New dimensions - Meta-dimensions

This technique enables us to add new useful dimensions to our table. This can be ``measures'' as discussed in section 2.3.1, extracted features, labels of identified clusters, or any kind of function of other variables. This is especially useful for getting other viewpoints of the data. It helps connecting the results of other algorithms (e.g. clustering) with the structure-finding techniques discussed previously. For continuous variables linear combination, logarithms, multiplication of variables, etc. may be useful. For example regression and neural networks use these transformations for classification (see sections 3.1.2 and 3.1.3).

It should be also mentioned that new dimensions are almost always used for dimensionality reduction. In linear regression n dimensions are replaced with n-1, n-k or 1 dimension(s), expressed e.g. as linear combinations of the original distribution. Several dimensions are replaced with fewer new dimensions. This is especially important in context of the dramatic complexity increase with the number of dimensions (section 1). Furthermore, a primary function is that a new dimension represents by itself dependencies and relations among the old dimensions.