A Statistical Model for Domain-Independent Text Segmentation
Masao Utiyama and Hitoshi Isahara
Communications Research Laboratory
2-2-2 Hikaridai Seika-cho, Soraku-gun,Kyoto, 619-0289 Japanmutiyama@crl.go.jp and isahara@crl.go.jp

Abstract
We propose a statistical method thatfinds the maximum-probability segmentation of a given text. This method
does not require training data because
it estimates probabilities from the given
text. Therefore, it can be applied to
any text in any domain. An experiment showed that the method is moreaccurate than or at least as accurate asa state-of-the-art text segmentation system.

1

Introduction

Documents usually include various topics. Identifying and isolating topics by dividing documents,
which is called text segmentation, is importantfor many natural language processing tasks, including information retrieval (Hearst and Plaunt,
1993; Salton et al., 1996) and summarization(Kan et al., 1998; Nakao, 2000). In information retrieval, users are often interested in particular topics (parts) of retrieved documents, instead of the documents themselves. To meet suchneeds, documents should be segmented into coherent topics. Summarization is often used for along document that includes multiple topics. A
summary of such a document can be composedof summaries of the component topics. Identification of topics is the task of text segmentation.
A lot of research has been done on text segmentation (Kozima, 1993; Hearst, 1994; Okumura and Honda, 1994; Salton et al., 1996; Yaari,
1997; Kan et al., 1998; Choi, 2000; Nakao, 2000).

A major characteristic of the methods used in thisresearch is that they do not require training data
to segment given texts. Hearst (1994), for example, used only the similarity of word distributions
in a given text to segment the text. Consequently,
these methods can be applied to any text in any
domain, even if training data do not exist. This
property is important when text segmentation isapplied to information retrieval or summarization,
because both tasks deal with domain-independent
documents.
Another application of text segmentation is
the segmentation of a continuous broadcast news
story into individual stories (Allan et al., 1998).
In this application, systems relying on supervised
learning (Yamron et al., 1998; Beeferman et al.,1999) achieve good performance because there
are plenty of training data in the domain. Thesesystems, however, can not be applied to domains
for which no training data exist.
The text segmentation algorithm described inthis paper is intended to be applied to the summarization of documents or speeches. Therefore,
it should be able to handle domain-independent
texts. The algorithm thus does not use any training data. It requires only the given documents forsegmentation. It can, however, incorporate training data when they are available, as discussed in
Section 5.
The algorithm selects the optimum segmentation in terms of the probability defined by astatistical model. This is a new approach fordomain-independent text segmentation. Previous
approaches usually used lexical cohesion to segment texts into topics. Kozima (1993), for exam-

7%89: !    1<;   11
1"   ple, used cohesion based on the spreading activation on a semantic network. Hearst (1994) used
the similarity of word distributions as measured
by the cosine to gauge cohesion. Reynar (1994)
used word repetition as a measure of cohesion.
Choi (2000) used the rank of the cosine, rather
than the cosine itself, to measure the similarity ofsentences.
The statistical model for the algorithm is described in Section 2, and the algorithm for obtaining the maximum-probability segmentation is
described in Section 3. Experimental results arepresented in Section 4. Further discussion and ourconclusions are given in Sections 5 and 6, respectively.

then
and
hold.
This means thatandcorrespond to eachother.
Under our assumptions,can be decomposed as follows:

different word distributions. We further assume
that different topics are statistically independentof each other. We also assume that the words
within the scope of a topic are statistically independent of each other given the topic.
Let
be the number of words in segment ,and letbe the -th word in . If we defineasdescribe the algorithm for finding the maximumprobability segmentation.

    =  0"   9       " 1   1<;   " 1   1 
1<; >5    ? 21   1  (3)1<; 2 ;
0? 21   1  as:
Next, we define
2 Statistical Model for Text
Segmentation? 21   1  @BA 1 C  1 21 DFDFG E .
(4)
We first define the probability of a segmentationof a given text in this section. In the next section,
? 21  is the1
where
number of words in 1 thatA
1
we then describe the algorithm for selecting theG
are the same as 2 and is the number of different
most likely segmentation.
7%8&: , where  be a text consisting of words
in . For example, if
Let
8
)
I

K
H
&
J
K
H
!
J
H
:

M

&
L
&
L
&
L
O
N
&HOIP , words, and let         be a segmen- &"J&QSR >and"L0TSU >"NOQL&L V, thenA
E , and GWYX .
, A
, A
A
tation of
consisting of  segments. Then the
Equation (4) is known as Laplace’s law (Manningprobability of the segmentation  is defined by:
? 21  can1999).
       " !   (1) andA 1 Schütze,
be defined as:
1A C 21  @%Z ? 21   1  1  651  (5)The most likely segmentation  # is given by:# %$&')(*, $&+ "   -!  ". (2) for Z ? 1  1  1  C 1 [@ 65 ? 1 . 1 ".
  65 ^] \ 2 (6)
2



/

"


\;
becauseis a constant for a given text .




