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# Effective Semantic Text Similarity Metric Using Normalized Root Mean Scaled Square Error

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The Pearson correlation is a performance measure that indicates the extent to which two variables are linearly related. When Pearson is applied to the semantic similarity domain, it shows the degree of correlation between scores of dataset test-pairs, the human and the observed similarity scores. However, the Pearson correlation is sensitive to outliers of benchmark datasets. Although many works have tackled the outlier problem, little research has focused on the internal distribution of the benchmark dataset's bins. A representative and well-distributed text benchmark dataset embody a wide range of similarity scores values; therefore, the benchmark dataset could be considered a cross-sectional dataset. Although a perfect text similarity method could report a high Pearson correlation, the standard Pearson correlation is unaware of correlated individual text pairs in a single dataset's cross-section due to outliers. Therefore, this paper proposes the normalized mean scaled square error method, inferred from the standard scaled error to eliminate the outliers. The newly proposed metric was applied to five benchmark datasets. Results showed that the metric is interpretable, robust to outliers, and competitive to other related metrics.
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Journal of Theoretical and Applied Information Technology
30th June 2019. Vol.97. No 12
© 2005 – ongoing JATIT & LLS
ISSN: 1992-8645 www.jatit.org E-ISSN: 1817-3195
3436
EFFECTIVE SEMANTIC TEXT SIMILARITY METRIC USING
NORMALIZED ROOT MEAN SCALED SQUARE ERROR
1ISSA ATOUM, 2MARUTHI ROHIT AYYAGARI
1Department of Software Engineering, The World Islamic Sciences and Education, Jordan
2College of Business, University of Dallas, Texas, USA
E-mail: 1issa.atoum@wise.edu.jo, 2rayyagari@udallas.edu
ABSTRACT
The Pearson correlation is a performance measure that indicates the extent to which two variables are linearly
related. When Pearson is applied to the semantic similarity domain, it shows the degree of correlation
between scores of dataset test-pairs, the human and the observed similarity scores. However, the Pearson
correlation is sensitive to outliers of benchmark datasets. Although many works have tackled the outlier
problem, little research has focused on the internal distribution of the benchmark dataset’s bins. A
representative and well-distributed text benchmark dataset embody a wide range of similarity scores values;
therefore, the benchmark dataset could be considered a cross-sectional dataset. Although a perfect text
similarity method could report a high Pearson correlation, the standard Pearson correlation is unaware of
correlated individual text pairs in a single dataset’s cross-section due to outliers. Therefore, this paper
proposes the normalized mean scaled square error method, inferred from the standard scaled error to
eliminate the outliers. The newly proposed metric was applied to five benchmark datasets. Results showed
that the metric is interpretable, robust to outliers, and competitive to other related metrics.
Keywords: Pearson, Absolute Error, Text Similarity, Correlation, Scaled Square Error, Outliers
1. INTRODUCTION
Under heavy noise conditions, extracting
the correlation coefficient between two sets of
stochastic variables is nontrivial [1]. The
performance of a Text Similarity (TS) method is
most often calculated by the Pearson correlation
between the human-mean scores (first variable or the
reference), and the method observed scores (second
variable). Formally, the performance of a text
similarity method is calculated as the covariance of
the two variables divided by the product of their
standard deviations, which is a figure value from -1
to 1. When the figure is high, it implies a high
correlation with the human scores; therefore, the
similarity method becomes favorable over another
method in a specific task.
Although Pearson correlation has been
theoretically approved and used in many domains,
the Pearson correlation if taken in isolation may
incidentally indicate invalid causation. It was shown
that correlation might indicate (humorously) that
babies are delivered by storks[2]. Similarly, and
using the same correlation, it was reported that the
consumption of cocoa flavanols results in an acute
improvement in visual and cognitive functions [3].
Therefore, the simplicity of a correlation could hide
the considerable complexity in interpreting its
meaning[4]. Moreover, the application of Pearson
correlation, as a linear relationship is limited to
predict the correlation in domains that are not
normally distributed. For example, it was shown that
the Pearson correlation is not a good predictor for the
reliability of characteristics of interest[5]. Despite
the ever increasing interests in other alternatives [6]–
[10], the Pearson correlation is still dominant in
domains of text similarity such as those related to the
SemEval tasks workshop series [11], [12].
