﻿E-Assessment using Latent Semantic Analysis in the Computer Science 
Domain: A Pilot Study 
Pete Thomas, Debra Haley, Anne deRoeck, Marian Petre 
Computing Research Centre, Department of Computing 
The Open University, Walton Hall, Milton Keynes, UK MK7 6AA 
P.G.Thomas;D.T.Haley;A.Deroeck;M.Petre [at] open.ac.uk 
 
Abstract 
Latent Semantic Analysis (LSA)  is a statistical 
Natural Language Processing (NLP) technique for 
inferring meaning from a text. Existing LSA-based 
applications focus on formative assessment in 
general domains. The suitability of LSA for 
summative assessment in the domain of computer 
science is not well known.  The results from the 
pilot study reported in this paper encourage us to 
pursue further research in the use of LSA in the 
narrow, technical domain of computer science. 
This paper explains the theory behind LSA, 
describes some existing LSA applications, and 
presents some results using LSA for automatic 
marking of short essays for a graduate class in 
architectures of computing systems.  
1 Introduction 
This paper describes a pilot study undertaken to 
investigate the feasibility of using Latent Semantic 
Analysis (LSA) for automatic marking of short 
essays in the domain of computer science. These 
short essays are free-form answers to exam 
questions - not multiple choice questions (MCQ). 
Exams in the form of MCQs, although easy to 
mark, do not provide the opportunity for deeper 
assessment made possible with essays.  
This study employs LSA in several areas that are 
under-researched. First, it uses very small corpora 
– less than 2,000 words compared to  about 11 
million words in one of the existing, successful 
applications (Wade-Stein & Kintsch, 2003). 
Second, it involves the specific, technical domain 
of computer science. LSA research usually 
involves more heterogeneous text with a broad 
vocabulary. Finally, it focuses on summative 
assessment where the accuracy of results is 
paramount. Most LSA research has involved 
formative assessment for which more general 
evaluations are sufficient. 
The study investigates one of the shortcomings 
of LSA mentioned by Manning and Schütze (1999, 
p. 564). They report that LSA has high recall but 
low precision. The precision declines because of 
spurious co-occurrences. They claim that LSA 
does better on heterogeneous text with a broad 
vocabulary.  Computer science is a technical 
domain with a more homogeneous vocabulary, 
which results, possibly, in fewer spurious co-
occurrences. A major question of this research is 
how LSA will behave when the technique is 
stretched by applying it to a narrow domain.  
Section 2 gives the history of LSA and explains 
how it works. Section 3 describes several existing 
LSA applications related to e-assessment. Section 
4 provides the motivation for more LSA research 
and reports on a pilot study undertaken to assess 
the feasibility of using LSA for automatic marking 
of short essays in the domain of computer science. 
Section 5 lists several open issues and areas for 
improvement that future studies will address. 
Finally, Section 6 summarises the paper. 
2 What is Latent Semantic Analysis? 
 “Latent Semantic Analysis is a theory and 
method for extracting and representing the 
contextual-usage meaning of words by statistical 
computations applied to a large corpus of text” 
(Landauer, Foltz & Laham, 1998). It is a 
statistical-based natural language processing (NLP) 
method for inferring meaning from a text
1
. It was 
developed by researchers at Bellcore as an 
information retrieval technique (Deerwester, 
Dumais, Furnas, Landauer & Harshman, 1990) in 
the late 1980s. The earliest application of LSA was 
Latent Semantic Indexing (LSI) (Furnas, et al., 
1988; Deerwester, et al., 1990). LSI provided an 
advantage over keyword-based methods in that it 
could induce associative meanings of the query 
(Foltz, 1996) rather than relying on exact matches.  
Landauer and Dumais (1997) promoted LSA as 
a model for the human acquisition of knowledge. 
They developed their theory after creating an 
information retrieval tool and observing 
unexpected results from its use. They claimed that 
                                                      
