Feature extraction is perhaps the most difficult task of the whole enterprise of data exploration. The components of the data vectors should be selected and preprocessed so that the relations between the representations of the data items would correspond to meaningful relations between the items. Considerable expertise in the application area may be required for building suitable feature extractors.
The adaptive-subspace SOM (ASSOM) [Kohonen, 1995a, Kohonen, 1995b, Kohonen, 1995c, Kohonen, 1996] is a step towards a more general-purpose feature extractor: it extracts invariant features from its input, features that are invariant to the particular transformation that has operated on the inputs.
The ASSOM could act as a learning feature extraction stage that produces invariant representations to be explored by the SOM, or in feature exploration. The ASSOM extracts the invariant features with filters that are formed automatically based on short sequences of input samples during the learning process. Insight into the processes that have produced the data set might then be gained by visualizing the resulting filters. The visualization is particularly easy since the representations of the ASSOM are ordered just as in the basic SOM.
In Publication 8 the study of the ASSOM algorithm is continued; both the theoretical treatment and the scope of the experimental simulations are broadened. It is demonstrated that features invariant to different kinds of transformations can be extracted, and that areas in which all units have been specialized to be invariant to one of the transformations emerge if several transformations have been present in the training data, albeit at different times.