"




0



The definitions of  and  are
1 and  21 are the
C \1 ." 21 _`1 E when\
where ]
given below, in that order.
C \ ." 21 acb otherwise. For
same word and ]




"


Z "H  J&HKJ!HKd ] "J&.eHO9D ] "HK.HK"D ] J!. HK"D
2.1 Definition of
example,"HK.HKfbgDFEgDWbhDiE%R .
We define a topic by the distribution of words in]that topic. We assume that different topics have
Equations (5) and (6) are used in Section 3 to 1 12

1
1 4 1  1  651 .
3

      can vary depending on
The definition of 1 1 our prior information about the possibility of segmentation  . For example, we might know theaverage length of the segments and want to incor0   .
porate it into
2.2 Definition ofOur assumption, however, is that we do nothave such prior information. Thus, we have to
use some uninformative prior probability.
We defineas  
0   @ [j (7)Equation (7) is determined on the basis of its de 
scription length, k  ; i.e.,0   fR jmlon , p
(8)

q


'
where k 
sr t  bits. This description
1

2

length is derived as follows:uSuppose that there are two people, a sender anda receiver, both of whom know the text to be segmented. Only the sender knows the exact segmentation, and he/she should send a message sothat the receiver can segment the text correctly.
To this end, it is sufficient for the sender to send
integers, i.e.,, because these
integers represent the lengths of segments andthus uniquely determine the segmentation once
the text is known.

v

vxwzy{v |zyz}z}~}zyCv-
5 v5

!v v

A segment length can be encoded using
bits, because
is a number between 1 and .
The total description length for all the segmentbits.3lengths is thusu !v

   to obtain # , because# %$&')(*, $&+ "   -!  f$!')(*,        can be decomposed as follows: (10)    r t '>5"   -!       r t '0C 21   1  r t '  
1<; 2 >5;     r t ' A 1 C 1 21 DWDWG E D Mr t ' 
1<; 2 ;   L&? 1  1   >51   .G^". (11)1<;

and we then minimize

where&L ? 1  1 >5  >51   .G^@  r t ' 1 ? 1 1 DiDFG E D r t ' 
2; A 2(12)

We further rewrite Equation (12) in the formof Equation (13) below by using Equation (5)and replacingwith, whereis the length of words, i.e.,the numberof word tokens in words. Equation (13) is used todescribe our algorithm in Section 3.1:

1  1   >51 
C



1






Generally speaking, takes a large value  9 6z6 
when the number of segments is small. On the     takes a large value when theother hand,    isnumber of segments is large. If onlyused to segment the text, then the resulting segmentation will have too many segments. By using
L&? 1  1 5  5 651   5 . G^


0









 and   , we can get a reasonboth
5p

n



w
"
|



able number of segments.
   r t ' Z C C1  1  1  1 1   >51 >51 DFDFG E22;
3 Algorithm for Finding theD'
Maximum-Probability Segmentation
(13)
rt 
To find the maximum-probability segmentation
Algorithm# , we first define the cost of segmentation  as 3.1
This section describes an algorithm for finding the   @f r t '    !  ". (9) minimum-cost
segmentation. First, we define theterms and symbols used to describe the algorithm.
Y  consisting ofGiven a text words,
we define  1 as the position between 1 | !v <<^and 1< , so that e is just before
and  isu ! v
just after .
¢¡C£¤.¦¥¨§ , where £u !v
Next, we define a graph¥£ isis a set of nodes andis a set of edges.
| !v

defined as£©%ª  1  b«F¬h« [­(14)
1
Stolcke and Omohundro uses description length priors
to induce the structure of hidden Markov models (Stolcke
and Omohundro, 1994).
2‘Log’ denotes the logarithm to the base 2.
3
We have usedasbefore. But we use
in this paper, because it is easily interpreted as a
description length and the experimental results obtained byusing
are slightly better than those obtained by us. An anonymous reviewer suggests using a Poising
son distribution whose parameter is , the average lengthof a segment (in words), as prior probability. We leave it
for future work to compare the suitability of various priorprobabilities for text segmentation.

