Polysemy Detection in Distributed Representation of
Word Sense
Kana Oomoto∗ , Haruka Oikawa∗ , Eiko Yamamoto† , Mitsuo Yoshida∗ , Masayuki Okabe‡ and Kyoji Umemura∗
∗ Department

arXiv:1709.08858v1 [] 26 Sep 2017

of Computer Science and Engineering, Toyohashi University of Technology, Toyohashi, Japan
k133309@edu.tut.ac.jp, h153312@edu.tut.ac.jp, yoshida@cs.tut.ac.jp, umemura@tut.jp
† Faculty of Economics and Information, Gifu Shotoku Gakuen University, Gifu, Japan
eiko@gifu.shotoku.ac.jp
‡ Faculty of Management and Information Systems, Prefectural University of Hiroshima, Hiroshima, Japan
okabe@pu-hiroshima.ac.jp

Abstract—In this paper, we propose a statistical test to determine whether a given word is used as a polysemic word or
not. The statistic of the word in this test roughly corresponds to
the fluctuation in the senses of the neighboring words and the
word itself. Even though the sense of a word corresponds to a
single vector, we discuss how polysemy of the words affects the
position of vectors. Finally, we also explain the method to detect
this effect.
Keywords—word2vec; polysemic word; distributed representation

I. I NTRODUCTION
Distributed representation of word sense provides us with
the ability to perform several operations on the word. One of
the most important operations on a word is to obtain the set of
words whose meaning is similar to the word, or whose usage
in text is similar to the word. We call this set the neighbor
of the word. When a word has several senses, it is called a
polysemic word. When a word has only one sense, it is called
a monosemic word. We have observed that the neighbor of a
polysemic word consists of words that resemble the primary
sense of the polysemic word. We can explain this fact as
follows. Even though a word may be a polysemic, it usually
corresponds to a single vector in distributed representation.
This vector is primarily determined by the major sense, which
is most frequently used. The information about a word’s minor
sense is subtle, and the effect of a minor sense is difficult to
distinguish from statistical fluctuation.
To measure the effect of a minor sense, this paper proposes
to use the concept of surrounding uniformity. The surrounding
uniformity roughly corresponds to statistical fluctuation in the
vectors that correspond to the words in the neighbor. We have
found that there is a difference in the surrounding uniformity
between a monosemic word and a polysemic word. This
paper describes how to compute surrounding uniformity for a
given word, and discuss the relationship between surrounding
uniformity and polysemy.
II. R ELATED W ORK
The distributed word representation can be computed as
weight vectors of neurons, which learn language modeling [1].
978-1-4673-9077-4/17/$31.00 c 2017 IEEE

We can obtain a distributed representation of a word using the
Word2Vec software [2] which enable us to perform vector
addition/subtraction on a word’s meaning. The theoretical
background is analyzed by [3], where the operation is to
factorize a word-context matrix, where the elements in the
matrix are some function of the given word and its context
pairs. This analysis gives us insight into how the vector is
affected by multiple senses or multiple context sets. If a word
has two senses, the obtained representation for the word will
be a linearly interpolated point between the two points of their
senses.
The importance of multiple senses is well recognized in
word sense detection in distributed representation. The usual
approach is to compute the corresponding vectors for each
sense of a word [4], [5]. In this approach, first, the context
is clustered. Then, the vector for each cluster is computed.
However, the major problem faced by this approach is that
all target words need to be assumed as polysemic words first,
and their contexts are always required to be clustered. Another
approach is to use external language resources for word sense,
and to classify the context [6]. The problem with this approach
is that it requires language resources of meanings to obtain the
meaning of a polysemic word. If we know whether a given
word is polysemic or monosemic thorough a relatively simple
method, we can concentrate our attention on polysemic words.
III. S ENSES AND C ONTEXTS
In this paper, we assume that the sense of a word is
determined by the distribution of contexts in which the word
appears in a given corpus. If a word comes to be used in new
contexts, the word comes to have a new sense. If we could
have an infinitely sizes corpus, this sense might converge into
the sense in the dictionary. In reality, the size of the corpus in
hand is limited, and some senses indicated in a dictionary may
not appear in the corpus. The distinction between the senses
in a dictionary and the senses in the corpus is important in
this paper, because it is crucial for discussing polysemy. All
discussions in this paper depend on the corpus in hand. We
now use the FIL9 corpus (http://mattmahoney.net/dc/textdata),
which primarily consists of a description of believed facts,
rather than conversations. We can expect that the senses that

