Linguistic description of phenomena evolving in time

The approach followed to define a computational model of phenomena is based on subjective perceptions of a domain expert, called from now on the “designer”. The more experienced the designer, with better understanding and use of NL in the appli-cation domain, the richer the model with more possibilities of achieving and respon-ding to final users’ needs and expectations. The designer uses the available resources, e.g., sensors, to acquire data about a phenomenon and uses her/his own experience to interpret these data and to model it. Then, the designer uses a computer to produce the needed linguistic utterances.

In the current project, the designer is a person experienced with the motion of the body while performing the Sun Salutation sequence, being able of modelling the exercise by using the data available from several on-body sensors. Furthermore, the designer takes into consideration the relevant information to be extracted during the analysis in order to provide a useful feedback for rehabilitation purposes.

In this section, the components of the Granular Linguistic Model of a Phenomenon (GLMP), the approach based on the Computational Theory of Perceptions followed

for developing computational systems able to generate linguistic descriptions of phe-nomena [37,290], are presented.

Computational perception (CP)

A CP is the computational model of a unit of information acquired by the designer about the phenomenon to be modelled. In general, CPs correspond to particular de-tails of the phenomenon at certain degrees of granularity. A CP is a couple (A,W ) where:

A= (a1, a2, . . . , an) is a vector of n linguistic expressions (words or sentences in NL) that represents the whole linguistic domain of the CP. Each a_i describes the value of the CP in each situation with specific granularity degree. These sen-tences can be either simple, e.g., ai=“The angle of the sensor is negative.” or more complex, e.g., a_i=“The symmetry of the calves during the first pose is high.”.

W= (w1, w2, . . . , w_n) is a vector of validity degrees w_i∈ [0, 1] assigned to each a_iin the specific context. The concept of validity depends on the application, e.g., it is a function of the truthfulness of each sentence in its context of use.

Perception mapping (PM)

PMs are used to create and aggregate CPs. A PM is a tuple (U,y,g,T ) where:

U is a vector of input CPs, U = (u1, u₂, . . . , u_n), where u_i= (A_ui,W_ui) and n is the number of input CPs. In the special case of first-order perception mappings (1-PMs), these are the inputs to the GLMP and they are values z ∈ R being provided either by sensors or obtained from a database.

y is the output CP, y = (Ay,Wy).

g is an aggregation function employed to calculate the vector of validity degrees assigned to each element in y, W_y = (w1, w2, ..., w_ny). It is an aggregation of input vectors, W_y = g(Wu1,Wu2, ...,Wun), where Wui are the degrees of validity

of the input perceptions. In fuzzy logic, many different types of aggregation functions have been developed. For example, g might be implemented using a set of fuzzy rules. In the case of 1-PMs, g is built using a set of membership functions as follows:

Wy= (µa1(z), µa2(z), . . . , µa_ny(z)) = (w1, w2, . . . , wny)

where W_y is the vector of degrees of validity assigned to each a_y, and z ∈ R is the input data.

T is a text generation algorithm that allows generating the sentences in A_y. In simple cases, T is a linguistic template, e.g., “The calves symmetry is {low | medium| high}”.

Granular Linguistic Model of a Phenomenon

The GLMP consists of a network of PMs. Each PM receives a set of input CPs and transmits upwards an output CP. It is said that each output CP is explained by the PMusing a set of input CPs. In the network, each CP covers specific aspects of the phenomenon with a certain level of granularity. Figure4.12shows an example of a GLMP, where the phenomenon can be described at a very basic level in terms of two variables providing two values, z₁and z₂, at a certain instant of time.

As mentioned above, first-order perception mappings (1-PM) are those which are input to the GLMP. These 1-PMs produce first-order computational perceptions (1-CP). On the other side, PMs whose inputs are CPs are called second-order perception mappings(2-PM) and their outputs are named 2-CPs.

Using different aggregation functions and linguistic expressions, the GLMP pa-radigm allows the designer to model computationally her/his perceptions. In the case of Figure4.12, the second order perception mapping 2-PM₃indicates that 2-CP₃can be explained in terms of the first order computational perceptions 1-CP1 and 1-CP2, i.e., how the validity of each item in 2-CP3is explained by those of 1-CP1and 1-CP2. Finally, the highest-order description of the phenomenon is provided, at the highest

Figure 4.12: Example of a Granular Linguistic Model of a Phenomenon.

level of abstraction, by 2-CP₄, explained by 2-PM₄in terms of 2-CP₃and 1-CP₂. No-tice that, by using this structure, one can provide not only a linguistic description of the phenomenon at a certain level, but an explanation in terms of linguistic expres-sions at a lower level.

Report generation

Once the GLMP is fed with input data, the aggregation functions are used to calcu-late the validity degrees corresponding to potentially hundreds of linguistic expres-sions. The input data depends on each particular application. In this case, it is motion data acquired by the proposed wearable sensing system. Now, the challenge consists of choosing the most adequate combination of these sentences to generate a useful linguistic description of the phenomenon evolution including the current state. The design of this report requires a deep analysis of the application domain of language and, therefore, the collaboration of an experienced final user.

For the proof of concept, here a simple report is used, made by choosing the lin-guistic expressions with the highest validity degree and including detailed explana-tions of a perception by using the conjunction “because”. In [291] other two different

types of report templates are developed.