1. Introduction
Sensations dynamically change while eating food. Temporal dominance of sensations (TDS) methods [
1,
2,
3] record the temporal evolution of multiple types of subjectively reported sensations. These methods have attracted considerable attention in the last decade [
4,
5], in part because they are considered more cost-effective than conventional time-series sensory evaluations such as the time-intensity method [
6,
7,
8].
Understanding the relationships between primary sensations such as flavor, taste, and texture, and higher-level sensations or judgments such as freshness and richness of tastes when eating food products is essential for determining the food values. Relationships between primary sensations and higher-level human responses, including emotions, have been intensively researched using static sensory evaluation methods [
9,
10,
11,
12,
13,
14,
15,
16]. For example, in [
10], primary sensations such as tastes and mouth feels of several vegetables and fruits were linked with higher-level of attributes such as
summery,
refreshing, and
fresh-made. These higher-level attributes are judged based on multi-sensory information, including multiple primary-sensory attributes. However, few studies have linked primary- and multi-sensory data over time. Okada et al. [
17] developed a method to establish a model of dynamic causality using temporal data of sensations and emotions related to food intake. They modeled the temporal influences among sensory, emotional, and preferential responses to strawberries using vector auto-regression and Granger causalities. Tachi et al. [
18,
19] developed a method for establishing state-space models of temporal dominance responses for sensations and emotions and used state variables functioning as memories to show how changes in sensory responses dynamically influence emotional responses. Silva et al. [
20] computed the relationship between the temporal changes in liking and the TDS or temporal dominance of emotions (TDE) results. However, this study did not focus on the relationships between sensations and emotions. Galmarini et al. conducted TDS and TDE tasks toward coffee during listening musics [
21], and investigated how the sensory and emotional attributes covaried. Their analysis was based on dominance duration and did not aim for the temporal evolution of sensory and emotional responses. Other dynamic analyses for TDS methods, such as those performed by [
22,
23,
24] dealt with only primary sensations and did not connect their results with time-evolving multi-sensory or complex sensory responses. Thus, only a few studies have linked the TDS method results for primary- and multi-sensory attributes. In addition, the studies performed by [
17,
18,
19] contain results that cannot be easily interpreted. Thus far, general methods for linking TDS data for primary sensation and higher-level of sensation or feelings have not been established.
This study linked the TDS results for primary- and multi-sensory attributes using canonical correlation analysis (CCA). This method links two groups of variables using latent variables, which explains the relationships among multiple variables in the two groups. One of the biggest differences between this and earlier studies [
17,
18] that attempt to link TDS and TDE models is the use of past information in the time-series data. Two earlier models [
17,
18] were retrospective and modeled the TDS and TDE results at a set time point using past information. In contrast, our model is concurrent and computes the change in an attribute of the TDS task for multi-sensory attributes at a set time point using changes in the attributes of the TDS task for primary-sensory attributes at the same time point. Researchers have discussed which retrospective or concurrent model is most appropriate for analyzing time-series data [
25,
26]. For example, Chen et al. [
25] compared retrospective, concurrent, and unified analysis of neuroimaging data. However, researchers have not yet discussed the possibility of using a concurrent model to link TDS tasks. One of the purposes of this study was to investigate this possibility.
We also investigated whether raw or differential time-series data (i.e., temporal dominance curves) of the TDS method are appropriate for CCA. Temporal dominance curves are the main TDS outputs [
2] and express the temporal evolution of the proportions in which individual attributes are dominant in sensations (see
Section 2.1). Raw time-series data contain long-term trends, but the samples at different moments are not independent, which may violate the assumptions of CCA or other multivariate analysis techniques. The effect of long-term trends is removed by differentiating raw time-series data. However, the loss of equilibrium information due to differentiation can be a disadvantage. Thus far, previous studies have not compared raw and differential time-series data in terms of TDS data. Hence, we establish two models based on raw (i.e., trend model) or differential time-series data (i.e., differential model). Then, we discuss their semantic validity.
We used the TDS methods to investigate the temporal evolution of the primary- and multi-sensory responses toward strawberries and statistically linked these responses by CCA. As aforementioned, thus far, no studies have attempted to link them by using concurrent models. We subsequently investigated whether the raw or differential time-series data produce a semantically more reasonable model. Strawberries are popular fruits used in earlier sensory studies [
17,
19,
27], which can be compared with our results.
