Analysis Of Sensometric Values And Cluster Analysis For Chocolates And Asian Cities
Sensometric analysis of chocolate attributes chosen by experts and amateurs
The sensometric values for the fourteen attributes regarding chocolates were analyzed on the basis of average contribution in product definition. The bar plot and heat map for average sesnometric scores of attributes have been plotted. It was evident that chocolate aroma, sweetness, and crispy texture were comparatively more essential qualities for choice and ranking of chocolates, for the experts.
The sensometric values for the amateurs concerning the fourteen attributes regarding chocolates were analyzed. The bar plot and heat map for average sesnometric scores of attributes have been plotted. It was evident that chocolate aroma, sweetness, chocolate aroma, and crispy texture were essential qualities for choice and ranking of chocolates, for the amateurs.
The responses of the experts and the amateurs were tested for reliability for exploratory factor analysis by Cronbach alpha. The response matrix of experts was found to be moderately reliable () and the responses of amateurs was found to be comparatively less reliable () to that of the experts. The trend of the reliability statistics indicated that the factor analysis based on experts’ opinions was more accurate than that of the amateurs.
The positive and negative correlations between the ratings of the attributes by the experts for various product ranges of chocolates have denoted by blue and green circles. Chocolate aroma was significantly positive with bitterness, astringency, and crispy flavor, whereas, milk aroma was associated positively sweetness, caramel flavor, vanilla flavor, and somewhat with texture of the chocolates. At this stage probable two factors were identified as chocolate and milk attributes of the chocolates. For the amateurs, highest negative correlation was identified for chocolate and milk flavor (r = 0.96), whereas, bitterness and chocolate flavor were found to be associated in a highly positive (r = 0.93) way.
The determinant value of the correlation matrix for experts was greater than 0.00001, signifying that there were no multicollinearity issues for exploratory factor analysis. A similar result was obtained for amateurs’ response, where multicollinearity was not a problem for the dataset. The Bartlett’s Test of Sphericity was used to test that the correlation matrix was an identity matrix and there was only one factor to be identified. The claim was rejected for the experts’ opinions at 1% level of significance (for arbitrary chosen sessions (9, 5). The amateur data set also indicated that the correlation matrix was significantly different to be an identity matrix at 1% level of significance. In test of adequacy of the sample data, Kaiser-Meyer-Olkin statistic was used, and the value was found to be closer to 1 (KMO = 0.91). This signified that the sample dataset was adequate for factor extraction. Parallel study for adequacy in amateur data revealed that (KMO = 0.83) there was enough data for factor analysis.
Reliability of responses using Cronbach alpha and exploratory factor analysis
The Scree plot identified two components having Eigen values greater than 1 in expert reviews. The output suggested extraction of two factors from the analysis. From the amateurs’ response sheet extraction of two factors was proposed.
Among PCA, ML, and PA methods of extractions, the principal axis (PA) extraction method was able to load all the components on two factors. Milk flavor, caramel flavor, milk aroma, vanilla flavor, stick texture, sweetness, and melting texture loaded on factor 1. Chocolate flavor, astringency, bitterness, chocolate aroma, acidity, granular texture, and crispy texture loaded on factor 2 of the analysis. All the components loaded with statistically significant association with the factors. The first factor was identified as the Milk Characteristic and the second factor was named as Chocolate Characteristic because of the components’ features.
In amateur data set the all the components loaded cleanly on two factors by Principal Components Analysis (PCA). Milk flavor, chocolate flavor, bitterness, sweetness, caramel flavor, chocolate aroma, vanilla flavor, crispy texture, milk aroma, and melting texture loaded on factor 1, whereas, sticky texture, acidity, astringency, and granular texture loaded on factor 2. Patter of factor loading indicated the confusion in judgment and decisions on likings. The factors could be identified as taste and feel of the chocolates.
Experts were particular in identifying the two sensometric factors of the analysis, based on components of the chocolates. Milk and chocolate are the two primary components in a chocolate and experts correctly identified the attributes in a proper alignment. On the other hand, amateurs were greatly inclined towards the taste factor of the chocolates. They ranked chocolates based on its taste and feel. The difference in ranking was pretty obvious in nature from the point of expertise and information about details of chocolates.
Conclusions
Reliability of the responses for factor analysis was greater for experts’ opinions compared to that of the amateurs. Item was reliability for experts’ views revealed that exclusion of milk aroma and milk flavor increased the Cronbach alpha from 0.48to 0.49. A very high positive correlation was observed for these two components of the study, whereas, chocolate and milk flavors were almost perfectly and negatively associated with correlation coefficient of – 0.97. There was a significant negative relation between bitterness and milk flavor, which made them to load on two different factors. The sample was found to be adequate and considerably different from unit matrix for accurate factor extraction. Individual KMO statistics were significantly high; the minimum value of 0.834 was noted for milk flavor of a chocolate. Sample size was found to be sufficiently large for proper EFA.
