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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Context based number normalization using skip-chain conditional random fields</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Linas Balcˇi u¯nas</string-name>
          <email>linasb20@gmail.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Lemma Part of speech (Noun</institution>
          ,
          <addr-line>Verb, Adjective,...) Case (Nominative, Genitive,...) Gender (Feminine, Masculine) Number, Singular, Plural</addr-line>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Vytautas Magnus University Kaunas University of Technology Kaunas</institution>
          ,
          <country country="LT">Lithuania</country>
        </aff>
      </contrib-group>
      <fpage>17</fpage>
      <lpage>21</lpage>
      <abstract>
        <p>-Verbalizing numeric text tokens is a required task for various speech-related applications, including automatic speech recognition and text-to-speech synthesis. In morphologically rich languages, such conversion involves predicting implicit morphological properties of a corresponding numeral. In this paper, we propose first-order skip-chain Conditional Random Field (CRF) models and various prepossessing techniques to leverage different contextual information. We show that our best skip-chain CRF models achieve over 80% accuracy on the set of 2000 Lithuanian sentences.</p>
      </abstract>
      <kwd-group>
        <kwd>Number normalization</kwd>
        <kwd>text normalization</kwd>
        <kwd>conditional random field</kwd>
        <kwd>natural language processing</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>I. INTRODUCTION</title>
      <p>
        Number normalization is the task of replacing numeric
tokens in a sentence by numerals (word tokens) using an
appropriate inflected form of a numeral. Number normalization
usually involves disambiguation as the same numeric token
needs to be mapped into different word forms depending on
the context (e.g. ’5 vaikai eina’ 7! ’Penki vaikai eina’ (five
children are going) vs. ’5 vaiku˛ ne˙ra’ 7! ’Penkiu˛ vaiku˛ ne˙ra’
(five children are missing)). Although number normalization
can be considered as a part of a broader task of text
normalization, formulating it as the separate task might be beneficial,
since the process of number normalization can be quite
complex depending on morphological features of a language. In
this paper, we describe the process of building and evaluating a
number normalization system for Lithuanian. However, some
techniques and models are language-independent and might be
applied to other languages. In Lithuanian, for example, number
’5’ depending on sentence context may represent any of 63
different words. Predicting this relationship directly is rather
difficult and it would require huge data-set to properly learn
Numeral grammar. A simpler approach is predicting Part Of
Speech (POS) tag and then generating numerals accordingly.
POS tag contains all necessary morphological information
to use language-specific grammar based numbers-to-words
system [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. This way possible result classes are shared across
all numbers and predicting POS tag can be formulated as
sequence labeling, rather than sequence-to-sequence task,
because of the one-to-one relationship.
c 2019 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0)
      </p>
    </sec>
    <sec id="sec-2">
      <title>II. RELATED WORKS</title>
      <p>
        As far as we know, there are no published works or
publicly available applications performing number
normalization based on the sentence context for Lithuanian. Although,
many languages deal with similar morphological
disambiguation problems. Russian and Lithuanian numbers share many
morphological properties, including types (cardinal, ordinal),
genders and cases. There are existing research and systems
for the Russian language on general text normalization,
handwritten language-general grammar [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], Recurrent Neural
Network (RNN) [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], and number normalization [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ].
      </p>
    </sec>
    <sec id="sec-3">
      <title>III. PREPROCESSING</title>
      <sec id="sec-3-1">
        <title>A. Data</title>
        <p>A small text corpus for training and evaluating text
normalization models was collected and manually annotated. It
consists of 1955 sentences containing 3143 numeric tokens.
Sentences were inspected by linguists who suggested a
numeral word form as an appropriate replacement for every
numeric token. In some ambiguous cases, a few reasonable
alternatives were proposed. Some ambiguities were related to
the use of the pronominal numeral forms (e.g. ’15 savaite˙’
(15th week) 7! ’penkiolikta savaite˙’ (non-pronominal form) or
’penkioliktoji savaite˙’ (pronominal form)). Other ambiguities
were related to numeral case (e.g. ’2019 vasar˛ı’ (2019
February) 7! ’du tu¯kstancˇiai devynioliktu˛ju˛ vasar˛ı’ or ’du tu¯kstancˇiai
devynioliktaisiais vasar˛ı’). All suffixes that represented a
’normalization hint’ were eliminated from the data set (e.g.