are mainly used in conversation would not appear in this
corpus.
In this paper, we analyze auxiliary verbs, which are polysemic words from a dictionary. If the corpus is limited to a
description of believed facts, we may regard auxiliary verbs as
monosemic words, since their contexts are limited. In addition,
we particularly analyze the relationship between the auxiliary
verb “may”, and name of the month “May”. In the dictionary,
these two are regarded as two different words, rather than as
two different senses of one word. By ignoring the upper/lower
case characters, these two words have same character sequence
and the word “may” becomes a polysemic word, which has
two types of context in the given corpus.
IV. P ROPOSED M ETHOD
Our proposed method is based on the following measures.
Let w
~ be the vector corresponding to the given word. Let
N be the size of the neighbor, such as 4. First, we choose
N neighboring words whose angle with the given word is
the smallest. This operation is already implemented in the
Word2Vec software. Let a~i (w)
~ be the vectors corresponding
to ith vector of the neighbor of the word.
We choose the uniformity of vectors, which can be regarded
as general case of triangle inequality. The uniformity of a set
of vectors is a ratio, i.e., the size of the vector of the vector
addition of the vectors divided by the scalar sum of the sizes
of the vectors. If and only if all directions of the vectors
are the same, the uniformity becomes 1.0. We compute
this uniformity for the neighbors, including the word itself.
Surrounding Uniformity (SU) can be expressed as follows:
SU (w)
~ =

|~s(w)|
~
PN
|w|
~ + i |a~i (w)|
~

where
~s(w)
~ =w
~+

N
X

a~i (w).
~

i

When computing SU, we consider the set of words whose
vectors are reliable. We choose these words as the most
frequently appearing words in corpus. The size of words is
denoted as limit. If a word is not in this set, or the word
does not have sufficient number of neighbors in this set, we
consider that the value of SU is undefined, and that the word
does not have this value.
Our method performs a statistical test to determine whether
a given word is used polysemously in the text, according to
the following steps:
1) Setting N , the size of the neighbor.
2) Choosing N neighboring words ai in the order whose
angle with the vector of the given word w is the smallest.
3) Computing the surrounding uniformity for ai (0 < i ≤
N ) and w.
4) Computing the mean m and the sample variance σ for
the uniformities of ai .

5) Checking whether the uniformity of w is less than m −
3σ. If the value is less than m − 3σ, we may regard w
as a polysemic word.
This is a basic statistical test [7] to detect outliers.
Note that we cannot compute the variance if some ai does
not have the value of SU. Further, it may be also possible that
all ai may have the same SU, sharing identical neighbors. In
this case, the variance becomes an extreme value, that is, 0. In
these cases, we consider that we cannot perform the statistical
test.
V. E XPERIMENTAL S ETTINGS AND E XAMPLES OF
C ALCULATION
We used FIL9, which is freely available as the test corpus
for Word2Vec and is derived from Wikipedia. We compute
200-dimensional distributed vector representations with default parameter. In this situation, all-uppercase are converted
into lower case. This is why all proper nouns are in lower
case in this example. First we selected stable words as the
1000 words that appear most frequently in the text. We
compute surrounding uniformity of these words. We define
the given word w and its neighboring word ai are limited
to stable words. We then determine the search scope for
stable neighboring words and set N , which is the number of
neighbors used to compute the surrounding uniformity, to 4.
For example, if there are 7 stable words in the search scope,
we use only the top 4 words to compute the surrounding
uniformity.
Table I shows the uniformity of auxiliary verbs in this
setting. We were able to compute the surrounding uniformity
for 160 words; for the remaining 840 words, there were fewer
than the required 4 stable neighboring words in the search
scope and the surrounding uniformity could not be determined.
For the case of the word “may”, neighbor words are “can”,
“should”, “might”, and “will”. Their surrounding uniformities
are, 0.9252 (“can”), 0.9232 (“should”), 0.9179 (“might”), and
0.9266 (“will”). Then m is equal to 0.9232, and σ is equal
to 0.0038. Therefore, m − 3σ is 0.9118, which is greater
than 0.8917 (“may”). Since the surrounding uniformity of the
word “may” is regarded as an outlier, we think of “may”
as polysemic. In this setting, the word “may” is polysemic
because the program works in a case-insensitive mode, and
the word “may” could be both an auxiliary verb and the name
of a month.
The next example is the word “might”, whose surrounding uniformity is smaller than every neighbor word. For
the word “might”, neighbor words are “would”, “could”,
“should”, and “cannot”. Their surrounding uniformities are
0.9266 (“would”), 0.9290 (“could”), 0.9232 (“should”), and
0.9224 (“cannot”). Hence, m is equal to 0.9253, and σ is
equal to 0.0032. Therefore, m − 3σ is 0.9157, which is less
than 0.9179 (“might”). We cannot say 0.9179 is an outlier, and
thus we cannot say the word “might” is polysemic.
Figure 1 shows the distribution of vectors. The vector of
“may” is placed in the interpolated position between “may”
as an auxiliary verb and “may” as the name of a month. Since

