Outlier analysis
in time-evolving sensory evaluation tasks
Hiroharu Natsume

Shogo Okamoto

Nanako Shimaoka

Tokyo Metropolitan UniversityTokyo, JapanTokyo Metropolitan UniversityTokyo, Japan

Nagoya University
Nagoya, Japan

Abstract—The temporal dominance of sensations (TDS)
method measures the time-evolving changes in subjectively reported sensations. This method has been used to obtain averageexperiences among panels, and there has been no method toanalyze individual differences in such dynamic experiences.
Therefore, we proposed a dissimilarity index to quantitatively
judge how two TDS tasks deviate and then successfully screened
an outlier among 51 TDS tasks for strawberries. The task judged
as an outlier was semantically different from the average task.
Index Terms—Sensory evaluation, Temporal dominance ofsensations

I. I NTRODUCTION
The temporal dominance of sensations (TDS) method [1]is a time-evolving sensory evaluation method that records
changes in multiple sensations over time while eating foodsand enjoying audiovisual contents. However, this method aims
to quantify the average experience among all panels (i.e.,assessors) and is believed to be unsuitable for analyzing individual differences. There have been few studies on individual
differences in TDS methods. The only example is the groupingof panels using a semi-Markov chain model [2]. There has
been no method to statistically analyze outliers from multiple
panels or TDS tasks. Therefore, we propose a method ofanalyzing individual differences and outliers in TDS task
results.
II. TDS TASKS AND CURVES FOR STRAWBERRIES
During the tasks of the TDS method, a graphic user interfacewith multiple buttons on a computer screen is used. Eachbutton has a label describing sensations. The panel exposed tosensory stimuli presses the button of an attribute that is closest
to the sensation that they consider the most dominant. Anotherbutton is then selected when the dominant sensation changes.
This operation lasts until the food in the mouth disappears or
the stimulus is no longer felt. A percentage of the panel thatconsider a certain sensation to be dominant at a given time,out of the total panel, is called the dominance proportion ofthe sensation. The time series of the dominance proportion iscalled the TDS curve, representing the average behavior of theentire panel.
We measured the taste, smell, and texture changes whileeating strawberries using the TDS method. Eight types ofThis study was supported in part by the Tojuro Iijima Foundation for Food
Science and Technology (#2020-40).

978-1-6654-1903-1/22/$31.00 2022 IEEEFig. 1: TDS curve while eating strawberries

attributes were used. These included taste, osmatic, and textural attributes. We collected TDS curves from 17 university
students while eating strawberries. One strawberry was eaten
in a single TDS method task. Each participant conducted threetrials, and 51 (17 × 3) samples were collected. The experiment
was approved by the Institutional Review Board of the Schoolof Engineering, Nagoya University (#20-20).
Fig. 1 shows the obtained TDS curves. The horizontal axis
is the normalized time, which takes the value of zero when thestrawberry is put into the mouth, and one when the strawberryis swallowed. Typically, sweet and juicy sensations dominatedin the early stage while eating strawberries. The experienceof fruitiness then became prominent. In the last phase, thesourness was dominantly felt by the panels.
III. D ISSIMILARITY INDEX FOR INDIVIDUAL TDS TASKSThe result of trial A of the TDS task is defined by a set ofbinary functions of the normalized time Ai (t) for attribute
i = 1, 2, . . . , q. q denotes the number of attributes usedin the TDS task. This function takes the value of either 0(not selected) or 1 (selected). The sum of Ai (t) at a certain
time t is 1 because multiple attributes can never be selected
simultaneously in the TDS method. To ensure that the sumof Ai (t) is 1, even when no attribute is selected, we defined
A0 (t), whose value is 1 only when no attribute is selected.

