Sparse p-adic data coding for computationally efficient and effective big data analytics

We develop the theory and practical implementation of p-adic sparse coding of data. Rather than the standard, sparsifying criterion that uses the $L_0$ pseudo-norm, we use the p-adic norm. We require that the hierar- chy or tree be node-ranked, as is standard practice in agglomerative and other hierarchical clustering, but not necessarily with decision trees. In order to structure the data, all computational processing operations are direct reading of the data, or are bounded by a constant number of direct readings of the data, implying linear computational time. Through p-adic sparse data coding, effi cient storage results, and for bounded p-adic norm stored data, search and retrieval are constant time operations. Examples show the e ffectiveness of this new approach to content-driven encoding and displaying of data.

We develop the theory and practical implementation of p-adic sparse
coding of data. Rather than the standard, sparsifying criterion that uses
the $L_0$ pseudo-norm, we use the p-adic norm. We require that the hierar-
chy or tree be node-ranked, as is standard practice in agglomerative and
other hierarchical clustering, but not necessarily with decision trees. In
order to structure the data, all computational processing operations are
direct reading of the data, or are bounded by a constant number of direct
readings of the data, implying linear computational time. Through p-adic
sparse data coding, effi cient storage results, and for bounded p-adic norm
stored data, search and retrieval are constant time operations. Examples
show the e ffectiveness of this new approach to content-driven encoding
and displaying of data.

Archived with thanks to P-Adic Numbers, Ultrametric Analysis, and Applications