1
 The researchers originally used the term LSI (Latent 
Semantic Indexing) to refer to the method. The 
information retrieval community continues to use the 
term LSI. 
LSA solves Plato’s problem, that is, how do people 
learn so much when presented with so little? Their 
answer is the inductive process: LSA “induces 
global knowledge indirectly from local co-
occurrence data in a large body of representative 
text” (Landauer & Dumais, 1997).  
From the original application for retrieving 
information, the applications of LSA have evolved 
to systems that more fully exploit its ability to 
extract and represent meaning. Recent applications 
based on LSA compare a sample text with a pre-
existing, very large corpus to judge the meaning of 
the sample.  
To use LSA, researchers amass a suitable corpus 
of text. They create a term-by-document matrix 
where the columns are documents and the rows are 
terms (Deerwester, et al., 1990). A term is a 
subdivision of a document; it can be a word, 
phrase, or some other unit. A document can be a 
sentence, a paragraph, a textbook, or some other 
unit. In other words, documents contain terms. The 
elements of the matrix are weighted word counts of 
how many times each term appears in each 
document. More formally, each element, a
ij
 in an i 
x j matrix is the weighted count of term i in 
document j. 
LSA decomposes the matrix into three matrices 
using Singular Value Decomposition (SVD), a 
well-known technique (Miller, 2003) that is the 
general case of factor analysis. Deerwester et. al., 
(1990) describe the process as follows.  
 
Let t = the number of terms, or rows 
      d =  the number of documents, or columns 
      X = a t by d matrix 
 
Then, after applying SVD, X = TSD, where 
 
m = the number of dimensions, m <= min(t,d) 
T =  a t by m matrix 
S = an m by m diagonal matrix, i.e., only 
diagonal entries have non-zero values 
D =  an m by d matrix 
 
LSA reduces S, the diagonal matrix created by 
SVD, to an appropriate number of dimensions k, 
where k << m, resulting in S'. The product of TS'D 
is the least-squares best fit to X, the original matrix 
(Deerwester, et al., 1990).  
The literature often describes LSA as analyzing 
co-occurring terms. Landauer and Dumais (1997) 
argue it does more and explain that the new matrix 
captures the “latent transitivity relations” among 
the terms. Terms not appearing in an original 
document are represented in the new matrix as if 
they actually were in the original document 
(Landauer & Dumais, 1997). LSA’s ability to 
induce transitive meanings is considered especially 
important given that Furnas et. al. (1982) report 
fewer than 20% of paired individuals will use the 
same term to refer to the same common concept.  
LSA exploits what can be named the transitive 
property of semantic relationships: If A→B and 
B→C, then A→C (where → stands for is 
semantically related to). However, the similarity to 
the transitive property of equality is not perfect. 
Two words widely separated in the transitivity 
chain can have a weaker relationship than closer 
words. For example, LSA might find that copy → 
duplicate → double → twin → sibling. Copy and 
duplicate are much closer semantically than copy 
and sibling. 
Finding the correct number of dimensions for the 
new matrix created by SVD is critical; if it is too 
small, the structure of the data is not captured. 
Conversely, if it is too large, sampling error and 
unimportant details remain, e.g., grammatical 
variants (Deerwester, et al., 1990; Miller, 2003; 
Wade-Stein & Kintsch, 2003). Empirical work 
involving very large corpora shows the correct 
number of dimensions to be about 300 (Landauer 
& Dumais, 1997; Wade-Stein & Kintsch, 2003).  
Creating the matrices using SVD and reducing 
the number of dimensions, often referred to as 
training the system, requires a lot of computing 
power; it can take hours or days to complete the 
processing (Miller, 2003). Fortunately, once the 
training is complete, it takes just seconds for LSA 
to evaluate a text sample (Miller, 2003).  
3 Using LSA for assessment 
3.1 Types of assessment 
Electronic feedback, or e-assessment, is an 
important component of e-learning. LSA, with its 
ability to provide immediate, accurate, 
personalised, and content-based feedback, can be 
an important component of an e-learning 
environment.  
Formative assessment provides direction, focus, 
and guidance concurrent with the learner engaging 
in some learning process. E-assessment can 
provide ample help to a learner without requiring 
added work by a human tutor. A learner can 
benefit from private, immediate, and convenient 
feedback.  
Summative assessment, on the other hand, 
happens at the conclusion of a learning episode or 
activity. It evaluates a learner’s achievement and 
communicates that achievement to interested 
parties. Summative assessment using LSA shares 
the virtues of formative assessment and can 
produce more objective grading results than those 
that can occur when many markers are assessing 
hundreds of student essays.  
The applications described in the next section 
use LSA to provide formative  assessment. Section 
4 discusses a pilot study that focuses on summative 
assessment. 
3.2 Existing applications 
Much work is being done in the area of using 
LSA to mark essays automatically and to provide 
content-based feedback. One of the great 
advantages of automatic assessment of essays is its 
ability to provide helpful, immediate feedback to 
the learner without burdening the teacher. This 
application is particularly suited to distance 
education, where opportunities for one-on-one 
tutoring are infrequent or non-existent (Steinhart, 
2001). Existing systems include Apex (Lemaire & 
Dessus, 2001), Autotutor (Wiemer-Hastings, 
Wiemer-Hastings & Graesser, 1999), Intelligent 
Essay Assessor (Foltz, Laham & Landauer, 1999), 
Select-a-Kibitzer (Miller, 2003), and Summary 
Street (Steinhart, 2001; Wade-Stein & Kintsch, 
2003). They differ in details of audience addressed, 
subject domain, and advanced training required by 
the system (Miller, 2003). They are similar in that 
they are LSA-based, web-based, and provide 
scaffolding, feedback, and unlimited practice 
opportunities without increasing a teacher’s 
workload (Steinhart, 2001). All of them claim that 
LSA correlates as well to human markers as human 
markers correlate to one another. See (Miller, 
2003) for an excellent analysis of these systems. 
4 E-Assessment pilot study  
Although research using Latent Semantic 
Analysis (LSA) to assess essays automatically has 
shown promising results (Chung & O'Neil, 1997; 
Foltz, et al., 1999; Foltz, 1996; Lemaire & Dessus, 
2001; Landauer, et al., 1998; Miller, 2003; 
Steinhart, 2001; Wade-Stein & Kintsch, 2003), not 
enough research has been done on using LSA for 
instructional software (Lemaire & Dessus, 2001). 
Previous studies involved both young students and 
university-age students, and several different 
knowledge domains. An open question is how LSA 
can be used to improve the learning of university-
age, computer science students. This section offers 
three characteristics that distinguish this research 
from existing research involving the use of LSA to 
analyse expository writing texts and reports on a 
pilot study to determine the feasibility of using 
LSA to mark students’ short essay answers to 
exam questions. 
4.1 Focuses of the experiment 
This subsection describes three facets of the 
experiment that involve under-researched areas, in 
the cases of the domain and the type of assessment, 
and an unsolved research question in the case of 
the appropriate dimension reduction value for 
small corpora. 
The study involves essays written by computer 
science (CS) students. CS, being a technical 
domain, has a limited, specialist vocabulary. Thus, 
essays written for CS exams are thought to have a 
more restricted terminology than do the expository 
writing texts usually analysed by LSA researchers. 
Nevertheless, the essays are written in English 
using a mixture of technical terms and general 
terms. Will LSA produce valid results?  
Accuracy is paramount in summative 
assessment. Whereas formative assessment can be 
general and informative, summative assessment 
requires a high degree of precision. Can LSA 
produce results with a high degree of correlation 
with human markers? 
The consensus among LSA researchers, who 
customarily use very large corpora, is that the 
number of dimensions that produces the best result 
is about 300. But because this study involved  just 
17 graded samples, the number of reduced 
dimensions has to be less than 17. Can LSA work 
with many fewer dimensions than 300? A broader 
question is whether LSA can work with a small 
corpus in a restricted domain. 
4.2 The Data 
The data for this experiment consisted of 
answers from six students to three questions in a 
single electronic exam held at the Open University 
in April 2002. The answers are free-form short 
essays. The training corpus for each question 
comprised 16 documents consisting of student 
answers to the same question and a specimen 
solution. Table 1 gives the average size (in words) 
of both the student answers graded by LSA and the 
corpus essays. 
 
