Classifying households by the (Sobolev) norms of their electricity consumption

Numerical time series, but especially periodic such, are characterized up to pertinent symmetries by families of norms. The electricity consumption by a household, recorded daily during a month's time, say, may then be encoded in a sequence of numbers; for example, as follows: the mean daily consumption, the mean daily variation of the consumption, the variation of the variation, the variation of the variation of the variation, etc. Now, replacing each of these numbers by the digits 0, 1, or 2, to say that a number is "low", "medium", or "high", in relation to a collection of households, one naturally partitions the collection by the strings of these three digits; the household labeled 102 ... has then medium daily consumption, low daily variation, but high variation of variation, etc. We generally discuss this innocent idea and examine it in three ways: by way of toy examples, through its mathematical model (in detail presented elsewhere) and by accordingly classifying some actual electricity consumption data. (C) 2014 The Authors, Published by Elsevier Ltd.