IMPROVING NAIVE BAYESIAN SPAM FILTERING

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1 Master Thesis IMPROVING NAIVE BAYESIAN SPAM FILTERING Jon Kågström Mid Sweden University Deartment for Information Technology and Media Sring 005

2 Abstract Sam or unsolicited has become a major roblem for comanies and rivate users. This thesis exlores the roblems associated with sam and some different aroaches attemting to deal with it. The most aealing methods are those that are easy to maintain and rove to have a satisfactory erformance. Statistical classifiers are such a grou of methods as their ability to filter sam is based uon the revious knowledge gathered through collected and classified s. A learning algorithm which uses the Naive Bayesian classifier has shown romising results in searating sam from legitimate mail. Tokenization, robability estimation and feature selection are rocesses erformed rior to classification and all have a significant influence uon the erformance of sam filtering. The main objective of this work is to examine and emirically test the currently known techniques used for each of these rocesses and to investigate the ossibilities for imroving the classifier erformance. Firstly, how a filter and wraer aroach can be used to find tokenization delimiter subsets that imrove classification is shown. After this, seven robability estimators are tested and comared in order to demonstrate which of them ameliorate the erformance. Finally a survey of commonly used methods for the feature selection rocess is erformed and recommendations for their use are resented. ii

3 Acknowledgments I would like to thank my suervisor Iskra Poova for guiding me in how to write a thesis. She has heled me to imrove the structure and ointed out where the content needed enrichment. For me it has been a learning rocess. I also want to thank everyone who makes an effort to fight sam, and there are a lot of you! iii

4 Glossary classifier A erson or machine that is sorting out the constituents of a substance. clique A maximum comlete subgrah of a grah. comlete grah All vertices are connected with each other. corus A collection of natural language text used for accumulating statistics. More secifically in this thesis a corus is a ma between a word (token) and its frequency. degrees of freedom Describe the number of values that are free to vary in a statistical calculation. delimiter A character that marks the beginning or end of a unit of data. entroy A measure of the disorder that exists in a system. feature A rominent art or characteristic. inducer An inducer is a machine learning algorithm that roduces a classifier that, in turn, assigns a class to each instance. misclassification An acctual sam classified as good, or an acctual good classified as sam. monotonicity The function f is monotone if, whenever x y, then f ( x) f ( y). Stated differently, a monotone function is one that reserves the order. mutually exclusive Describing two events, conditions, or variables which cannot occur at once. n-gram n features are considered at a time. null hyothesis Predicts that two distributions are the same. robability distribution A list of the robabilities associated with each of its values. Throughout this work discreet robability distributions are used and they are non-continuous. The robability mass function is denoted by x ) where x i is a random discrete variable. samle sace The set of all ossible outcomes of an exeriment. significance level Is the decision criterion for acceting or rejecting the null hyothesis. sace Character used to searate words. sam Unsolicited usually commercial sent to a large number of addresses. token A distinguishing characteristic (feature). transitivity In mathematics, a binary relation R over a set X is transitive if it holds for all a, b, and c in X, that if a is related to b and b is related to c, then a is related to c. unigram Only one feature is considered at a time. See also n- ( i iv

5 white-sace χ -distribution gram. The characters, sace, tab, line-feed and other characters that leaves an emty sace. The shae alters as the degrees of freedom change. The area under the curve will grow as the degrees of freedom increase making it more symmetrical. With more than 30 degrees of freedom it aroximates the normal distribution. v

6 Abbreviations ASCII BNS ELE HTML IP ISP KL knn L-S MLE NB NNet SA SBS SBFS SFS SFFS SMTP SVM XML American Standard Code of Information Interchange Bi-normal searation Exected Likelihood Estimate Hyer Text Marku Language Internet Protocol Internet Service Provider Kullback-Liebler k-nearest Neighbor Ling-Sam Maximum Likelihood Estimate Naive Bayesian Neural Network SamAssassin Sequential Backward Selection Sequential Backward Floating Selection Sequential Forward Selection Sequential Forward Floating Selection Simle Mail Transfer Protocol Suort Vector Machine Extensible Marku Language vi