In Spite Of the simplicity and
interpretability of the Pearson correlation in the text
similarity domain [13]–[15], the cosine similarity is
among others getting attention from scholars,
especially in word embeddings applications [16],
[17]. It was pointed out that Pearson correlation does
not provide enough justifiable results in software
engineering domain [18].Therefore, the Pearson
correlation should be adapted or modified to handle
software engineering issues related to software
requirements engineering and testing [19]–[21] .
One major problem of Pearson correlation
is the outliers. Outliers have a reflective influence on
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June 2019. Vol.97. No 12
© 2005 – ongoing JATIT & LLS
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the slope of the regression line, and consequently on
the value of the correlation coefficient. The problem
is known in the literature as the Anscombe’s quartet
[22] problem, as shown in Figure 1. The Anscombe's
quartet comprises four datasets that have nearly
identical Pearson's correlation (0.816), yet they
appear very different when graphed. Therefore,
datasets distributions should be analyzed to handle
outliers.
When a benchmark dataset is designed, it
usually works competitively over pairs of text in at
least three bins of the dataset that vary in similarity
from low (L), medium (M), to high similarity (H).
An appropriate similarity method should work well
in all cases of dataset scores, L, M, and H. The
inherent problem of the standard Pearson correlation
is the way of calculation. The standard Pearson
correlation does not take into consideration the
cross-sectional property of the dataset; instead, it
considers all values, including outliers. Therefore, a
high Pearson correlation does not guarantee the
suitability of the similarity method to its application
Based on the assumption that a useful
benchmark dataset is cross-sectional, we claim that
there are at least four different similarity methods,
low-similarity-method (α), medium-similarity-
method (β), high-similarity-method (Ω), and the
optimal similarity method (𝛿). The α method is fair
when the dataset (or the cross-section) has low
human scores, while the β method is fair when the
dataset (or the cross-section) has high human scores.
In contrast, the optimal method (𝛿) should work
with all cases of the dataset.
Figure 2 explains the problem with the four
types of similarity methods using our crafted demo
dataset. The demo dataset reports 0.7 correlation for
α, β, and Ω methods and 1.0 for the optimum method
(𝛿). On the first hand, an α method (Figure 2a) has a
high correlation with text pairs that has low
similarity as per human-means (pairs 1-3). On the
second hand, an method (Figure 2c) has a high
correlation with text pairs that have high similarity
as per human-means (pairs 7-9). In contrast, the β
method (Figure 2b) has a high correlation with text
pairs that has medium similarity as per human-
means (pairs 4-6).
Figure 2a is an example with a similarity
method that works very well on text pairs that have
low similarity while Figure 2b is an example with a
similarity method that works very well on text pairs
that have a medium similarity, and Figure 2c is an
example with a similarity method that works very
well on text pairs that are literary similar. The
objective is to find a suitable similarity measure that
works very well on all benchmark scales. Therefore,
a useful method should reduce the errors between
actual and observed scores. Therefore, for a task that
needs to discover similar text such as plagiarism, the
(Ω) is favorable, and for tasks that need to find
irrelevant text (irrelevant documents) the method (α)
is suitable. Therefore, the standard Pearson method
was not able to consider variabilities in text
similarity scores. The goal is to choose a method that
gives high correlation, such as the optimum method
in Figure 2d.
Although there are many alternatives to
Pearson correlation, most text similarity
competitions (e.g., SemEval series [11], [12] ) uses
Pearson correlation as a standard. Nevertheless,
many types of research are pushing toward making a
Figure 1 Effect of outliers on Pearson’s
correlation (Anscombe)
Figure 2 Effect of Similarity method on Pearson’s
correlation (r=0.7 for a,b,c; r=1.00 for d)
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new correlation measure in the text similarity
domain. However, most of the ranked correlation
methods such as Spearman[7] and the Kendall tau
correlation[23] methods suffer from ties and are
suitable for datasets that are ranked in nature [24].
Therefore, the aim is to find a method that handles
issues of the Pearson correlation and providing
alternatives that were not studied deeply in the
semantic similarity domain.
