Statistical analysis
As the one-way ANOVA results showed that ten vegetable oils
have a statistically significant difference (P < 0.05) on the solubility
of each VAC at the 95% confidence level, mean values were further
transformed using MATLAB 2013a (The MathWorks, Inc. Natick,
Massachusetts, USA). Firstly, a principal component analysis (PCA)
was performed to reduce the dimensionality of our data set (individuals:
vegetable oils; variables: VACs) by linear combination
into new coordinate systems which are completely uncorrelated
with each other. The mean concentrations in ten oily extracts were
taken for the determination of principal components so as to
compare the solubility of ten vegetable oils in a two-dimensional
graph. Subsequently, an agglomerative hierarchical clustering
(AHC) was applied to classify the closest individuals into clusters
according to an aggregation criterion. The Ward's hierarchical
clustering was used to calculate dissimilarities from the Euclidean
distances and aggregation criterion corresponding to the minimization
of the within-cluster inertia and the maximization of
between-cluster inertia. This method led to a partition of vegetable
oils into homogenous clusters (low within-variability) in terms of
concentrations of six VACs extracted, which are different from
others with a high between-variability. A dendrogram was finally
obtained to illustrate the aggregations made at each successive
stage of the analysis