’2019aisiais’ was replaced by ’2019’). This had an effect of making
training subset of the corpus more interesting for the training
algorithm, increased the complexity of the normalization task,
and reduced the normalization accuracy estimates on the test
subset of the corpus.</p>
        <p>
          Sentences of the corpus were pre-processed by the Hidden
Markov Models (HMM) based POS tagger [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ]. Every text
token was labeled with the so-called ’detailed’ (or composite)
morphological label that contained the following information:
        </p>
        <p>Since important prediction decisions are based on tagger
provided POS tags and lemmas, to ensure optimal
performance, morphological annotations were hand-corrected in
training-testing data-set. When using morphological analysis
data, it is beneficial to divide POS tags into sub-labels to
build more abstract grammar rules and filter out redundant
information.</p>
      </sec>
      <sec id="sec-3-2">
        <title>B. Number grammar</title>
        <p>
          Similar more saturated Natural Language Processing (NLP)
sequence labeling tasks, POS tagging and Named Entity
Recognition (NER), does not require hand-written
languagespecific grammar rules to achieve state-of-the-art [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ]
performance. Long-Short Term Memory neural networks coupled
with Conditional Random Fields (LSTM-CRF) based
datadriven sequence labeling approaches prove to be insufficient
to achieve desired number normalization quality, considering
training-data availability limitations. To efficiently leverage
small data-set, morphosyntactic knowledge should be
exploited for crafting language and task-specific grammar rules.
        </p>
        <p>All rules are constructed as conditional functions without
any prior weighting. Here are different techniques used to
approximate and generalize number relationship with sentence
context:</p>
        <p>Lemma classification. (Replacing certain word lemmas
with a dedicated class name, for example, month names
with ’%Month’)
Number classification. (See Table I)
Verb classification. (Based on syntactic features of
controlling case of other POS)
Syntactic linking (See Section V. Long-Distance
Dependencies)</p>
        <p>In this paper, mainly variations of Conditional Random
Fields (CRF) are explored, since CRF got better baseline
performance than its neural version (LSTM-CRF) and appears
to be more suitable for particular data-set and grammar
ruleset.</p>
      </sec>
      <sec id="sec-3-3">
        <title>A. Sub-Label models</title>
        <p>
          To create a single sequence tagging model for this task, we
would need 79 (different combinations of sub-labels shown in
Table II) detailed morphological labels corresponding to the
output classes. With the currently available corpus, this would
cause significant data scarcity problems. There are no training
examples for a considerable number of classes and many
others are barely represented. A good way to address this data
scarcity problem is creating three independent CRF models
for Case, Type, Gender prediction and to combine these
predictions at a later stage. This is preferable since there is no
direct dependency relationship between these morphological
categories and operating with sub-labels allows creating a
more abstract rule-set. Although, it is worth noting that
sublabel dependencies have been proven useful for NLP sequence
labeling using CRF [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ] in combination with composite labels.
Additionally exploiting composite label dependencies might be
beneficial for number normalization as well, and it is worth
exploring in future research.
        </p>
        <p>
          The linear-chain structure is usually used for sequence
labeling CRF since additionally modeling non-linear
relationships requires complicated inference algorithms and prior
specification of such dependencies [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ], [
          <xref ref-type="bibr" rid="ref12">12</xref>
          ]. For number
normalization, a simplified version of Skip-chain Conditional
Random Field (S-CRF) can be used, as shown in the gender
prediction model comparison in Figure 1 and Figure 2 (for
readability reasons, we only show English glossary sentence
example of Lithuanian model). Both graphs are representations
of Viterbi algorithm decoding (the same structure is used
for encoding). Circles correspond to nodes and arrows to
transitions. The weight of node or transition is calculated as
the sum of its conditional feature-set weights (unigrams for
node and bigrams for transition). ’f’ and ’m’ are notations
for ’feminine’ and ’masculine’ genders, while ’0’ represents
a class for non-number tokens, which are not to be changed
by the normalization task. The blue path is the correct path
selected by the Viterbi algorithm. In Linear-chain CRF
(LCRF) most bigram features are useless since they connect with
non-number tokens (in Figure 1 none of transition weights are
significant). This means we effectively have zeroth-order CRF.