Hyndman and Koehler [25] proposed the
scaling absolute error methods to scale down
observed values in the finance domain. Compared to
the relative error methods, the scaling absolute error
method is independent of the scale of the observed
data, and it can remove the problems of undefined
means and infinite variance. Hyndman extended the
scaling absolute error method to the Mean Squared
Scaled Error (MSSE).
In our context, the absolute error measure is
the difference between the text-pair human score and
the similarity method observed score. The MSSE is
a function of absolute error of human and observed
scores concerning the mean variability of observed
scores. Consequently, the MSSE should be able to
reduce the absolute errors presented in Figure 2. We
normalize the MSSE (NMSSE) to a scale between 0
to 1 using the exponent function. The NMSSE,
compared to Pearson correlation, ranks text
similarity methods based on the target text
Practically, and as a proof of concept, our
proposed metric shows the divergence of some
commonly cited works. Although the LSA measure
of [26] reported good Pearson correlation, it is
misjudging text-pairs scores reporting an absolute
relative error approaching 80%. Moreover, methods
that depend on large corpus tend to overestimate
scores of text pairs [27]. The objective of this paper
is to propose a new approach that could be used to
eliminate data outliers and provide a performance
metric to select the best text similarity method.
First, Pearson and its related measures are
explained. Next, the proposed metric is explained.
Then, the metric is evaluated. After that, we
highlight the research implications and limitations.
Finally, the paper is concluded.
2. RELATED WORKS
2.1. Pearson Correlation
The Pearson correlation has been proposed
long back [28], yet it still applicable as an evaluation
metric for many SemEval tasks workshop series
[11], [12].
The Pearson correlation is calculated as the
covariance of the two variables divided by the
product of their standard deviations[29]. In the text
similarity domain, the variables are the human-mean
scores’ group and the related observed test-score
group. So, if we have one dataset scores {,...,}
that represent the human-mean scores of a list of text
pairs and another dataset { 𝑜,..., 𝑜 }
containing 𝑛 observed scores (from a text similarity
method), the Pearson's correlation coefficient, 𝑟, is
shown in (1).
𝑟 ℎℎ
 𝑜𝑜
̅
ℎℎ
 .
𝑜𝑜
̅
 (1)
Where 𝑛 is the the number of text pairs.,𝑜 are the
ith score of human-mean (i.e., reference) and test
(observed) scores text pairs.
and 𝑜
are the mean
of the gold standard and test scores respectively.
2.2. Ranking Methods
The Spearman method [7] is considered
one of the most cited alternative methods to Pearson
correlation; however, it is not used regularity in text
similarity domain because it works on ranked data,
which is not reasonable in text similarity [24].
Similarly, the Kendall tau correlation[23], which
calculates the proportion ranks between datasets, is
rarely seen in text similarity domain.
Several other methods measure the gain of
a document based on its position in the result list [8]–
[10]; however, these methods suffer from ties and
are not suitable for scaled text similarity
measures[30]. The Hoeffding’s D method, a non-
parametric measure, measures the difference
between the joint ranks and the product of their
marginal ranks[31]. The distance correlation as its
name implied, is based on the distance (usually
Euclidian ) to measure the dependence between two
variables[32], [33]. The maximal information
coefficient (MIC) is a measure of the strength of the
linear or non-linear association between two
variables[34]; however, it does not perform well in
low sample size[35].
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2.3. Error methods
Error methods are used to quantify the
difference or percentage between actual and forecast
values. The absolute error computes the amount of
error in a trial. The relative error is an extension to
the absolute error with relative to the original real
value. These methods are easy-to-use [36].
3. PROPOSED METRIC
Equation (2) defines the absolute error (𝐴E) of a
text pair 𝑗, as the difference between human scores
(actual, ) score and the observed scores
(predicted,
) of a text similarity measure.
𝐴
E|
ℎ
| (2)
𝑆
𝐴
E
ℎ
 𝑛 (3)
The scaled error (𝑆) for each text pair 𝑗
is given by equation (3) , where 𝑛 is the number of
text pairs in the benchmark dataset. The
is the
mean of the observed method similarity score. Then
the mean scaled square error (MSSE) is defined by
equation (4).