¥ is defined as
between words are candidates for segment boundhowever, to modify the algorithm¥®%ª>¯ 1 2  b°«4¬²± 3 « d­ . (15) soaries.thatIttheis easy,
text can only be segmented at particular positions, such as the ends of sentences or¥where the edges are ordered; the initial vertex andparagraphs. This is done by using a subset of
¯
1
1
2
2
the terminal vertex ofare  and  , respecin Equation (15). We use only the edges whose
tively. An example of is shown in Figure 1.
initial and terminal vertices are candidate bound¯ 1<   1< ¤  2 . aries
We say that 1 2 covers
that meet particular conditions, such as be¯This means that 1 2 represents a segment
ing
theof sentences or paragraphs. We then
 1<   1C ¤  2 . Thus, we define the cost L 1 2 of obtain theendsminimum-cost
path by doing Steps 1¯
edge 1 2 by using Equation (13):and 2. The minimum-cost segmentation thus obL 1 2 %L0? 1< < 1< ¤  2   .G^". (16) tained meets the boundary conditions. In this paper, we assume that the segment boundaries are atG
the ends of sentences.
where is the number of different words in .
andGiven these definitions, we describe the algorithm to find the minimum-cost segmentation or
maximum-probability segmentation as follows:¬²± 3 « L 12

¯ 1 2 b¨«of edgefor
Step 1. Calculate the costby using Equation (16).



Step 2. Find the minimum-cost path from.

  toAlgorithms for finding the minimum-cost path ina graph are well known. An algorithm that can
provide a solution for Step 2 will be a simpler version of the algorithm used to find the maximumprobability solution in Japanese morphologicalanalysis (Nagata, 1994). Therefore, a solution canbe obtained by applying a dynamic programming(DP) algorithm.4 DP algorithms have also beenused for text segmentation by other researchers(Ponte and Croft, 1997; Heinonen, 1998).
The path thus obtained represents thewhen edges
minimum-cost segmentation incorrespond with segments. In Figure 1, forexample, if
is the minimum-cost path,thenis the minimum-cost
segmentation.
The algorithm automatically determines thenumber of segments. But the number of segments
can also be specified explicitly by specifying thenumber of edges in the minimum-cost path.
The algorithm allows the text to be segmented
anywhere between words; i.e., all the positions¯ &¯¦?³´¯³"µ¶ ¨?· ¶ ¸ ³9· ¶ ¹¸µ9·

4
A program that implements the algorithm described inthis section is available at http://www.crl.go.jp/jt/a132/members/mutiyama/softwares.html.

3.2 Properties of the segmentation
Generally speaking, the number of segments obtained by our algorithm is not sensitive to thelength of a given text, which is counted in words.
In other words, the number of segments is relatively stable with respect to variation in the text
length. For example, the algorithm divides anewspaper editorial consisting of about 27 sentences into 4 to 6 segments, while on the other
hand, it divides a long text consisting of over 1000
sentences into 10 to 20 segments. Thus, the number of segments is not proportional to text length.
This is due to the termin Equation (11).
The value of this term increases as the number ofwords increases. The term thus suppresses the division of a text when the length of the text is long.
This stability is desirable for summarization,
because summarizing a given text requires selecting a relatively small number of topics from it.
If a text segmentation system divides a given text
into a relatively small number of segments, thena summary of the original text can be composedby combining summaries of the component segments (Kan et al., 1998; Nakao, 2000). A finer
segmentation can be obtained by applying ouralgorithm recursively to each segment, if necessary.5

Mr t ' 

5

We segmented various texts without rigorous evaluationand found that our method is good at segmenting a text into a
relatively small number of segments. On the other hand, themethod is not good at segmenting a text into a large number of segments. For example, the method is good at segmenting a 1000-sentence text into 10 segments. In such acase, the segment boundaries seem to correspond well with
topic boundaries. But, if the method is forced to segment
the same text into 50 segments by specifying the number of

e14
e01
g0

e35

e13

w1

g1

w2

g2

e45
w3

g3

w4

g4

w5

g5

Figure 1: Example of a graph.

4

Experiments

racy.

