Data analysis
Step 8: Decrease all error variables (multiplying them with a constant d)
4.4 Hybrid neuro-fuzzy system
4.4.2 GLMP designed for postural balance assessment
consi-ders that the transitions are shorter by taking into account the derivatives information with a lower “virtual” threshold. However, this approach is still valid for being used in the current proposal. Once the poses are segmented, with the aim to analyse just that part of the signal in order to assess at the highest level the postural balance of the subject, the data taken into consideration will correspond to the central 80% of the poses segmented, giving the subject the required time to stabilize the acquired posture.
which can be described by the following template:
a[1:3]θ
i → “The variance of the angle of sensor ‘i’ in pose {j} is {low | medium | high}.”
The validity degrees are obtained from the trapezoidal membership functions shown in Figure4.23, which were designed empirically.
0 0.40.50.6 1 2 3 4 4.5 5 5.5 6
Variance(θ)
0.0 0.2 0.4 0.5 0.6 0.8 1.0
Membershipdegree
Low Medium High
Figure 4.23: Trapezoidal membership functions for the variance of the angle.
Variance of the angle of the sensor during the exercise (PMRF, PMLF, PMPBW, PMRC, PMLC)
PMRF, PMLF, PMPBW, PMRCand PMLC(where RF, LF, PBW, RC and LC stand for Right Forearm, Left Forearm, Partial Back Waist, Right Calf and Left Calf) are 2-PMs which describe the variance of the angle of the sensors while performing all the poses. The aggregation functions calculate the corresponding validity degrees as
shown in Eq.4.10:
wiRF=
Ti
∑
t=0
wiθ1[t]
Ti , wiLF =
Ti
∑
t=0
wiθ2[t]
Ti , wiPBW =
Ti
∑
t=0
wiθ3[t]
Ti
wiRC=
Ti
∑
t=0
wiθ
4[t]
Ti , wiLC=
Ti
∑
t=0
wiθ
5[t]
Ti (4.10)
The output CPs are described by the following templates:
a[1:3]RF → “The variance of the angle of the sensor on the right forearm during the exercise is {low| medium | high}.”
a[1:3]LF → “The variance of the angle of the sensor on the left forearm during the exercise is {low| medium | high}.”
a[1:3]PBW → “The variance of the angle of the sensor on the back waist during the exercise is {low| medium | high}.”
a[1:3]RC → “The variance of the angle of the sensor on the right calf during the exercise is {low| medium | high}.”
a[1:3]LC → “The variance of the angle of the sensor on the left calf during the exercise is {low| medium | high}.”
Stability of the forearms and the calves during the exercise (PMF, PMC)
These PMs merge the data corresponding to the variance of the forearms and the calves in order to provide information about the stability of the limbs. The aggrega-tion funcaggrega-tions calculate their validity degrees as shown in Eq.4.11:
wiF = w(3−i+1)
RF+ w(3−i+1)
LF
2 , wiC =w(3−i+1)
RC+ w(3−i+1)
LC
2 (4.11)
The output CP of PMF, for example, would include the following set of NL sentences:
a1F → “The stability of the forearms during the exercise is low.”
a2F → “The stability of the forearms during the exercise is medium.”
a3F → “The stability of the forearms during the exercise is high.”
While dealing with the pure linguistic system described in the previous section, it was noticed that, depending on the values obtained for the validity degrees, the NL sentences provided by the output CPs would be more or less meaningful. For exam-ple, considering two different sets of validity degrees for the current PM: w1F = 0.94, w2F = 0.06, w3F = 0.00 and w1F = 0.52, w2F = 0.48, w3F = 0.00, and taking the sen-tence corresponding to the maximum validity degree, the output would correspond in both cases to a1F: “The stability of the forearms during the exercise is low.”. Ho-wever, it is obvious that the “relevance” or “importance” of this sentence, or how it could be perceived by a clinician or a patient, is not the same for the two sets. In the first one, w1F is clearly the maximum validity degree with a significant difference from the others (0.94 with respect to 0.06), while in the second set, this difference is much smaller (0.52 with respect to 0.48). With the aim to provide a more meaningful description of the phenomenon and to improve the usability of texts, it is proposed to include a modifier of intensity, as commonly done in human discourse [318]. The quantifier chosen to be considered when the maximum validity degree corresponds to the first or the third sentence (therefore to modify the adjectives “low” or “high”, while it would not have much sense in natural language applying it to the adjective
“medium”) is quite.
In this context, the standard deviation among the weights provided by the PM is taken into consideration. If the standard deviation calculated is below a determined threshold, fixed experimentally at 0.2, which means that there is not a large difference among the weights, this quantifier is included in the text. Considering this, the output CPof PMF includes the following set of NL sentences:
a1F → “The stability of the forearms during the exercise is (quite) low.”
a2F → “The stability of the forearms during the exercise is medium.”
a3F → “The stability of the forearms during the exercise is (quite) high.”
Equivalently, the output CP of PMCis expressed by the following sentences:
a1C → “The stability of the calves during the exercise is (quite) low.”
a2C→ “The stability of the calves during the exercise is medium.”
a3C→ “The stability of the calves during the exercise is (quite) high.”
Stability of the back waist during the exercise (PMBW)
The other PM in this level transforms the variance of the angle of the sensor in the back waist in order to obtain its stability by calculating the corresponding validity degrees as described in Equation4.12.
wiBW= w(3−i+1)
PBW (4.12)
The template of the output CP is:
a[1:3]BW → “The stability of the back waist during the exercise is {low | medium | high}.”
Postural balance during the exercise (PMPB)
The PM at the highest level provides the output CP yPBwith a description of the pos-tural balance based on the stability of each part of the body. The aggregation function (gPB) calculates the validity degree (wiPB) of each sentence as shown in Eq.4.13:
wiPB= wiF+ wiBW+ wiC
3
∑
j=1
wjF+ wjBW+ wjC
(4.13)
Considering the use of the quantifier quite as before, the output CP yPBincludes the following set of NL sentences:
a1PB → “The postural balance while performing the Sun Salutation is (quite) low.”
a2PB→ “The postural balance while performing the Sun Salutation is medium.”
a3PB → “The postural balance while performing the Sun Salutation is (quite) high.”