Cluster analysis of 25 cities in the Asian Continent using hierarchical and partitional clustering techniques
Reliability for amateurs was found to be 0.38, which was found to increase up to 0.4 for removal of chocolate and milk flavor from the dataset. The most important aspect was identified as the sticky texture, and astringency of the chocolates. Caramel flavor was the dominant reason for reliability purpose. Here, chocolate flavor and bitterness had highly positive correlation, whereas relation between chocolate and milk flavor, and sweetness and bitterness were highly negative. The sample was found to be adequate and considerably different from unit matrix for accurate factor extraction. Individual KMO statistics were significantly high; the minimum value of 0.834 was noted for milk flavor of a chocolate. Sample size was found to be large for EFA. The preference for ranking the chocolates was solely based on taste and feel of the chocolate. From the correlation between the factors, it was noted that no oblique rotation was required for EFA (Hanna, de Araújo, Vilarino, & Mayhew, 2016).
For the distance matrix data for Asian continent, Hierarchical clustering and Partition clustering were performed to identify the zones of the location of the twenty five cities in the dataset. The distance matrix was evaluated for exploratory purpose by the following heat map and spring map. The red marked cells indicated the distances which pointed towards the closeness of another country. The spring map was drawn to identify the proximity of two cities. The bold line signified those counties which can isolated easily in a cluster. The dataset was scaled by shifting the origin to median and changing the scale by absolute deviation from median.
Default hierarchical clustering is “complete” method. In the study AGNES based methods along with Ward’s method was used for comparative purpose. The resulting dendograms from the four methods have been provided below for cluster identification. From all the methods, 5 clusters were identified from the visualization of the dendograms.
From the hanging tree it was easy to locate the five clusters or zones of cities. The country wise picture has been provided in the following matrix. Though, Karachi and Madras are two far off destinations, they still load to a same cluster.
The Pearson’s and Spearman’s correlation matrices were plotted graphically for all the methods of hierarchical clustering. All the methods were found to have yield almost similar results, with average method leading the table. The spearman’s correlation plot in the successive figure established the efficiency of average method in this study for hierarchical clustering.
The 3d map for the two dimensional distance matrix indicated five separate zones for clustering. The clusters were later identified using the Elbow Method. Considering the optimality (minimalist) of total within clusters sum of squares, 3 clusters with 7, 5, and 13 cities were identified. The cluster numbers were later changed to 5 for proper portioning of the cities.
Considering the number of clusters = 5, the cluster plotting yielded five clusters with 6, 2, 3, 9, and 5 cities. The cluster with 9 cities was located near the Bangkok and Singapore region. Nine countries clustered due to proximity in that region.
The partitional clustering was based on choice of k-means or centers. Initial processing suggested 3 clusters of cities with minimum total within clusters sum of squares at 75.4%. Later, appropriate choice of clusters was decided on the basis of Elbow method, considering the previous methods of cluster analysis. The 3d plot was an indicative figure in this case. Five zones were identified, which were i) near Bangkok region, ii)near Delhi region, iii) near Yokahama region, iv) near Bangalore region, and v) near Istanbul region.
No outlier distance was identified from the matrix, and proper choice of zones or clusters of countries was identified to be 5. The initial clustering was able to reduce the SS of the total clustering, but with formation of clusters with far-off countries. The solution with k=5 number of partitioning was found to be appropriate from point of view of practical significance.
Conclusions
Both the hierarchical clustering and partitional clustering were efficient clustering technique. But, considering the choice of clusters, hierarchical clustering was easy to interpret because of the clear picture of the cluster loadings in dendograms. The k-means clustering had the power of generating the optimal partitioning of the data points with minimum total within clusters sum of squares.
In the present study, hierarchical clustering was efficient in deciding the number of clusters compared to partitional clustering. In partitional clustering mutually exclusive spherical shaped clusters were obtained. And in hierarchical clustering, based on agglomerative approach and divisive approach, the countries were assumed as individual clusters and then clustered form bottom to top direction in the tree (Yates et al., 2015).
References
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Yates, L. R., Gerstung, M., Knappskog, S., Desmedt, C., Gundem, G., Van Loo, P., … & Li, Y. (2015). Subclonal diversification of primary breast cancer revealed by multiregion sequencing. Nature medicine, 21(7), 751.