Transitions that are actually important are between numbers.
To implement such dependencies we make two sequences - full
(original) and skip (numbers only). We build unigram features
only for number tokens but from the full sequence. This way
our unigram features exactly match those of the linear-chain
model. Next, bigram features are built from the skip sequence.
For encoding and decoding, we use skip sequence as well,
since we do not build any feature functions for non-number
tokens. Skip-chain models, as described above, have unaltered
unigram and improved bigram function sets (for number
tokens), while being significantly faster (see graph simplification
shown in Figure 1 and Figure 2). Our implementation uses a
modified version of the CRFSharp toolkit [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ].
noun has crucial morphological information. For example,
with successful identification, we no longer need to predict
the gender of a numeral, since it is directly determined by the
noun.
0
f
m
0
        </p>
        <p>Although skip-chain structure quite reliably models some
important long-distance relationships, it is not able to capture
distant dependencies between number and non-number tokens
(e.g. in ’3 didžiu˛ju˛ mobiliojo ryšio operatoriu˛’ 7! ’triju˛
mobiliojo ryšio operatoriu˛’ (three major mobile network
operators) numbers ’3’ case is determined by words ’operatoriu˛’
(operators) case). CRF is generally unable to leverage such
features and requires either hybridization such as
LSTMCRF, or additional pre-processing. We propose identifying
position-distance independent relationships using an ad-hoc set
of linkage rules and formulating perceived syntactic links as
conditional functions of CRF. For Lithuanian language, we
discern three directly related parts of speech (Noun, Verb,
Preposition) in the number normalization task. For each, we
use a different set of linkage rules, to identify related tokens
to every number in the sentence, effectively performing partial
syntactic analysis. To link prepositions and verbs to numbers,
our rules solely rely on morphological labels provided by the
POS tagger. For nouns, the task of linking could be more
precisely formulated as an identification of a noun which
represents an object or quantity being counted by some number
in the sentence. This is extremely important since countable
7
0
f
m
7
f
m
red
0
f
m
red
0
apples
0
f
m
apples
0</p>
      </sec>
      <sec id="sec-3-4">
        <title>A. Countable noun identification</title>
        <p>We determine the most likely countable noun in a
twostep process. First, for a given numeric token d we select
all potentially countable noun tokens fnig according to the
ad-hoc set of linkage rules for nouns. We can not make an
educated choice among selected nouns on the basis of available
morphosyntactic annotation since noun morphology does not
have the property of ’countability’. To discriminate among
potential countable nouns, semantic analysis is needed. We
need to rate the set of selected nouns fnig according to some
’countability’ measure that is dependent on the numeric
token d being normalized and select the noun nbest with the
highest (d; ni) rating nbest = arg max (d; ni)</p>
        <p>
          Suppose that we have vector embeddings v(n); v(n) 2 RD
for every noun n, that were obtained by an algorithm such as
’word2vec’ [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ]. Suppose that we also designed a mapping
that maps every numeric token d into a vector (d); (d) 2
RD such that (d) is the representative embedding of the set
of nouns that are frequently counted by the numeric token d.
If both assumptions are correct, we can rate the set of potential
countable nouns by estimating cosine similarity between each
selected noun and the corresponding representative vectors,
i.e.
        </p>
        <p>(d; ni) = cosine-similarity( (d); v(ni))
(1)</p>
        <p>We have tested a few different approaches to design the
above-mentioned mapping (d). We sought large unannotated
text corpus for number and noun adjacent co-occurrences
and made noun frequency lists per every numeric token that
was found (around 350 thousand co-occurrences). Information
present in a frequency list can be aggregated into a single
vector by estimating the weighted average of noun embeddings
making up that list. Thus a representative (or central)
embedding vector can be obtained per every numeric token. Although
this tabular mapping from numeric tokens into representative
vectors can be used in (1), it has serious limitations. The table
contains many unreliable vectors for rare numbers, because
of the lack of co-occurrences in the unannotated corpus. To
circumvent the limitations of this tabular mapping we used
the Neural Network (NN) approach to build a continuous
cooccurrence model. We built two different neural networks: one
with a single input (corresponding to the mathematical value of
the numeric token) and one with 7 inputs, corresponding to the
decomposition of the numeric token into sub-parts (thousands,
hundreds,...) and including number features similar to Table I.
