Statistical Significance and Utility of Data-Driven Functional

Dependencies of Wine Quality Data of Numerical Attributes

HYONTAI SUG

Department of Computer Engineering,

Dongseo University,

47 Jurye-ro, Sasang-gu, Busan, 47011,

REPUBLIC OF KOREA

regression tests. We can check their explanatory power by way of adjusted R-squared, as well as other statistics

like multicollinearity, the Durbin-Watson test for independence, and the F value for suitability of the regression

models. For the experiment, we used the wine quality data set of Vinho Verde in the UCI machine learning

library, and we found out that only 48.7% and 30.7% of functional dependencies found by the algorithm called

FDtool have explanatory power for the red wine and white wine data set respectively. So, we can conclude that

we should be careful when we want to apply the functional dependencies found by the algorithm. In addition,

as a possible application of the found functional dependencies in the conditional attributes of the data sets, we

have generated a series of random forests by dropping redundant attributes that appear on the right-hand side of

the explanatory functional dependencies and acquired good results. So, we can also conclude that we may

reduce our efforts by not collecting the data of the redundant attribute to check the wine quality because we can

1 Introduction

Vinho Verde, literally ‘green wine’, is a Portuguese

wine produced mainly in the region around the

Minho River in northwestern Portugal. Vinho Verde

has nothing to do with the grape variety, and it

means young wine, which is the opposite of aged

wine and is consumed within one year of being

bottled. Wine certification and quality assessment

Wine quality assessment is generally assessed by

physicochemical and sensory tests. Physicochemical

tests are used to characterize wine to several

physicochemical factors, while sensory tests rely on

human experts, and determining wine quality based

on data has attracted many research interests, [2],

Alcohol sweetens the wine and affects its body feel,

chlorides dictate the saltiness and acidity of the wine,

and density determines the body feel of the wine.

{alcohol} -> {density}, {density}->{alcohol},

{chlorides} -> {density}, {density}->{chlorides}

{alcohol, chlorides} -> {density}, and so on.

Even though the above examples are some

extremes, we can see the fact that we may have

many functional dependencies that may not be real

functional dependencies if we decide on functional

dependencies by stored data only.

On the other hand, a statistical method to check

regression test, and this approach is very novel in

the research area of functional dependency by data.

Therefore, we want to select functional

dependencies of the wine quality data set by doing

the regression test for the same attribute sets which

are found to have functional dependencies by data

algorithmically, and also select attributes on the

right-hand side in the functional dependencies as

redundant attributes. As a possible application, we

may use the found fact to generate machine learning

2 Related Work

Functional dependencies are used to determine the

attributes of relations or relation variables, [8], and

serve as a criterion for judgment for normalization.

Several algorithms have been proposed to discover

model was obtained as 0.73, [20]. Because the wine

data set has some redundant attributes, a Pearson

correlation coefficient-based table, called a heat

map, was used to remove some redundant attributes

and shows good accuracies, especially in the

random forest among four different classifiers, [21].

By permuting attributes of the white wine data set

decrease in accuracy or how the prediction gets

A recent study implemented an automated

found, we try to do statistical tests. After the

statistical tests, we select functional dependencies

having explanatory power.

Since the attribute values of the right-hand side

are determined by the attribute values of the left-

hand side because of the many-to-one property of

functional dependency, we can consider the

As a possible application of the found statistical

4 Experimentation

There are two wine data sets available in the UCI

machine learning repository, [28]. The ‘Wine’ data

set has 178 instances, while the ‘Wine quality’ data

set has up to 4,898 instances. We chose the ‘wine

the data set is well-known and contains a large

eleven conditional attributes and one decisional

conditional attributes were conducted in the original

data set.

The data set has 1,599 records and has 11

conditional attributes and one decisional attribute,

named ‘quality’. The 11 conditional attributes

consist of numerical attributes as in Table 2.

data set

. . . . . .

. . . . . .

{alcohol, free_sulfur_dioxide, residual_sugar,

total_sulfur_dioxide, citric_acid} -> { pH}

{alcohol, free_sulfur_dioxide, residual_sugar,

total_sulfur_dioxide, citric_acid} -> {chorides}

Table 3 shows the total number of functional

side of the found functional dependencies based on

Because FDtool finds simple many-to-one

explains the dependent variable in the regression

model. In general, it should exceed 20%, and the

higher this number, the higher the explanatory

power. However, this value increases even with the

addition of a dependent variable that does not

explain the dependent variable well, so an adjusted

R-squared value is used. 301 functional

dependencies have adjusted R-squared values

exceeding 20%. So, only 48.7% of found functional

dependencies based on data have explanatory power.

0.05, we can consider all the regression models of

the 301 FDs are suitable. Table 4 shows the

summary.

having adjusted R-squared values of 20% or more

Table 6 shows the accuracies of the random forests.

All experiments are performed in 10-fold cross-

validation.

dropping some part of attributes

white wine data set

have a value between 1.364 and 1.749, so we can

consider they are closer to the d value of 2, which

means they are less auto-correlated. In the analysis

of variance, all the significance probabilities for the

F test are 0.0, and since they are less than the

significance level of 0.05, we can consider all the

regression models of the 122 FDs are suitable.

combined result of Table 8 and Table 9.

Note that we have no explanatory FDs for RHS

attributes, citric_acid, volatile_acidity, chlorides,

and sulphate for the white wine data set.

Multicollinearity was also considered for FDs

having adjusted R-squared value of 20% or more.

All the VIF are in the range of 1.004 ~4.552 except

one FD, {alcohol, density, sulphate, fixed_acidity,

residual_sugar, volatile_acidity} -> {pH} with

each attribute in the LHS of an FD, {alcohol,

density, sulphate, fixed_acidity, residual_sugar,

volatile_acidity} -> {pH}

residual_sugar for the white wine data set, thus we

could save our efforts in data collection.

5 Conclusion

algorithms may not be real functional dependencies,

values, and because a functional dependency has to

satisfy many-to-one relationship between attributes

values only, and the algorithms do not check all the

possible attribute values that are not present in the

data. In this paper, we show how we can determine

whether the found functional dependencies have the

statistical significance of explanatory power by

doing a multivariate linear regression test for each

algorithmically found functional dependency to

experiment, we used the wine quality data set of

Vinho Verde in the UCI machine learning library,

and we found that only 48.7% of functional

dependencies found by the algorithm called FDtool

have explanatory power for the red wine data set,

while only 30.7% of functional dependencies have

explanatory power for the white wine data set. From

these findings, we can conclude that we should be

careful when we want to take advantage of the

functional dependencies found by the algorithm

at the right-hand side of the explanatory functional

also conclude that we can reduce our efforts by not

collecting redundant attribute values to check wine

attribute values as possible in mass-produced wines

like Vinho Verde. Further developments for more

numerical attributes to reduce the number of found