  
Question 
A 
Question 
B 
Question 
C 
Corpus 
documents 112 35 131 
Student 
answers 108 31 88 
Table 1: Average document size 
 
The corpus training documents had been marked 
previously by three trained human markers. The 
average marks were assigned to each corpus 
document. To provide a standard on which to 
judge the LSA results, each of the answers from 
the six students was marked by three human 
markers and awarded the average mark. 
4.3 The LSA Method 
The following steps were taken three times, once 
for each question on the exam.  
• Determine the words, or terms, in the corpus 
documents after removing punctuation and 
stop words. (No attempt has yet been made 
to deal with synonyms or word forms, such 
as plurals, via stemming.) 
• Construct a t x d term frequency matrix M, 
where t is the number of terms  in the corpus 
and d is the number of documents – 17 in 
this experiment. Each entry tf
ij 
is the number 
of times term i appears in document j. 
• Weight each entry tf
ij 
in M using the simple 
weighting scheme: 1 + log(tf
ij
). 
• Perform singular value decomposition of the 
weighted term frequency matrix resulting in 
M
weighted
 = TSD
T
. 
• Choose an optimum dimension, k, to reduce 
M
weighted. 
 (see the next subsection for details) 
• Compute B = SD
T
 - the reduced weighted 
frequency document 
• Construct a vector, a, of weighted term 
frequencies in a student-answer document. 
• Compute the reduced student-answer vector 
a' = aTS
T
 