NN had 200 output units.</p>
        <p>The evaluation of these models is shown in Table III. The
baseline performance is obtained by the simple rule "take
the first potentially countable noun to the right of a numeric
token". Accuracy is measured using whole CRF training data,
extracting situations where a choice between two or more
nouns (2.41 avg.) is needed.</p>
        <p>We evaluate models with 5-fold cross-validation (except for
countable noun identification in Section V, since training and
testing data-sets were obtained from different sources). The
accuracy of different models is shown in Table IV. Combined
accuracy estimates the accuracy of all three models. The
combined answer is considered to be correct if all three
sublabels are correct.</p>
        <p>It is worth noting, that our model is focused on
grammatically correct, as ’spoken’ number normalization. This might
not be desirable for systems like text-to-speech synthesis,
hence a more standardized approach can be chosen. For
Lithuanian language, numeral definiteness property could be
removed from the prediction model, since it is not strictly
constrained by grammar. This would increase language
correctness and improve Type prediction models and combined
accuracy as shown last line of Table IV (best performing model
without definiteness property).</p>
        <p>Accuracies above represent the lower bound accuracies of
the real-world number normalization performance. Firstly, in
certain situations, some sub-label prediction mistakes might
be irrelevant for numeral generation. For example, both ’5,
Cardinal, Genitive, Feminine’ and ’5, Cardinal, Genitive,
Masculine’ will generate the same word representation ’penkiu˛’.
Secondly, real-world sentences often contain suffixes (e.g.
’Kovo 11-a˛ja˛’ 7! ’Kovo vienuolikta˛ja˛’ (March 11th)) that
either offer an unambiguous hint that solves the number
normalization problem or at least provides most of the needed
morphological information, which can be used to correct
prediction mistakes.</p>
        <p>
          In this paper, we describe the number normalization
disambiguation model, which is needed to develop a context
dependant number-to-words system. Sequence-labeling
approach allows us to normalize countable abbreviations and
symbols (next to number) effortlessly, since countable noun
morphological form can be extracted from predicted label
(e.g. ’nuo 5%’ (from 5%) 7! ’nuo penkiu˛ procentu˛’). Our
implementation based on this model is publicly available [
          <xref ref-type="bibr" rid="ref15">15</xref>
          ]
and in the future will be integrated into a full Lithuanian text
normalization system.
        </p>
        <p>Number normalization errors are often directly dependant
on morphological analysis mistakes and we are currently
working on improving both vocabulary-grammar and
disambiguation sides of Lithuanian POS tagging to consequentially
increase number normalization accuracy.</p>
        <p>
          Currently, we use ’word2vec’ [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ] algorithm trained on
relatively small text corpus to produce word embeddings.
Although various improvements have been made in encoding
text semantic information to vectors [
          <xref ref-type="bibr" rid="ref16">16</xref>
          ], [
          <xref ref-type="bibr" rid="ref17">17</xref>
          ] and using more
advanced method and larger corpus would likely improve our
model performance.
        </p>
        <p>Our achieved number normalization accuracy could be
further improved by expanding annotated training data since
a considerable amount of errors are a direct result of data
scarcity. Although, our approach generally lacks semantic and
syntactic language understanding, so performing full syntactic
sentence analysis in the preprocessing stage would be highly
beneficial.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>ACKNOWLEDGMENT</title>
      <p>This research was supported by the project “Semantika 2“
(No. 02.3.1-CPVA-V-527-01-0002). Special gratitude goes to
our colleagues Lina Majauskaite˙ and Dovile˙ Stukaite˙ who
helped us in collecting and annotating text corpus.</p>
    </sec>
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