute a subset of dimensions which can together differentiate two groups of individuals.
The FSA is then employed to identify a subset of dimensions that can best predict a particular class of subjects.
8 We venture here to add a variation, that attempts to award dominance on subsets of the dimensions.
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