TABLE I
AUXILIARY VERBS , THEIR NEIGHBORING WORDS , AND SURROUNDING UNIFORMITIES . T HE NEIGHBORING WORDS OF AN AUXILIARY VERB CONSIST OF
OTHER AUXILIARY VERBS . T HE WORD “ MAY ” HAS A SMALL SURROUNDING UNIFORMITY, ALTHOUGH ITS NEIGHBORING WORDS CONSIST OF
AUXILIARY VERBS .
word (w)

neighboring words (ai , N = 4)

could
will
would
must
can
should
cannot
might
may

would
would
could
cannot
cannot
must
must
would
can

will
must
will
will
must
could
can
could
should

might
could
might
should
could
might
could
should
might

surrounding uniformity

must
should
should
could
will
will
might
cannot
will

0.9290
0.9266
0.9266
0.9253
0.9252
0.9232
0.9221
0.9179
0.8917

test
significant

“ should” neighboring words
must
could
“ may” neighboring words
should
can

will
might

may
“ january” neighboring words
january
february
november
march

december

Fig. 1. Relation of the words: “should”, “may”, and “january”. The distributed representation of the word “may” is placed near other auxiliary verbs.
Regarding the linear nature of Word2Vec, it is natural that the position should be between auxiliary verbs and the names of the months.

the word “may” is more frequently used as auxiliary verb,
the vector is placed near other auxiliary verbs. However, the
position of “may” could be an outlier for other auxiliary verbs.
In addition, we should show the results of names of months
because these names will have the same contexts when the
word is used as the name of a month. The word “may” has
other contexts as auxiliary verbs. The word “august” has the
sense of an adjective in the dictionary. The word “march” has
a sense of a verb. Other names are monosemic words in the
dictionary. Table II shows the surrounding uniformity for all
the names of the months.
If we apply the test, only the word “may” passes the test.
The example that fails the test is the word “august”, whose
surrounding uniformity is also smaller than every neighbor
word. For the case of the word “august”, m is equal to 0.9808,
and σ is equal to 0.0005. Therefore, m − 3σ becomes 0.9793,
which is less than 0.9802 (“august”). We cannot say the word
“august” is polysemic, but the value of uniformity is very close
to the lower bound. Other names have a greater uniformity
than the corresponding lower bound. In summary, the proposed
method can detect the polysemic “may”, but cannot detect the

polysemicity of “august” and “march”.
Although we can claim nothing if the statistical test fails,
even the negatives have a practical value for this test. For the
case of the word “august”, it can be used as an adjective.
Although we cannot say the word “august” is polysemic
from the proposed procedure, we cannot claim that the word
“august” is monosemic. We think this failure is caused by a
few, if any, contexts of “august” as an adjective. In that case,
the clustering context will be difficult in practice. Therefore,
the proposed test will be meaningful even for a negative result,
when the result is used to judge whether further analysis of
the context is worthwhile. This discussion should be also true
for the word “march”, which may be used as a verb.
There are other interesting words for which the proposed method detects polysemicity. These words are “james”,
“mark”, and “bill”. The neighboring words are names of
persons, such as “john”, “richard”, “robert”, “william”,
“david”, “charles”, “henry”, “thomas”, “michael”, and “edward”. “mark” and “bill” have the same spell of the regular
noun. The word “james” does not have such words and is
subject to error analysis.