MSSE𝑆
𝑛 (4)
The lowest value of MSSE is zero when the
absolute error of actual and predicted values is zero
and is infinity when all predicted values are
identical; that is the mean of observed scores (
)
equals every predicted value (
). Therefore, we
normalize the values of the MSSE between (0,1) to
allow a quantitative comparison between different
datasets as shown in equation (5). Where the
𝑀𝑆𝑆𝐸 as shown in equation (4), and 𝑒 is the
exponent value. The NMSSE equals the value of 1
when the error is at the maximum and 0 when the
error is very low. Therefore, for ranking similarity
methods, the lower NMSSE the better.
NMSSE1𝑒 (5)
4. EVALUATION AND DISCUSSION
4.1. Datasets used in the Experiments
Table 1 shows the set of datasets used in the
experiment. The datasets are split into two
categories: development (6,427 text pairs) and test
datasets (1,909 text pairs). The goal of the split was
to support text similarity measures that depended on
pre-training or test training[12]; however, in our
case, we used both datasets for the selected text
measures. We filter datasets from stopwords using
the nltk stop words’ list.
4.2. Selected Text Similarity Measures
For this paper, the selected text measures
illustrate the applicability of the proposed metric
over a wide range of text similarity measures, as
shown in Table 2.
Table 1 Benchmark datasets
Dataset Dev. Test Total Description
Demo Crafted
Dataset - 9 9
We prepare this dataset to illustrate similarity measures’
problems and to apply the proposed metric on a simple to view
dataset.
STS -30 - 30 30 30-sentence pairs collected by Li [37] based on dictionary
definitions of words from [38].
SemEval STS
1500 1379 2879
The datasets include text from image captions, news headlines,
and user forums which are part of the text similarity tasks of
SemEval series [12]
SICK 4927 500 5427
Sentences Involving Compositional Knowledge (SICK) are
English sentences from the 8K ImageFlickr and the SemEval
2012 STS MSR-Video Description dataset[39]
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Table 2 Methods used in this experiment
Method Description
α Method A demo method used on our crafted demo dataset. An α method is a similarity method used to
demonstrate a text similarity method that is leaned toward dissimilar text pairs. The method produces
an observed score that is 95% accurate to the human-means for the first three pairs and value at random
for the remaining pairs.
β Method A demo method used on our crafted demo dataset. A β method is a similarity method used to demonstrate
a text similarity method that is leaned toward moderately similar text pairs. The method produces an
observed score that is 95% accurate to the human-means for the 4-6 pairs and value at random for the
remaining pairs.
Ω Method A demo method used on our crafted demo dataset. An Ω method is a similarity method used to
demonstrate a text similarity method that is leaned toward high similar text pairs. The method produces
an observed score that is 95% accurate to the human-means for the 6-9 pairs and value at random for
the remaining pairs.
𝛿 method A demo method to show the method that scores the highest Pearson score. The method produces an
observed score that is 95% accurate to the human-means scores.
InferSent InferSent (INF for shorthand), a sentence embedding trained on fastText vectors of Facebook research.
INF is BiLSTM with max pooling that was trained on the 570k English sentence pairs of SNLI dataset.
[40].
GSE The universal Google’s sentence encoder (GSE) converts any text to a semantic vector. The semantic
measure is based on deep learning on the semantic space. We use the Encoder 2 from Google
TensorFlow Hub.
TSM Text Similarity Measure (TSM) is a WordNet measure that calculates the semantic similarity of two
sentences using information from WordNet and corpus statistics [27].
WMD The Word Mover's Distance (WMD) method uses the word embeddings of the words in two texts to
measure the minimum amount that the words in one text need to "travel" in semantic space to reach the
words of the other text [41]. We use the pre-trained word vectors of Glove (840B tokens) and fastText
word vectors W2V (2 million-word vectors).
SIF The Smooth Inverse Frequency (SIF) uses less weight to solely unrelated words, and so word
embeddings are weighted based on the estimated relative frequency of a word in a reference corpus and
the common component analysis technique [42]. We use the pre-trained word vectors of Glove (840B
tokens) and fastText word vectors W2V (2 million-word vectors).