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This allows us to compare the similarity between the two trials,
for which the times elapsed until the first attribute selected isdifferent. t is a discrete value because it is calculated by acomputer. The width of the discretization is expressed as ∆t.
We defined the dissimilarity index between two TDS tasks
A and A0 as follows:v
qR uXuX
2010t(1)d(A, A ) = √Ai (k∆t) − Ai (k∆t)
2R k=0 i=0where R and q are the number of discretized points of thenormalized time (R = 1000) and attributes used in the TDStasks (q = 8), respectively. This formula averages the geometric distances (Euclidean distances) of the two trials, along the0normalized time, when trials A and A are viewed as coordi000nates (A0 (t), A1 (t), . . . , Aq (t)) and (A0 (t), A1 (t), . . . , Aq (t))
in the q + 1 dimensional space. As mentioned above, the sumof Ai (t) at a certain time√√ t is 1. Therefore, the maximum
Euclidean distance is 2. Dividing the entire value by 2
makes the maximum value of d equal to 1. Consequently , thed value ranges from 0 to 1, with 0 being the perfect match
between the two TDS tasks, and 1 is the complete mismatch.

Fig. 2: Distribution of d values. The right-most sample isoutside 95% of the distribution.

IV. O UTLIER ANALYSIS OF TDS TASKS USINGDISSIMILARITY INDEX

When the results of the n trials for attribute i are expressed
as A1i (t), A2i (t), . . . , Ani (t), their average is the dominanceproportion:
n1X jA (t)Pi (t) =n j=1 i(2)where n is the number of TDS trials (n = 51). We thencomputed the dissimilarity between trial k and the average
dominance proportions, that is, d(Ak , P ). Although Pi (t)is not a binary function, we can compute the dissimilarity
between Ak and the average by applying (1) because the Euclidean distance can be defined for non-binary and continuous
Pi (t) values.
Here, we used the experimental data of strawberries toidentify potential outliers among the set of dissimilarities fromthe average.
 The set of dissimilarities for all the TDS tasks
is C = x|x = d(Ak , P ), k = 1, 2, . . . , n . We applied theKolmogorov-Smirnov test on C and found p = 0.38 > 0.05.
The assumption of normality was not rejected. Fig. 2 shows
the distribution of d values.
We judged samples that do not fall within 95% of thedistribution, that is, [−∞, 1.64σ] as an outlier, where σ is thestandard deviation. Based on this criterion, one sample, shown
as orange in Fig. 2 was judged to be an outlier. Fig. 3(a) shows
Ai (t) of this trial. Fig. 3(b) shows the second farthest trial fromthe average, although it was not categorized as an outlier.
The panel in Fig. 3(a) selected juicy, fruity and aromaticin the first half period. These results are consistent with theaverage behavior shown in Fig. 1. However, this panel selectedaromatic in the second half period, which is not prominent
in the average curves. In addition, this panel selected green,

Fig. 3: Selected attributes in the trials most and second farthestfrom the average

which exhibited a low dominance proportion on average.
Hence, this trial deviates from the average trend, especiallyin the second half of the period.
The panel shown in Fig. 3(b) first selected watery, and thensweet in the middle phase, consistent with the average trend.
However, the other selections, including juicy in the last phase,
do not match the average trend. Therefore, this panel alsodeviates largely from the average curve shown in Fig. 1.
V. C ONCLUSION
We proposed a dissimilarity index for TDS tasks. Thus far,such individual analysis methods have yet to be developed forTDS methods. We applied the proposed dissimilarity index
on the 51 TDS tasks for strawberries and found one potential
outlier. This outlier is semantically different from the average
temporal dominance curves of the 51 tasks. The validity ofthis index remains to be studied in the future.
R EFERENCES[1] International Standardization Organization, “ISO 13299: 2016, Sensory
analysis—Methodology—General guidance for establishing a sensory
profile,” 2016.
[2] H. Cardot, G. Lecuelle, P. Schlich, and M. Visalli, “Estimating finite
mixtures of semi-Markov chains: an application to the segmentation oftemporal sensory data,” Journal of the Royal Statistical Society Series C(Applied Statistics), vol. 68, no. 5, pp. 1281–1303, 2019.

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