TABLE II
NAMES OF THE MONTHS , THEIR NEIGHBORING WORDS , AND SURROUNDING UNIFORMITIES . O NLY “ MAY ”, WHICH HAS THE SMALLEST SURROUNDING
UNIFORMITY, PASS THE STATISTICAL TEST. A LTHOUGH THE WORD “ MAY ” MIGHT BE USED AS THE NAME OF A MONTH , THE CORRESPONDING VECTOR
IS NEAR THE AUXILIARY VERBS .
word (w)

neighboring words (ai , N = 4)

december
january
october
june
april
november
february
march
september
july
august
may

november
february
november
july
march
december
january
december
december
june
september
can

october
december
december
march
december
october
december
april
august
december
july
should

march
november
february
december
september
september
march
june
april
august
june
might

VI. E VALUATION
First, we set the value of limit to 1000, and N to 4. We
then performed the statistical test of these 1000 words. From
these, 33 words passed test, and we assume that these words
belong to the set POLY. Further, we are unable to performs
the statistical test for 127 words. We say that the remaining
840 words belong to the set MONO.
As evaluation, we attempted to measure the agreement of
human judgment for the all words of POLY and MONO.
However, during the valuation, we found that many of the
errors come from the problem of Word2Vec. For example,
the vector of “sir” and the vector of “william” are very close
because “sir william” should be very close to “william”. This
is similar for “w” and “george”.
Therefore, we first selected words whose 10 neighboring
words seem reasonable neighbors for human judgments, and
performed human judgments of polysemicity. We also focused
the words that have bigger SU than 0.75. This is because the
statistical test will be reliable when SU is large. Table III
shows that list of words that passed the test, and have higher
SU than 0.75. Table III shows all the words in POLY that are
judged by human. Similarly Table IV shows all the words in
MONO that are judged by human. We have sampled words
from MONO because there are many words in MONO. In
these tables, the SU of surrounding words are also presented.
Table V shows the confusion matrix for computer human
judgment. As there exists a case for which the number is
less than or equal to 5, we need Yate’s continuity correction.
It achieves statistical significance with level of α = 0.05.
The disagreement in POLY in Table V for the word “james”
attracted our attention.
VII. E RROR ANALYSIS
The disagreement in MONO could be because we chose 3σ,
which can detect polysemicity in extremely apparent cases.
Even so, the word “james” passes the proposed statistical test.
Therefore, the word “james” is worth investing in.

surrounding uniformity
september
march
september
april
july
january
october
february
november
september
april
will

0.9817
0.9816
0.9815
0.9814
0.9810
0.9810
0.9809
0.9806
0.9804
0.9804
0.9802
0.8917

test
significant

After examining the context of “james”, we found that it can
be used as the name of river and a person. Table VI shows
the various names and how many times the name is used with
the word “river”. The word “james” is most frequently used
with “river”. This may make the word pass the statistical test.
VIII. D ISCUSSION
The majority of the polysemicity presented in this paper
exists due to the Word2Vec compute the distributed representation after ignoring cases. This polysemicity might not be
regarded as polysemicity with more careful preprocessing.
The behavior of proposed method depends on the Word2Vec
options and the size of the corpus. If Word2Vec does not have
a reasonable neighbor that consists of words of similar usage,
the proposed method cannot work effectively. In addition, a
problem arising due the use of Word2Vec for our application
is the placement of the vector “sir” and the vector “william”
in similar position. Therefore, we may need to utilize another
method to compute the distributed representation of words.
We use the FIL9 corpus for the experiment. Though this
corpus is freely available to everyone, the size may not be
sufficient. Although we can detect the polysemicity of “may”,
we cannot detect the polysemicity of “august” and “march”.
The statistical test cannot detect the right answer if we do not
have sufficient data; therefore, this failure may be interpreted
as insufficient usage of “march” as verb, and “august” as
adverb, owing to its origin from Wikipedia, which is in essence
a description of facts.
We believe we need to find a way to select the number
of neighbors to improve the accuracy of the test. To make
the statistical test more accurate, we need more samples from
the neighbors. At the same time, since we assume that we can
measure the statistical fluctuation from the neighbors, we need
to exclude words of a different nature from the neighbors. It is
natural that the right number for a neighbor may be different
according to the word. The number that we choose is the

TABLE III
E VALUATED W ORDS AND ITS NEIGHBOR THAT PASSES THE STATISTICAL TEST.
word (w)

neighboring words and neighboring word’s SU (ai , N = 4)

may
james
mark
bill

can
john
peter
peter

(0.9252)
(0.9067)
(0.8675)
(0.8675)

should
robert
michael
david

(0.9232)
(0.8984)
(0.8881)
(0.8945)

might
richard
david
michael

(0.9179)
(0.8984)
(0.8945)
(0.8881)

will
william
smith
richard

(0.9266)
(0.8950)
(0.8702)
(0.8984)