4.3. NMSSE Illustrated over the Demo Dataset
For illustration and showing various cases
of text similarity measures over a wide range of
datasets, we use a demo dataset for this experiment.
Table 3 shows the list of crafted text pair’s scores
over four crafted methods α, β, Ω, 𝛿 methods as
described in Table 2. The table shows the cross-
sections of the dataset (bins 1 to 3), and the score for
each individual pair using the crafted methods.
Figure 3 shows the Pearson correlation,
Spearman, and the proposed NMSSE metric of the
data in Table 2. The figure also shows the Pearson
correlation for the text pairs 1-3, 4-6,7-9 legend as
Pearson_Q1, Pearson_Q2, Pearson_Q3 respectively.
Results show that methods that are good to measure
no similar text method) have high Pearson
correlation on the first three text pairs (Pearson_Q1),
while methods that are good to measure high similar
text (Ω method) has high correlation on the last three
text pairs (Pearson_Q3). In the middle between the
two methods, the β method shows a high Pearson
correlation between the 4-6 pairs (Pearson_Q2).
The reported findings of the three demo
methods indicate that the absolute error between
human scores and predicted scores is low. Therefore,
for a task that needs to discover similar text such as
plagiarism the () is favorable and for semantic
tasks (irrelevant documents) that needs to find
irrelevant text the (α) method is appropriate.
Figure 3 Crafted dataset Pearson correlation
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1.00
Pearson N MSSE Pearson_Q1 Pearson_Q2 Pearson_Q3
α β Ω
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Table 3 The demo similarity methods
Bin
Pair Human
α
Sim.
β
Sim.
Sim. 𝛿
Sim.
1 1 0.01 0.01 0.29 0.47 0.01
2 0.12 0.12 0.00 0.19 0.11
3 0.23 0.22 0.01 0.16 0.21
2 4 0.34 0.73 0 .33 0.33 0.30
5 0.45 0.27 0.43 0.10 0.41
6 0.57 0.76 0.54 0.93 0.51
3 7 0.68 0.79 0 .61 0.64 0.60
8 0.79 0.40 0.24 0.75 0.75
9 0.90 0.67 0.70 0.85 0.81
In contrast, the 𝛿 method, the best method,
has a smooth absolute error except for the outlier
shown in the pair number 8. The best method (𝛿)
shows the lowest errors over the dataset.
The unproductive performance of Pearson
correlation shown in Figure 3 is illustrated in Figure
4. According to Figure 4, the NMSSE is the lowest
for the α method because the α method was doing
well in pairs 1-3. The NMSSE also was the lowest
for the method since the method is doing well
for pairs 7-9. The same thing could be applied to the
β method since the β method was doing well for pairs
4-6. The best optimum method 𝛿 shows lower values
for NMSSE for all the three cross-sections of the
dataset.
Table 4 shows the statistics of the demo
data as per equations (2) – (4). Although α, β are
similar in absolute error, they are different in scaled
errors because β is higher in the MASE as shown the
Figure 4. The root cause of this problem is that as
ℎ
increase, the denominator in the equation (3)
increase and as a result, the value of the equation is
reduced. If
≅ℎ
, that is the value of the predicted
score is like the mean of all predictions, we will get
the highest possible error. Although method has
the highest test score mean variability (
ℎ
 ),
it ranked as the third method using the NMSSE. As
shown in Figure 5, the scaled errors are reduced
when the method matches the type of the similarity
method.
Figure 4 NMSSE performance over sections of datasets
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Figure 5 Scaled errors over different measures
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Table 4 Statistics of the crafted dataset
α β 𝛿
e

1.52 1.51 1.59 0.39
ℎ
ℎ

2.38 1.76 2.4 2.04
𝑆

5.74 7.72 5.35 1.72
MAE 0.17 0.17 0.16 0.04
MASE 0.64 0.86 0.59 0.19
Pearson 0.70 0.70 0.70 1.00
Spearman 0.70 0.67 0.62 1.00
NMSSE 0.47 0.58 0.48 0.17
Furthermore, we calculate the variability
between a performance metric (including the
NMSSE) on the whole dataset and the value of the
compared metric on each section of the dataset Q1,
Q2, and Q3. The target is that we should select the
performance metric that has the lowest variability; a
metric that works well in many situations. Figure 6
shows the variability between Pearson, Spearman,
and the proposed NMSSE concerning the three
sections of the dataset; pairs 1-3,4-6,7-9
respectively. The lowest variability was in NMSSE
for the best method, 𝛿. Whereas the Pearson measure
shows a higher variability due to outliers in each
dataset section. We deduce that NMSSE is effective
in scaling data and in removing outliers. However,
the NMSSE shows a relatively higher variability in
the Q1 dataset because most datasets in this section
has low similarity scores that will affect the
denominator in equation (3).