6. Discussion
Our study results show that trend or differential models are suitable for computing the CCA of the concurrent values in dominance proportion curves. In the trend model, five pairs of canonical variables connected primary- and multi-sensory attributes. According to
Table 3, 73% and 87% of the variances of the dominance proportion values of the primary- and multi-sensory attributes, respectively, were explained by these canonical variables. These values may be compared with those of trajectory plots of TDS curves in earlier studies. For example, Nguyen et al. [
35], Lenfant et al. [
36], Merlo et al. [
37], and Nguyen and Wismer [
38] reported that principal components explained 52–83% of the variances of temporal dominance curves while eating wheat flakes, yoghurts, and hamburgers, respectively. Although there is no standard about these values, those in the present study and earlier studies are comparable, indicating that the TDS curves were well explained by the latent variables. The number of latent variables was smaller than the number of multi-sensory attributes (six) by only one variable. Thus, the contraction effect of the model was not large. The meaning of four of the five canonical variables can be reasonably interpreted, but it is difficult to interpret the fifth canonical variables. In the differential model, primary- and multi-sensory attributes were connected by four pairs of canonical variables. According to
Table 3, 50% and 59% of the variances in the differential dominance proportions of primary- and multi-sensory attributes, respectively, were explained. Interpreting the second and third canonical variables was difficult. Considering these points comprehensively, the trend model is more suitable for analyzing dominance proportion curves than the differential model. However, we cannot conclude that either model is superior solely from the examples of strawberries. Similar studies are necessary for other foods in the future.
Figure 5 summarizes the trend model for strawberries with major connection lines between the attributes and canonical variables. Note that the first canonical variable pair indicates the time elapsed and is not shown. The canonical variables were named for convenience. These four types of canonical variable pairs determine the dynamic behavior of the dominance proportions of strawberries. In the early phase of the eating experience, juicy-fruity (second canonical variable) and juicy-sour (fourth canonical variable) factors are prominent primary-sensory aspects. These factors are likely caused by the juice coming out after initial biting and indicate that the fruity aroma and taste associated with the juice caught the attention of the panels. The participants also felt the ripeness and freshness of strawberries during the early phase. This agrees with [
31] where the freshness of strawberries was largely judged by juiciness after their visual factors such as the surface shine and bruises. In our model, ripeness was not related to
green whereas unripe strawberries were characterized by the green taste and aroma in a study using strawberries [
27]. This difference may be because underripe strawberries were intentionally included in [
27] whereas apparently underripe strawberries were not used in the present study. The third and fifth canonical variables were relatively large in the middle phase. As shown in
Figure 3a, no sensory attributes were dominant in this phase, leading to a feeling of mildness (represented by the fifth canonical variable pair). Subsequently, a refreshing feeling becomes dominant (as represented by the third canonical variable). The last phase is represented by the fourth canonical variable pair, which represents an intensely sour taste and refreshing feeling.
Refreshing was defined as “pleasantly cool” as in
Table 2. In general, this attribute is favorable in evaluating fruits [
39]. In [
39],
refreshing was felt for juicy, sweet, and sour mandarins, and
refreshing appeared to be judged based on multiple types of basic tastes. For the strawberries in the present study,
refreshing was connected with
sour and
juicy by the fourth canonical variable. Furthermore,
refreshing was prominently connected with
watery by the third canonical variable. The meanings of
refreshing may differ among different types of fruits; however, regarding strawberries and mandarins, sourness is a potentially common factor. For strawberries, sourness in the last eating phase is generally accepted by consumers [
40].
Our study suggests that the concurrent model can link the results of the TDS methods for primary- and multi-sensory attributes. However, in order to determine which of the concurrent or retrospective models are more suitable, a variety type of foods need to be tested whereas only strawberries were tested in the present study. The two models, i.e., the concurrent model in this study and retrospective models in [
17,
18] contain some points that remain semantically validated. Both models need further studies.
We conducted two types of TDS tasks by using primary- and multi-sensory attributes. According to ISO standards [
2], very different attributes, such as sensory and emotional attributes, should not be tested in the same temporal dominance tasks. However, there is no general method to classify very different sensory attributes. Hence, following earlier studies [
29], we classified attributes into three categories as in
Section 3. We found that attribute categorization is difficult because some attributes span multiple categories. A similar problem was reported in [
29] where several attributes among more than one hundred for describing experiences related to touch were categorized as both sensory and evaluative. The panels in the present study categorized
pleasurable, which is the translation of
kokochiyoi in Japanese, into multi-sensory; however,
pleasurable also may include the aspect of evaluative attributes.
Kokochiyoi can be also translated as comfortable and delightful. The results of attribute categorization task may depend on the cultures and expertise of the panels considering that some attributes used by the experts, such as
earthy and
caramel [
27] were not selected by the non-expert panels in the present study. Different categorization leads to different results of CCA, which limits the generality of our approach. Furthermore, the present study lacks a demonstration of uncertainties of canonical variables. As shown in
Figure 4, some canonical values fluctuate around zero at some moments. It is meaningful to know whether those values are statistically different from zero.