4.1

Material

4.2 Experimental procedure and results

We used publicly available data to evaluate oursystem. This data was used by Choi (2000) tocompare various domain-independent text seg(Choi,
mentation systems.6 He evaluated2000), TextTiling (Hearst, 1994), DotPlot (Reynar, 1998), and Segmenter (Kan et al., 1998) byusing the data and reported that
achieved thebest performance among these systems.
The data description is as follows: “An artificial test corpus of 700 samples is used to assess
the accuracy and speed performance of segmentation algorithms. A sample is a concatenation often text segments. A segment is the first sentences of a randomly selected document from theBrown corpus. A sample is characterised by therange .” (Choi, 2000) Table 1 gives the corpus
statistics.

º>º

º´º





v »¼*½!½ »¼¿¾ À¼¿Á Â¼Q½!½

Range of# samples

400

100

100

100

The sample texts were preprocessed – i.e., punctuation and stop words were removed and the remaining words were stemmed – by a program using the libraries available in Choi’s package. The
texts were then segmented by the systems listed
in Tables 2 and 3. The segmentation boundaries
were placed at the ends of sentences. The segmentations were evaluated by applying an evaluation program in Choi’s package.
The results are listed in Tables 2 and 3.
isthe result for our system when the numbers of segments were determined by the system.
isthe result for our system when the numbers of segand
ments were given beforehand.8
are the corresponding results for the systems described in Choi’s paper (Choi, 2000).9

Í b>b
Í b´b nÎ p
º´º º>º nÎ pÏÒ Ð!Ð »¼¿½!ÑÑ½ » ¼¿Ñ ¾ Ñ À ¼QÑ ÑÁ Â¼*Ñ ½!Ñ ½ Ñ ÑÂ!Â
Table 2: Comparison of Ã \ : the numbers of segprob

Table 1: Test corpus statistics. (Choi, 2000)

Ã \\Ã

edges in the minimum-cost path, then the resulting segmentation often contains very small segments consisting of only
one or two sentences. We found empirically that segments
obtained by recursive segmentation were better than thoseobtained by minimum-cost segmentation when the specified
number of segments was somewhat larger than that of theminimum-cost path, whose number of segments was automatically determined by the algorithm.
6
The data is available fromhttp://www.cs.man.ac.uk/˜choif/software/
C99-1.2-release.tgz.
We usednaacl00Exp/data/ 1,2,3 /
3-11,3-5,6-8,9-11 /*,which is contained in the package, for our experiment.
7Let
be a correct segmentation and let
be a segmentation proposed by a text segmentation system: Then the

Æ Ç9È

ÄÅ Å

13%
18%
4.9E-36%
10%
2.5E-56%
10%
7.5E-8

Total
10%
13%
9.7E-12

ments were determined by the systems.

Segmentation accuracy was measured by theprobabilistic error metricproposed by Beefer7
man, et al. (1999). Low
indicates high accu-

Ä

11%
13%
7.9E-5É/Ê9Ë¦ÌÃ\ÔÕ9?Æ Ç9È yCÉ/Ê!Ë¦Ì9

Ó>Ó

In these tables, the symbol “ ” indicates thatthe difference inbetween the two systems isstatistically significant at the 1% level, based onÖ“numberis the probability that a randomly
chosen pair of words a distance of words apart is inconsistently classified; that is, for one of the segmentations the pairlies in the same segment, while for the other the pair spansa segment boundary” (Beeferman et al., 1999), where ischosen to be half the average reference segment length (inwords).
8
If two segmentations have the same cost, then our systems arbitrarily select one of them; i.e., the systems selectthe segmentation processed previously.
9
The results forin Table 3 are slightly different
from those listed in Table 6 of Choi’s paper (Choi, 2000).
This is because the original results in that paper were basedon 500 samples, while the results in our Table 3 were basedon 700 samples (Choi, personal communication).

Ò Â!Â/×Ø{ÙÖÏÒ Ð!Ð ×ØoÙ »¼Q½!Ñ Ñ½ »¼T¾ À ¼TÑ ÑÁ Â¼¿Ñ ½!Ñ ½ Ñ Ñ
Â!Â/×ØoÙ
Table 3: Comparision of Ã \ : the numbers of segprob

10%12%
2.7E-4

9%
11%
0.080

7%
10%
2.3E-35%9%
1.0E-4

Total
9%
11%
6.8E-9ments were given beforehand.

tilinguality of systems. For English, Klavans, etal. describe a segmentation corpus in which thetexts were segmented by humans (Klavans et al.,1998). But, there are no such corpora for otherlanguages. We are planning to build a segmentation corpus for Japanese, based on a corpus
of speech transcriptions (Maekawa and Koiso,2000).