4.4. Practical Evaluation of NMSSE
Table 5-7 shows the performance of the
NMSE, Pearson correlation, Spearman, and the
MAE for the selected methods presented in Table 2.
The scores were calculated using the weighted
average method based on the number of text pairs in
both development and test benchmark datasets. The
predicted values and human-mean scores were
normalized to be in range 0 to 1 to normalize errors
for method.
The NMSSE proposes to rank text
similarity methods. As Table 5 shows, if an
application is looking for an alternative text
similarity method, the GSE is preferred over other
methods as they have the lowest NMSSE. The only
restriction in this scenario is that the application
should be based on any dataset that imitates a similar
domain to the SICK dataset. On the STS dataset
(Table 6) the SIF method is the best method as it got
the lowest NMSSE. However, on the 30-pair dataset
(STS-65) shown in Table 7, the SIF had the lowest
NMSSE. We emphasize that the proposed metric is
smooth-grained with the benchmark dataset, which
gives an advantage of our metric over other methods.
Figure 6 Variability over data segments
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1.1
1.6
Pe arso n Sp ea rma n NMS SE P ear so n Spe a rma n N MS SE P ear so n Spe a rma n N MS SE
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Table 5 Weighted Scores on the SICK dataset (Dev, Test)
GSE INF SIF (W2V) SIF (GLOVE) WMD (GLOVE) WMD (W2V) TSM
Pearson 0.820.76 0.73 0.72 0.64 0.64 0.48
Spearman 0.770.70 0.61 0.59 0.59 0.59 0.43
MAE 0.090.12 0.16 0.15 0.43 0.43 0.15
NMSSE 0.430.54 0.52 0.53 1.00 1.00 0.98
Table 7 STS65 scores
GSE INF SIF (W2V) SIF (GLOVE) WMD (GLOVE) WMD (W2V) TSM
Pearson 0.78 0.80 0.80 0.73 0.69 0.74 0.52
Spearman 0.80 0.79 0.77 0.79 0.63 0.68 0.47
MAE 0.27 0.39 0.12 0.16 0.47 0.42 0.35
NMSSE 0.91 1.00 0.37 0.50 1.00 1.00 1.00
Table 6 Weighted Scores on STS dataset (DEV, Test)
GSE INF SIF (W2V) SIF (GLOVE) WMD (GLOVE) WMD (W2V) TSM
Pearson 0.78 0.75 0.73 0.72 0.55 0.61 0.36
Spearman 0.77 0.74 0.70 0.71 0.55 0.61 0.37
MAE 0.23 0.21 0.18 0.20 0.37 0.38 0.24
NMSSE 0.88 0.92 0.72 0.83 1.00 1.00 0.94
Figure 7 Ranking methods using NMSEE
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0.18
0.96
0.62 0.59
0.41
1.00
0.00
0.20
0.40
0.60
0.80
1.00
1.20
Pearson Spearman MAE NMSSE
GSE INF SIF TSM WMD
Journal of Theoretical and Applied Information Technology
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© 2005 – ongoing JATIT & LLS
ISSN: 1992-8645 www.jatit.org E-ISSN: 1817-3195
3444
The application of the NMSSE handles the
problematic issues of Pearson correlation, as shown
in Figure 7. The figure shows the weighted scores
over all the five benchmark datasets. The leaders are
the GSE and the INF methods as they have the
lowest SSE compared to other methods. Over the
datasets, the traditional edge counting method TSM
method outperformed the frequency (SIF) and word
distance method (WMD) due to the addition of
knowledge from WordNet exploited by the TSM.
