Linguistic summaries of locally periodic time series

Abstract

International audienceThis paper proposes a method to linguistically summarise the local periodic components of a time series: it identifies subparts of the data which are periodic, together with their periodicity degree and period, and provides a linguistic description thereof. The generated sentences can be illustrated by the example " Approximately from March to June, the series is highly periodic with a period of exactly 2 weeks ". The method proposed to identify local periodic zones relies on the determination of relevant auto-adaptive windows, based on an analytical expression of the probability distribution of the considered periodicity criterion. The linguistic description generation, in the protoform approach framework, expresses three core aspects of the identified periodic intervals, namely their time context or localisation in time, their periodicity and their period. Intensive experiments performed on both artificial and real data validate the proposed method

Strengths of Fuzzy Techniques in Data Science

“…We focus on the analysis of periodicity of time series, which can obviously be approximative or described imprecisely, for instance of the form "M any x s are A most of the time" [18]. To analyze the regularity of high and low values, the periodicity of such behaviors and their approximate duration can for instance be achieved through an efficient scalable and robust method [19] requesting neither any hypothesis on the data nor any tuning of parameters, automatically detecting groups of high and low values and providing simple natural language descriptions of the periodicity.…”

Personalized linguistic summaries in smartphone-based monitoring of bipolar disorder patients

“…For example, in [25], Wilbik et al focus on potential changes in time and introduce modication of summaries into the linguistic medoid prototypes, that may be exemplied with the following sentence: Mrs. Wilbewski is much better this week than she was last week. Moyse et al [21] focus on local periodic components of a time series and propose summaries like Approximately from March to June, the series is highly periodic with a period of exactly 2 weeks. For further extensions of linguistic summaries see also the evaluative linguistic expressions introduced by Novak [22] Within this research, we focus on the patientdependent and disease-state-dependent linguistic summaries.…”

Some Notes on Extracting Linguistic Summaries Built with Epistemic Modalities and Natural Language Connectives of Equivalence

“…Over the last years, the group of temporally-related linguistic summaries has been an object of intensive theoretical study and application-oriented development. Although the body of results is still rather modest, as compared to previously mentioned groups of linguistic summaries, however, it consists of strong computational models (see [11,14,15] for interesting and valuable examples). Again, all of them are in many ways related to the original concept of linguistic variable [20] and Zadeh's paradigm of computing with words [13,24,25].…”

“…It supports the way in which this class of summarizing statements can be evaluated against their pragmatic adequacy and commonsense consistency, and further applied to practical contexts. Such support is ensured by an original theory of modal language grounding (the grounding theory for short) which was presented in parts elsewhere: detailed sub-theories of natural language grounding relevant to protoforms (6)- (7) in [30,36] and sub-theories related to protoforms (8)- (11) in [29,31,32,35].…”