• Determine the corpus document that best 
matches the student-answer by comparing a' 
with the column vectors in B. 
• Award the student-answer the mark 
associated with the most similar corpus 
document using the cosine similarity 
measure. 
4.4 Determining the optimum dimension 
reduction (k) 
• This experiment reduced the SVD matrices 
using k = 2 .. number of corpus documents – 
1, or k = 2 .. 16. For each value of k, the 
LSA method produced a mark for each 
student-answer. 
• The experiment compared the six LSA 
marks for the student-answers with the 
corresponding average human mark using 
Euclidean distance. 
• The experiment revealed that, for this 
corpus, k = about 10 gave the best matches 
across the three questions. 
 
4.5 Results 
The four graphs below show the results obtained. 
Question A
0
1
2
3
4
5
6
7
123456
Student
Po
i
n
t
s
 A
w
a
r
d
e
d
Graded by Human
Graded by LSA
 
Figure 1: LSA marks for question A 
Question B
0
1
2
3
4
5
6
7
123456
Student
Poi
n
t
s
 Aw
ar
ded
Graded by Human
Graded by LSA
 
Figure 2: LSA marks for question B 
Question C
0
1
2
3
4
5
6
7
8
123456
Student
P
o
in
t
s
 A
w
a
r
d
e
d
Graded by Human
Graded by LSA
 
Figure 3: LSA marks for question C 
Total
0
2
4
6
8
10
12
14
16
123456
Student
Po
i
n
t
s
 A
w
ar
d
e
d
Graded by Human
Graded by LSA
 
Figure 4: LSA marks for total 
4.6 Discussion  
This experiment investigated the feasibility of 
using LSA to assess short essay answers. The 
results shown in Figures 1 – 3 suggest that LSA-
marked answers were similar to human-marked 
answers in 83% (15 of 18) of the answers tested.  
LSA seemed to work well on five of the six 
student-answers for Question A, all the answers for 
Question B, and four of the six answers for 
Question C. For the three clearly incorrect 
answers, LSA gave a higher score than did the 
human markers for the answer to question A and 
one higher mark and one lower mark than did the 
human markers for the answers to question C.   
To quantify these visual impressions, the study 
used the Spearman’s rho statistical test for each of 
the three questions. Only one of the three questions 
shows a statistical correlation between LSA and 
human marks: question B shows a statistical 
correlation significant at the 95% level.   
These results, while unacceptable for a real-
world application, are encouraging given the 
extremely small corpus size of only 17 documents, 
or about 2,000 words for questions A and C and 
about 600 words for question B. This pilot study 
solidified our understanding of how to use LSA, 
the importance of a large corpus, and how to 
approach further research to improve the results 
and increase the applicability of the results of this 
pilot study. 
5 A roadmap for further research 
5.1 The corpus 
LSA results depend on both corpus size and 
corpus content.  
5.1.1 Corpus size 
Existing LSA research stresses the need for a 
large corpus. The corpora for the pilot study 
described in this paper were very small. In 
addition, the documents are too few in number to 
be  representative of the student population. An 
ideal corpus would provide documents that give a 
spread of marks across the mark range and a 
variety of answers for each mark. Future studies 
will use a larger corpus. 
5.1.2 Corpus content 
Wiemer-Hastings, et. al (1999) report that size is 
not the only important characteristic of the corpus. 
Not surprisingly, the composition of the corpus 
effects the results of essay grading by LSA. In 
addition to specific documents directly related to 
their essay questions, Wiemer-Hastings, et. al used 
more general documents. They found the best 
composition to be about 40% general documents 
and 60% specific documents. 
The corpora used for this pilot study comprised 
only specific documents - the human marked short 
essays. Future work will involve adding sections of 
text books to enlarge and enrich the corpus with 
more general documents.   
5.2 Weighting function 
The pilot study used local weighting - the most 
basic form of term weighting. Local weighting is 
defined as tf
ij
 (the number of times term i is found 
in document j) dampened by the log function: local 
weighting = 1 + log (tf
ij
 ). This dampening reflects 
the fact that a term that appears in a document x 
times more frequently than another term is not x 
times more important.  
The study selected this simple weighting 
function  to provide a basis on which to compare 
more sophisticated functions in future work. Many 
variations of weighting functions exist; two are 
described next. 
5.2.1 Log-entropy 
Dumais (1991) recommended using log-entropy 
weighting, which is local weighting times global 
weighting. Global weighting is defined as 1 – the 
entropy or noise. Global weighting attempts to 
quantify the fact that a term appearing in many 
documents is less important than a term appearing 
in fewer documents. 
 
