### abstract ###
A  SYMBOL -adic modification of the split-LBG classification method is presented in which first clusterings and then cluster centers  are computed which locally minimise an energy function
The outcome for a fixed dataset  is independent of the prime number  SYMBOL  with finitely many exceptions
The methods are applied to the construction of  SYMBOL -adic classifiers in the context of learning
### introduction ###
The field  SYMBOL  of   SYMBOL -adic numbers is of interest  in hierarchical classification  because of its inherent hierarchical structure  CITATION
A great amount of work deals with finding  SYMBOL -adic data representation (e g \  CITATION )
In  CITATION , the use of more general   SYMBOL -adic numbers for encoding hierarchical data was advocated in order to be able to include the case of non-binary dendrograms into the scheme without having to resort to a larger prime number  SYMBOL
This was applied in  CITATION  to the special case of data consisting in words over a given alphabet and where proximity of words is defined by the length of the common initial part
There,  an agglomerative  hierarchic  SYMBOL -adic clustering algorithm was described
However, the question of finding optimal clusterings of  SYMBOL -adic data was not raised
Already in  CITATION , the performance of classical and  SYMBOL -adic classification algorithms was compared in the segmentation of moving images
It was observed that the  SYMBOL -adic ones were often more efficient
Learning algorithms using  SYMBOL -adic neural networks are described in  CITATION
Inspired by   CITATION , our main concern in this article will be a  SYMBOL -adic adaptation of the so-called split-LBG method  which finds energy-optimal clusterings of data
The name ``LBG'' refers to the initials of the authors of  CITATION , where it is described first
Their method is to find cluster centers, and then to group the data around the centers
In the next step, the cluster centers are split, and more clusters are obtained
This process is repeated until the desired class number is attained
For  SYMBOL -adic data, this approach does not make sense:  first of all, cluster centers are in general not unique; and secondly, because the dendrogram is already determined by data, an arbitrary choice of cluster centers is not possible---this can lead to incomplete clusterings
Hence, we first find clusterings by refining in the direction of highest energy reduction, until the class number exceeds a prescribed bound
Thereafter, candidates for cluster centers are computed: they minimise the cluster energy
The result is a sub-optimal method for   SYMBOL -adic classification which splits a given cluster into its maximal proper subclusters
A variant discards first all quasi-singletons, i e \ clusters of  energy below a threshold value
The  a posteriori  choice of centers turns out useful for  constructing % efficient classifiers
A first application of some of the methods described here to event history data of building stocks is described in  CITATION
There,  the classification algorithm is performed on different  SYMBOL -adic encodings of the data in order to compare the dynamics of some sampled municipal building stocks
After introducing notations in Section , we briefly describe the classical split-LBG method in Section
Section  reformulates the minimisation task of split-LBG in  the  SYMBOL -adic setting, and describes the corresponding algorithms
The issue on the choice of the prime  SYMBOL  is dealt with in Section
Section   constructs classifiers and presents an adaptive learning method in which accumulated clusters of large energy are split