7 Notation α Significance level. χ Chi square statistics. λ Weight of each good message. A Alhabet. B Number of bins (distinct items). C Class vector. D Delimiter set EW Acc Extended Weighted Accuracy. F Feature vector. IG Information Gain. J Fitness function. KL Kullback-Liebler divergence. L Label vector. M Message corus. n Number of good messages classified as good. gg n Number of good messages classified as sam. gs Number of sam messages classified as sam. n ss n Number of sam messages classified as good. sg N Total number of training instances. N j Frequency of frequency of items seen j times. Precision MLE Maximum likelihood estimator. Absolute estimator. Abs Lalace estimator. La Exected likelihood estimator. ELE Lidstone estimator. Lid Witten Bell estimator. WB Good Turing estimator. GT Rob Bayesian estimator. value Calculated robability in classical statistics. P Probability. PR Probability ratio. Q Production of a tokenizer. r Recall. R Rank. t Threshold value for sam cutoff. T Tokenizer. W Weighted accuracy. Acc vii

8 X, Y Events. viii

9 Table of Contents Introduction.... The roblem of sam.... Research objectives....3 Thesis Outline... Method Literature Survey Exerimental work Techniques to eliminate sam Hiding the address Pattern matching, whitelists and blacklists Rule based filters Statistical filters verification Distributed blacklists of sam sources Distributed blacklist of sam signatures Money stams Proof-of-work stams Legal measures Conclusion Statistical Classifiers Features and classes Text categorization Basics about Probability Theory Bayes theorem Classical vs. Bayesian statistics Using statistics Using statistics Objective and subjective robabilities Inference differences Examle of statistical sam classification Classical statistics Bayesian statistics Naive Bayesian Sam Filtering The model Naive Bayesian Classifier Measuring the erformance Precision and recall Weighted accuracy Cross validation... 9 ix

10 5.3.4 Benchmark coruses Message tokenization Definitions Delimiter Interaction Non-transitivity Non-monotonicity Dimensionality reduction in the search for a good delimiter subset Filters and wraers Probability estimation Absolute Estimate ( abs ) Lalace Estimate ( la ) Exected Likelihood Estimate (ELE) ( ELE ) Lidstone Estimate ( Lid ) Witten Bell smoothing ( WB ) Good Turing Estimate ( SGT ) Bayesian smoothing ( Rob ) Feature Selection Information Gain χ statistics Probability Ratio Exerimental Results Delimiter selection Filter for delimiter selection using KL-divergence Wraer aroach for delimiter selection Exerimental settings Results Analysis Conclusion Future work Probability estimation Exerimental settings Results Analysis Conclusion Future work Feature selection Exerimental settings Results Analysis Conclusion Future work Summary... 5 x

11 References xi

12 List of Figures Figure. A model of Naive Bayesian sam filtering...5 Figure. Pseudo code insired by (Sance & Sajda 998) for the modified SFFS...3 Figure 3. Illustration of the filter selection rocedure....4 Figure 4. Illustration of the wraer selection rocedure...5 Diagram. ( x MLE i ) = 0. 8 is smoothed by Rob as the data oints increase....9 Diagram. Performance as the number of delimiters increase...39 Diagram 3. Performance as a function of the number of features selected on PU...46 Diagram 4. Performance as a function of the number of features selected on PU...47 Diagram 5. Performance as a function of the number of features selected on PU Diagram 6. Performance as a function of the number of features selected on PUA...48 Diagram 7. Performance as a function of the number of features selected on SA...48 Diagram 8. Performance as a function of the number of features selected on L-S Diagram 9. The average time to classify one message for the different feature selectors...49 Table. Illustration of the non-transitive relationshi between delimiters.... Table. Coruses used in the exeriments...33 Table 3. Delimiter subsets used as base-line Table 4. Delimiters subsets automatically found by the SFFS for different coruses Table 5. Performance of the different delimiter subsets on Ling-Sam Table 6. Performance of the different delimiter subsets on SamAssassin...38 Table 7. Performance of the different delimiter subsets on Personal Table 8. Probability estimators tested on PU...4 Table 9. Probability estimators tested on PU...4 Table 0. Probability estimators tested on PU3...4 Table. Probability estimators tested on PUA...4 Table. Probability estimators tested on Ling-Sam...43 Table 3. Probability estimators tested on SamAssassin Table 4. Mean results for λ =...43 Table 5. Mean results for λ = Table 6. Mean results for λ = Table 7. Overall erformance of the tested estimators...45 xii