We noticed that the WMD method got the highest
NMSSE due to the scaled error value which was (10-
6); consequently, the NMSSE will be high as the
denominator of equation (2) becomes low. The root
cause of the low scaled error was due to the predicted
values of the WMD method that had a mean of 0.5;
In other words, the average of the difference between
the prediction of the scores and the mean of the
prediction approaches zero. Figure 8 shows the
WMD method scores and the human scores for the
1380 text pairs of the STS test benchmark dataset.
The figure shows that the WMD is overestimating or
underestimating scores by almost a constant value.
Therefore, the WMD got the lowest NMSSE.
4.5. Comparing NMSSE with Related Methods
To our knowledge, no complete performance metric
could be used for the text similarity domain. We
carry out a comparison between the proposed
NMSSE and other methods over the following
criteria:
A. Interpretability: a useful performance metric
should be easy to use and interpret; therefore,
its output can be easily compared within a
predefined scale.
B. Dependency: a useful metric should find the
dependency between the human scores and
the predicted scores.
C. In-group relationship: a useful metric should
indicate how each value in the group is related
to each other. As the human scores in a
benchmark dataset have a range of values
between 0 to 5, the predicted scores should
have similar consistent behavior.
D. Robustness to outliers: performance metrics
should resolve outliers’ issues without
affecting the ultimate performance metric
score.
Figure 8 NMSEE of WMD over STS dataset
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
‐19 81 181 281 381 481 581 681 781 881 981 1081 1181 1281 1381
Prediction
Hscor e
Journal of Theoretical and Applied Information Technology
30th June 2019. Vol.97. No 12
© 2005 – ongoing JATIT & LLS
ISSN: 1992-8645 www.jatit.org E-ISSN: 1817-3195
3445
E. scale: a performance metric that has a
numeric value (e.g., 0 to 1) is quantifiable
when compared to other values resulted from
other related applications.
Table 8 shows the comparison of our metric
and a list of selected metrics where the stands for
the availability of the criterion while stands for a
non-applicable criterion. Although most of the
compared methods are interpretable (A), they suffer
from outliers (D). The MAE can be made
interpretable by getting the relative or percentage
error. The drawback of the MAE is that it does not
take into consideration the in-group predicted scores
(C), and it does not provide a standard scale (E). We
underline that we are not looking to replace Pearson
correlation but to add extra information that could be
utilized to researchers in natural language processing
and machine learning communities.
Table 8 Comparison of the proposed metric and related
approaches
Criterion NMSSE Pearson Ranking
Methods
MAE
A
B
C
D
E
5. IMPLICATIONS
The implication of this research is
theoretical and practical. The new measure suggests
a re-look to the ongoing usage of the Pearson
correlation for a long time. In practice, applications
should select the similarity method with the lowest
possible normalized error. Although the scaled error
method was borrowed from a non-related domain
(the finance domain), the new proposed normalized
scaled square error could be used in other domains
where outliers play a significant effect in natural
language processing task. Since the proposed metric
is robust to outliers and provides an interpretable
scaled value, it would be practical in comparing text
in domains such as plagiarism detection and text
entailments.
6. LIMITATION
Despite the fact that the proposed method
is superior in ranking and text evaluation,
researchers need to do more research before
generalizing results. The method was applied to five
datasets only, and it was not applied practically in
any semantic text similarity task.
The research direction should target to
generalize the results with text similarity by
annotating current and new datasets to allow the
comparison of the proposed approach with other
alternatives. Therefore, further experiments are
needed to test the situations where we would prefer
the Pearson correlation over the proposed
normalized means scaled square error method.
In the future, the proposed approach should
be evaluated using simulations and applying the
proposed method on a large empirical dataset.
7. CONCLUSION
This paper proposes a new semantic
similarity metric that could be used to compare and
rank semantic similarity methods. The proposed
metric reduces dataset noise by scaling absolute
error with the mean of the absolute difference of
observed scores with observed mean scores. The
metric was compared with Pearson, Spearman, and
the Mean Absolute Error. Results showed that the
new proposed normalized scaled square error is
effective in reducing skewness and is applicable in
domains with different observed scores. In the
future, we plan to run several simulations over the
new metric and evaluate the metric with extra-large
benchmark datasets.
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