Anna Wilbik

Linguistic summarization of time series using a fuzzy quantifier driven aggregation

We propose new types of linguistic summaries of time-series data that extend those proposed in our previous papers. The proposed summaries of time series refer to the summaries of trends identified here with straight line segments of a piecewise linear approximation of time series. We first show how to construct such an approximation. Then we employ a set of features (attributes) to characterize the trends such as the slope of the line segment, the goodness of approximation and the length of the trend. The derivation of a linguistic summary of a time series is then related to a linguistic quantifier driven aggregation of trends. For this purpose we employ the classic Zadehs calculus of linguistically quantified propositions but, extending our previous works, with different t-norms in addition to the basic minimum. We show an application to the analysis of time-series data on daily quotations of an investment fund over an eight year period, present some interesting linguistic summaries obtained, and show results for different t-norms. The results are very promising.

A distance metric for a space of linguistic summaries

Producing linguistic summaries of large databases or temporal sequences of measurements is an endeavor that is receiving increasing attention. These summaries can be used in a continuous monitoring situation, like eldercare, where it is important to ascertain if the current summaries represent an abnormal condition. It is therefore necessary to compute the distance between summaries as a basis for such a determination. In this paper, we propose a dissimilarity measure between summaries based on fuzzy protoforms, and prove that this measure is a metric. We take into account not only the linguistic meaning of the summaries, but also two quality evaluations, namely the truth values and the degrees of focus. We present examples of how the distance metric behaves and show that it corresponds with intuition.

On some types of linguistic summaries of time series

The purpose of this paper is to propose the use of linguistic quantifiers for the linguistic summarisation of time series, notably in terms of trends. To characterize the data trends, we use three parameters: dynamics of change, duration and variability and apply to them the fuzzy linguistic summaries of data (databases) in the sense of Yager. We Introduce the two types of linguistic summaries, one based on frequency and one based on duration

Linguistic Summarization of Time Series Under Different Granulation of Describing Features

We consider an extension to a new approach to the linguistic summarization of time series data proposed in our previous papers. We summarize trends identified here with straight segments of a piecewise linear approximation of time series. Then we employ, as a set of features, the duration, dynamics of change and variability, and assume different, human consistent granulations of their values. The problem boils down to a linguistic quantifier driven aggregation of partial trends that is done via the classic Zadehs calculus of linguistically quantified propositions but with different t-norms. We show an application to linguistic summarization of time series data on daily quotations of an investment fund over an eight year period.

Linguistic summarization of sensor data for eldercare

Ubiquitous passive, as well as active, monitoring of elders is a growing field of research and development with the goal of allowing seniors to live safe active independent lives with minimal intrusion. Much useful information, fall detection, fall risk assessment, activity recognition, early illness detection, etc. can be inferred from the mountain of data. Healthcare must be human centric and human friendly, and so, methods to consolidate the data into linguistic summaries for enhanced communication and problem detection with elders, family and healthcare providers is essential. Long term trends can be most easily identified using summarized information. This paper explores the soft computing methodology of protoforms to produce linguistic summaries of one dimensional data, motion and restlessness. The technique is demonstrated on a 15 month sensor collection for an elder participant.

A Fuzzy Measure Similarity Between Sets of Linguistic Summaries

In this paper, we consider the problem of evaluating the similarity of two sets of linguistic summaries of sensor data. Huge amounts of available data cause a dramatic need for summarization. In continuous monitoring, it is useful to compare one time interval of data with another, for example, to detect anomalies or to predict the onset of a change from a normal state. Assuming that summaries capture the essence of the data, it is sufficient to compare only those summaries, i.e., they are descriptive features for recognition. In previous work, we developed a similarity measure between two individual summaries and proved that the associated dissimilarity is a metric. Additionally, we proposed some basic methods to combine these similarities into an aggregate value. Here, we develop a novel parameter free method, which is based on fuzzy measures and integrals, to fuse individual similarities that will produce a closeness measurement between sets of summaries. We provide a case study from the eldercare domain where the goal is to compare different nighttime patterns for change detection. The reasons for studying linguistic summaries for eldercare are twofold: First, linguistic summaries are the natural communication tool for health care providers in a decision support system, and second, due to the extremely large volume of raw data, these summaries create compact features for an automated reasoning for detection and prediction of health changes as part of the decision support system.

Linguistic Summaries of Time Series via an OWA Operator Based Aggregation of Partial Trends

We extend our approach to the linguistic summarization of (numerical) time series. The main issue boils down to the identification of trends in time series that are characterized by a set of attributes followed by their appropriate aggregation. We propose to use the OWA (ordered weighted averaging) operators for the aggregation of partial trends as an alternative to the use of the classic Zadehs calculus of linguistically quantified propositions, the Sugeno integral and the Choquet integral. The use of the OWA operators provides a convenient unified aggregation means that can be used to derive diverse types of summaries. The results obtained confirm a high human consistency of linguistic summaries derived.

Linguistic Prototypes for Data From Eldercare Residents

We present a model for the analysis of time series sensor data collected at an eldercare facility. The sensors measure restlessness in bed and bedroom motion of residents during the night. Our model builds sets of linguistic summaries from the sensor data that describe different events that may occur each night. A dissimilarity measure produces a distance matrix D between selected sets of summaries. Visual examination of the image of a reordered version of D provides an estimate for the number of clusters to seek in D. Then, clustering with single linkage or non-Euclidean relational fuzzy c-means produces groups of summaries. Subsequently, each group is represented by a linguistic medoid prototype. The prototypes can be used for resident monitoring, two types of anomaly detection, and interresident comparisons. We illustrate our model with real data for two residents collected at TigerPlace: the “aging in place” facility in Columbia, MO, USA.

Towards an efficient generation of linguistic summaries of time series using a degree of focus

We present an approach to a more efficient generation of linguistic summaries using the traditional degree of truth and a degree of focus based mechanism for discarding nonpromising summaries. We use the approach to derive linguistic data summaries to subsume the past performance of an investment (mutual) fund, and then present numerical results on the efficiency of the truncation process proposed. It turns out that the mechanism proposed is efficient and makes possible to disregards between 75% to 99% possible summaries.

Linguistic Summarization of Time Series by Using the Choquet Integral

We further extend a new approach to a linguistic summarization of time series proposed in our previous works (cf. Kacprzyk, Wilbik and Zadrozny [1,2,3,4,5]) in which we put forward the use of a fuzzy linguistic quantifier driven aggregation of trends (partial scores) via the traditional Zadeh calculus of linguistically quantified propositions and the Sugeno integral. Here we use for this purpose the Choquet integral that has been widely advocated for many decision analytic and economic problems. The results are intuitively appealing and the method is effective and efficient.