13 Introduction. The roblem of sam Internet has oened new channels of communication; enabling an to be sent to a relative thousand of kilometers away. This medium of communication oens doors for virtually free mass ing, reaching out to hundred of thousands users within seconds. However, this freedom of communication can be misused. In the last coule of years sam has become a henomenon that threatens the viability of communication via . It is difficult to develo an accurate and useful definition of sam, although every user will quickly recognize sam messages. Merriam-Webster Online Dictionary defines sam as unsolicited usually commercial sent to a large number of addresses. Some other than commercial uroses of sam are to exress olitical or religious oinions, deceive the target audience with romises of fortune, sread meaningless chain letters and infect the receivers comuter with viruses. Even though one can argue that what is sam for one erson can be an interesting mail message for another, most eole agree that sam is a ublic frustration. Sam has become a serious roblem because in the short term it is usually economically beneficial to the sender. The low cost of as a communication medium virtually guaranties rofits. Even if a very small ercentage of eole resond to the sam advertising message by buying the roduct, this can be worth the money and the time sent for sending bulk s. Commercial sammers are often reresented by eole or comanies that have no reutation to lose. Because of technological obstacles with infrastructure, it is difficult and time-consuming to trace the individual or the grou resonsible for sending sam. Sammers make it even more difficult by hiding or forging the origin of their messages. Even if they are traced, the decentralized architecture of the Internet with no central authority makes it hard to take legal actions against sammers. Sam has increased steadily over the last years, according to Brightmail. At resent, March 004, 6% of all s on the internet are sam comared to 45% a year ago. The major roblem concerning sam is that it is the receiver who is aying for the sam in terms of their time, bandwidth and disk sace. This can be very costly even for a small comany with only 0 emloyees who each receive 0 sam s a day. If it takes 5 seconds to classify and remove a sam, then the comany will send about half an hour every day to searate sam from legitimate . The statistics shows that 0 sam messages er day is a very low number for a comany that is suscetible to sam. There are other roblems associated with sam. Messages can have content that is offensive to eole and might cause general sychological annoyance, a large amount of sam messages can crash unrotected mail servers, legitimate ersonal s can be easily lost and more. There is an immediate need to control the steadily growing sam flood. A great deal of on-going research is trying to resolve the roblem. However, users are imatient and therefore there is a growing need for raidly available anti-sam solutions to rotect them. Merriam-Webster Online Dictionary, htt:// Brightmail, htt://brightmail.com/,

14 . Research objectives There are many different aroaches available at resent attemting to solve the sam issue. One of the most romising methods for filtering sam with regards to erformance and ease of imlementation is that of statistical filters. These filters learn to distinguish (or classify) between sam and legitimate messages as they are being used. In addition, they automatically adat as the content of sam messages changes. The objective of this thesis is to exlore the statistical filter called Naive Bayesian classifier and to investigate the ossibilities for imroving its erformance. After dissecting the segments of its oeration, this work focuses on three secific areas described below. Before a message can be classified as either sam or legitimate it is first slit into tokens; this rocess is called tokenizing. As this text is being read, tokenizing into tokens (words) is actually taking lace as sace is being used as a delimiter. Similarly an message can be slit into tokens using sace or any other character as delimiter. The first objective of this work is to examine how the selection of delimiters affects the classifier s erformance and to offer recommendations for choosing delimiters. The classification of some messages as sam is based uon the knowledge gathered from the statistics about tokens aearing in revious messages. When a message is to be classified; each token is looked u in the training data. For examle, the token Viagra may have aeared 5 times in revious sams and 0 times in revious legitimate e- mails. These are the frequencies of a token in the training data. From these frequencies it is ossible to estimate the robability that a token is found in a sam or legitimate . The most straight forward technique is to divide the frequency by the total number of tokens reviously seen. Higher frequencies give better robability estimates. But whenever a token is either not resent in any of the revious messages or it has a low frequency, there are better ways of estimating its robability. Our second objective is to examine how different robability estimators affect the sam classification erformance. A feature is a characteristic of an object. For examle in image recognition a feature could be a color and in the case of classifying s it is a token or a word. messages are written using natural languages which contain thousands of distinct words. The number of words is the dimensionality of the message. The rimary urose of feature selection is to reduce the dimensionality in order to increase the seed of the comutation. Our third objective was to conduct comarative analyses between three commonly used feature selection methods..3 Thesis Outline The thesis is structured in seven chaters. Chater two discusses the method used. Chater three briefly describes currently develoed techniques to eliminate sam aiming to show that all existing schemes are not fully develoed and do not offer comlete sam elimination. It also emhasizes that statistical filters have, so far, roved to be the most successful method in dealing with sam.