The log-entropy term weight for term i in doc j =  
()
()
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
∗
−∗+
∑
numdocs
gf
tf
gf
tf
tf
i
ij
i
ij
ij
log
log
11log  
where  
ij
tf  – term frequency – the frequency of term i in 
document j 
i
gf  – global frequency – the total number of 
times term i occurs in the whole collection 
5.2.2 tfidf 
Sebastiani (2002) claims the most common 
weighting is tfidf, or term frequency inverse 
document frequency. 
 
( )
jk
dttfidf ,  = ()
()
k
jk
tTr
Tr
dt
#
log,# ∗  
where #( t
k
, d
j
 ) denotes the number of times t
k
 
occurs in d
j
#Tr(t
k
) denotes the document frequency of term t
k
, 
that is, the number of documents in Tr in which t
k
 
occurs. 
 
Future studies will examine the effects of 
applying various term weighting functions. 
5.3 Similarity measures 
The pilot study used two different similarity 
measures. It used the cosine measure to compare 
the test document with the corpus documents. It 
used Euclidean distance to choose k, the number of 
reduced dimensions that produced the best results 
overall. Other measures exist and will be tried in 
future studies. 
Ljungstrand and Johansson (1998) define the 
following similarity measures: 
Inner product (dot) measure: 
M( X, Y ) =  
∑
=
n
i
ii
yx
1
Cosine measure: 
M( X, Y ) = 
∑∑
∑
==
=
n
i
i
n
i
i
n
i
ii
yx
yx
11
1
 
Manhattan distance measure: 
M( X, Y ) = 
∑
=
−
n
i
ii
yx
1
 
Euclidean distance measure (2-norm): 
M( X, Y ) = ()
∑
=
−
n
i
ii
yx
1
2
 
m-norm measure: 
M( X, Y ) = ()
m
n
i
m
ii
yx
1
1
⎟
⎠
⎞
⎜
⎝
⎛
∑ −
=
,  m ∈ N 
Where X = (x
1
,x
2
,...,x
n
) and Y = (y
1
,y
2
,...,y
n
) are two 
n-dimensional vectors. 
Figure 5. Similarity Measures 
5.4 Corpus pre-processing 
Removing stop words is one type of pre-
processing performed for this study. Explicitly 
adding synonym knowledge and stemming are two 
additional ways of preparing the corpus that future 
research will consider. Stemming involves 
conflating word forms to a common string, e.g., 
write, writing, writes, written, writer would be 
represented in the corpus as writ.  
5.5 Dimension reduction 
Choosing the appropriate dimension, k, for 
reducing the matrices in LSA is a well known open 
issue. The current consensus is that k should be 
about 300. No theory yet exists to suggest the 
appropriate value for k. Currently, researchers 
determine k by  empirically testing various values 
of k and selecting the best one. The only heuristic 
says that k << min(terms, documents). An 
interesting result from the study reported in this 
paper is that even though k had to be less than 17, 
the number of documents in our corpora and thus 
much less than the recommended value of 300, 
LSA produced statistically significant results for 
one of the three questions tested.  
Future studies will continue to investigate the 
relationship among k, the size of the corpus, the 
number of documents in the corpus, and the type of 
documents in the corpus. 
6 Summary 
This paper introduced and explained LSA and 
how it can be used to provide e-assessment by both 
formative and summative assessment. It provided 
examples of existing research that uses LSA for e-
assessment. It reported the results of a pilot study 
to determine the feasibility of using LSA to assess 
automatically essays written in the domain of 
computer science. Although just one of the three 
essay questions tested showed that LSA marks 
were statistically correlated to the average of three 
human marks, the results are promising because 
the experiment used very small corpora. 
Future studies will attempt to improve the results 
of LSA by increasing the size of the corpora, 
improving the content of the corpora, 
experimenting with different weighting functions 
and similarity measures, pre-processing the corpus, 
and using various values of k for dimension 
reduction. 
7 Acknowledgements 
The work reported in this study was partially supported by 
the European Community under the Innovation Society 
Technologies (IST) programme of the 6th Framework 
Programme for RTD - project ELeGI, contract IST-002205. 
This document does not represent the opinion of the European 
Community, and the European Community is not responsible 
for any use that might be made of data appearing therein. 

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