SU

computer

human

0.8917
0.8788
0.8249
0.8196

poly
poly
poly
poly

poly
mono
poly
poly

TABLE IV
E VALUATED W ORDS THAT DOES NOT PASS THE STATISTICAL TEST.
word (w)

neighboring words and neighboring word’s SU (ai , N = 4)

december
november
august
three
will
two
richard
henry
tv
make
pennsylvania
french
spanish
dutch
go
radio
move
founded
child
studies

november
december
september
four
would
three
robert
edward
television
give
ohio
italian
french
french
get
television
get
established
daughter
research

(0.9810)
(0.9817)
(0.9804)
(0.9730)
(0.9266)
(0.9730)
(0.8984)
(0.8848)
(0.8293)
(0.8150)
(0.8295)
(0.8116)
(0.8177)
(0.8177)
(0.8465)
(0.8293)
(0.8465)
(0.7967)
(0.8420)
(0.7810)

october
october
july
five
must
five
william
william
radio
find
michigan
dutch
english
german
come
tv
turn
formed
woman
study

(0.9815)
(0.9815)
(0.9804)
(0.9730)
(0.9253)
(0.9730)
(0.8950)
(0.8950)
(0.8037)
(0.8465)
(0.8336)
(0.8132)
(0.7765)
(0.8128)
(0.7838)
(0.8293)
(0.7800)
(0.7899)
(0.7672)
(0.7798)

march
september
june
six
could
four
john
charles
shows
get
virginia
german
dutch
spanish
take
network
go
introduced
mother
education

(0.9806)
(0.9804)
(0.9814)
(0.9737)
(0.9290)
(0.9730)
(0.9067)
(0.8922)
(0.7953)
(0.8465)
(0.7748)
(0.8128)
(0.8132)
(0.8164)
(0.7892)
(0.7835)
(0.8116)
(0.7835)
(0.8796)
(0.7542)

september
january
april
seven
should
zero
david
richard
network
makes
township
english
italian
english
move
news
find
built
children
philosophy

(0.9804)
(0.9816)
(0.9810)
(0.9737)
(0.9232)
(0.9221)
(0.8945)
(0.8984)
(0.7835)
(0.7517)
(0.8171)
(0.7765)
(0.8116)
(0.7765)
(0.8010)
(0.7342)
(0.8465)
(0.7464)
(0.7246)
(0.7632)

SU

computer

human

0.9817
0.9810
0.9802
0.9730
0.9266
0.9221
0.8984
0.8922
0.8293
0.8201
0.8186
0.8177
0.8164
0.8132
0.8116
0.8037
0.8010
0.7967
0.7829
0.7798

mono
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono

mono
mono
mono
mono
mono
mono
mono
mono
poly
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono
mono

TABLE V
C ONFUSION M ATRIX OF THE AGREEMENT BETWEEN COMPUTER AND HUMAN JUDGMENTS . I T SHOWS STATISTICAL SIGNIFICANCE BY USING X 2 TEST.
computer

mono

poly

total

mono

19

1

20

poly

1

3

4

total

20

4

24

human

TABLE VI
F REQUENCIES OF A PERSON ’ S NAME AND THE NAME FOLLOWED BY THE WORD “ RIVER ”. T HE NAME “ JAMES ” IS THE MOST FREQUENTLY USED NAME
WITH THE WORD “ RIVER ”.
name
james
john
robert
richard
william
henry
michael
charles
edward
david

freq
27678
61374
21491
16838
29310
19779
17854
14998
23123
11745

river

freq

ratio (river/name)

james river
john river
robert river
richard river
william river
henry river
michael river
charles river
edward river
david river

202
76
1
0
0
0
0
0
112
0

0.007298
0.001238
0.000047
0.000000
0.000000
0.000000
0.000000
0.000000
0.004844
0.000000

minimum value for the statistical test, and has room to adjust
for improvement.
We computed the neighbor and surrounding uniformity of
the 1000 most frequently used words in FIL9. We observed
that proper nouns tend to have a large surrounding uniformity,
whereas prepositions tend to have a small surrounding uniformity. It is an interesting observation that the surrounding
uniformity reflects the part of speech information, although it
is difficult to determine the class of a word from the value of
the surrounding uniformity alone. For the ease of confirming
this observation, the obtained table can be downloaded from
the reference (http://www.ss.cs.tut.ac.jp/FIL9SU/).
IX. C ONCLUSION
In this paper, we proposed a method to detect polysemy
based on the distributed representation by Word2Vec. We
computed the surrounding uniformity of word vector and
formed a statistical test. We illustrated several examples to
this measure, and explained the statistical test for detecting
polysemy. In addition, we have also discussed the feasibility
of this test.
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(Springer Texts in Statistics). Springer, 2004, ch. 10, pp. 149–173.