15 Chater four gives an overview of statistical classifiers and rovides the reader with some necessary basic mathematical understanding for this work. Chater five resents a general concetualized model of a Naive Bayesian sam filter and exlains the theory used by the Naive Bayesian classifier. This chater also contains the currently used techniques for the three hases erformed rior to the classification of messages starting with an examination of how the selection of delimiters affects the classifier erformance. Following this seven different aroaches are resented for smoothing the robabilities for the training data and finally three different methods for selecting features are demonstrated. Chater six is devoted to the exerimental work erformed. It contains three sections, each with its own conclusions and one for each exeriment. In this way the results resented in the sections are summarized and the conclusions are derived. Chater seven is a summarization of all the work erformed. 3

16 Method The methodology used throughout the thesis consisted of a theoretical study requiring a literature survey and ractical work involving several exeriments.. Literature Survey Articles found on the Internet are the most commonly used research material for this work. Google and Citeseer 3 were frequently used to find articles of interest. The sam henomenon is still in its infancy and it was therefore natural to use the Internet as the main source of information. The theory behind statistical filters is well established and a number of books on statistics served as rimary literature in this area. Books on Formal Languages, Artificial Intelligence and Discrete Mathematics were often consulted throughout the work on this thesis.. Exerimental work The exerimental work is suorted by some theoretical background. The emirical results obtained were verified with the theoretical ones whenever they were available. To carry out the exeriments a test environment in C++ was built. In order to avoid rebuilding the environment for different tests, exeriments were defined in an XML file that is read at run-time. For examle, the corus to use, robability estimator and feature selection method are defined in the XML file. 3 htt://citeseer.ist.su.edu/ is a database with articles. 4

17 3 Techniques to eliminate sam There are several aroaches which deal with sam. This section briefly summarizes some common methods to avoid sam and briefly describes the sam filtering techniques used at resent. 3. Hiding the address The simlest aroach to avoid sam is to kee the address hidden from sammers. The e- mail address can be revealed only to trusted arties. For communication with less trusted arties a temorary account can be used. If the address is ublished on a web age it can be disguised for siders 4 by inserting a tag that is requested to be removed before relying. Robots will collect the address with the tag, while humans will understand that the tag has to be removed in order to retrieve the correct address. For most users this method is insufficient. Firstly, it is time consuming to imlement techniques that will kee the address safe, and secondly, the disguised address could not only mislead robots, but also the inattentive human. Once the address is exosed, there is no further rotection against sam. 3. Pattern matching, whitelists and blacklists This is a content-based attern matching aroach where the incoming is matched against some atterns and classified as either sam or legitimate. Many rograms have this feature which is often referred to as message rules or message filters. This technique mostly consists of a lain string matching. Whitelists and blacklists, which basically are lists of friends and foes, fall into this category. Whenever an incoming is matched against an entry in the whitelist, the rule is to allow that through. However whenever an has a match against the blacklist, it is classified as a sam. This method can reduce sam u to a certain level and requires constant udating as sam evolves. It is time consuming to determine what rules to use and it is hard to obtain good results with this technique. In Mertz D. 00 some simle rules are resented. The author claims that he was caable of catching about 80% of all sam he received. However, he also stated that the rules used had, unfortunately, relatively high false ositive rates. Basically, this technique is a simler version of the more sohisticated rule based filters which are discussed below. 3.3 Rule based filters This is a oular content-based method deloyed by sam filtering software such as SamAssassin 5. Rule-based filters aly a set of rules to every incoming . If there is a match, the is assigned a score that indicates saminess or non-saminess. If the total score exceeds a threshold the is classified as sam. The rules are generally built u by regular exressions and they come with the software. The rule set must be udated regularly as sam changes, in order for the filtering of sam to be successful. Udates are retrieved via the Internet. The tests results from the comarison of anti-sam rograms resented in Holden 003 show that SamAssasin finds about 80% of all sam, while statistical filters (discussed later) find close to 99% of all sam. 4 siders, or robots, are comuter rograms that scans and collects address from Internet. 5 SamAssasin, htt:// 5