Úa one-sided -test of the null hypothesis of equalmeans. The probability of the null hypothesis
being true is displayed in the row indicated by“prob”. The column labels, such as “”, indicate that the numbers in the column are the averages ofover the corresponding sample texts.
“Total” indicates the averages ofover all thetext samples.
These tables show statistically that our system
is more accurate than or at least as accurate as. This means that our system is more accurate
than or at least as accurate as previous domainindependent text segmentation systems, because
has been shown to be more accurate than previous domain-independent text segmentation systems.10

PÛU

Ã\

Ã\

5.2 Related work

º´º
º´º

5

Discussion

5.1

Evaluation

Evaluation of the output of text segmentation systems is difficult because the required segmentations depend on the application. In this paper, wehave used an artificial corpus to evaluate our system. We regard this as appropriate for comparing
relative performance among systems.
It is important, however, to assess the performance of systems by using real texts. These
texts should be domain independent. They should
also be multi-lingual if we want to test the mul10

ÏÒ Ð!Ð ÒÏ Ð!Ð&Ï ÜÜ Ð!Ð Ï Ð!Ð&Ü
Â!Â Â!Â
Ï Ð!Ð Ý ½&}»!ÀÒ Â Ý ½&} Þ´ÂÏ Ð!Ð&Â!Üß
Ý ½&}»!àÒ Â!Â ÜßÝ ½&} Þ´¾

Speed performance is not our main concern in this paper. Our implementations ofandare not optimum. However,and, which are implemented inC, run as fast asand, which are implemented inJava (Choi, 2000), due to the difference in programming languages. The average run times for a sample text were
sec.
sec.
sec.
sec.

on a Pentium III 750-MHz PC with 384-MB RAM running
RedHat Linux 6.2.

ä

Our proposed algorithm finds the maximumprobability segmentation of a given text. Thisis a new approach for domain-independent text
segmentation. A probabilistic approach, however,has already been proposed by Yamron, et al. fordomain-dependent text segmentation (broadcast
news story segmentation) (Yamron et al., 1998).
They trained a hidden Markov model (HMM),
whose states correspond to topics. Given a word
sequence, their system assigns each word a topic
so that the maximum-probability topic sequenceis obtained. Their model is basically the same asthat used for HMM part-of-speech (POS) taggers(Manning and Schütze, 1999), if we regard topics
as POS tags.11 Finding topic boundaries is equivalent to finding topic transitions; i.e., a continuous
topic or segment is a sequence of words with thesame topic.
Their approach is indirect compared with ourapproach, which directly finds the maximumprobability segmentation. As a result, their model
can not straightforwardly incorporate features
pertaining to a segment itself, such as the average
length of segments. Our model, on the other hand,
can incorporate this information quite naturally.
Suppose that the length of a segment follows
a normal distribution, with a mean ofand standard deviation of (Ponte and Croft,1997). Then Equation (13) can be augmented toâ  á¤ãä å./åá&L C 1  1  5 651 5   . 5Gm. ä . å^. æç."èé.~ê¤
5p

n






w
|

 æ¿  r t ' Z ? C1  1  1  1 1 C C >51 651 DiDWG E
2
;
Dhè r t ' 2 Dhê r t '  ? 1  1 E  >51  .å . (17)
â 
ä
11

The details are different, though.

æ:DaèëDaê8®E

where. Equation (17) favors segments whose lengths are similar to the average
length (in words).
Another major difference from their algorithm
is that our algorithm does not require training data
to estimate probabilities, while their algorithm
does. Therefore, our algorithm can be applied todomain-independent texts, while their algorithm
is restricted to domains for which training data
are available. It would be interesting, however,to compare our algorithm with their algorithm forthe case when training data are available. In sucha case, our model should be extended to incorporate various features such as the average segment length, clue words, named entities, and soon (Reynar, 1999; Beeferman et al., 1999).
Our proposed algorithm naturally estimates theprobabilities of words in segments. These probabilities, which are called word densities, havebeen used to detect important descriptions ofwords in texts (Kurohashi et al., 1997). Thismethod is based on the assumption that the density of a word is high in a segment in which theword is discussed (defined and/or explained) insome depth. It would be interesting to apply our
method to this application.

6

Conclusion

We have proposed a statistical model for domainindependent text segmentation. This method finds
the maximum-probability segmentation of a given
text. The method has been shown to be moreaccurate than or at least as accurate as previous
methods. We are planning to build a segmentation corpus for Japanese and evaluate our method
against this corpus.

Acknowledgements
We thank Freddy Y. Y. Choi for his text segmentation package.

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