18 The advantage of rule-based filters is that they require no training to erform reasonably well. Rules are imlemented by humans and they can be very comlex. Before a newly written rule is ready for use, it requires extensive testing to make sure it only classifies sam as sam and not legitimate messages as sam. Another disadvantage of this technique is the need for frequent udates of the rules. Once the sammer finds the way to deceive the filter, the sam messages will get through all filters with the same set of rules. 3.4 Statistical filters In Sahami et al. 998, it is shown that it is ossible to achieve remarkable results by using a statistical sam classifier. Since then many statistical filters have aeared. The reason for this is simle; they are easy to imlement, have a very good erformance and require a little maintenance. Statistical filters require training on both sam and non-sam messages and will gradually become more efficient. They are trained ersonally on the legitimate and sam s of the user. Hence it is very hard for a sammer to deceive the filter. A more in-deth discussion on statistical filters will follow in the next chater verification verification is a challenge resonse system that automatically sends out a one-time verification to the sender. The only way for an to ass through the filter is if the sender successfully resonds to the challenge. The challenge in the verification is often a hyerlink for the sender to click. When this link is clicked, all s from that sender are allowed through. Bluebottle 6 and Choic 7 are two such systems. The advantage of this method is able to filter almost 00% of the sam. However, there are two drawbacks associated with this method. The sender is required to resond to the challenge which necessitates extra care. If this challenge is not recognized the will be lost. Verifications can also be lost due to technical obstacles such as firewalls and other resonse systems. It can also cause roblems for automated resonses such as online orders and newsletters. The verification also generates more traffic. 3.6 Distributed blacklists of sam sources These filters use a distributed blacklist to determine whether or not an incoming is sam. The distributed blacklist resides on the Internet and is frequently being udated by the users of the filter. If a sam asses through a filter, the user reorts the to the blacklist. The blacklist is udated and will now rotect other users from the sender of that secific . This class of blacklists kees a record of known sam sources, such as IP numbers that allow SMTP relaying. The roblem involved in using a filter entirely relying on these blacklists is that it will generally classify many legitimate s as sam (false ositive). Another downside is the time taken for the networked based looku. These solutions may be useful for comanies assuming that all their e- 6 Bluebottle, htt:// 7 Choic , htt:// 6

19 mail communications are with other serious non-listed businesses. Comanies offering this service include MAPS 8, ORDB 9 and Samco Distributed blacklist of sam signatures These blacklists work in a same manner to that described in 3.6. The difference is that these blacklists consist of sam message signatures instead of sam sources. When a user receives a sam, that user can reort the message signature (tyically a hash code of the ) to the blacklist. In this way, one user will be able to warn all other users that a certain message is sam. To avoid non-sam being added to a distributed blacklist, many different users must have reorted the same signature. Sammers have found an easy way to fool these filters; they simly add a random string to every sam. This will revent the from being detected in the blacklist. However sam fighters attemt to overcome this roblem by adating their signature algorithms to allow some random noise. The advantage being that these kinds of filters rarely classify legitimate messages as sam. The greatest disadvantage is they are not able to recall much of the sam. Viul s Razor uses such a blacklist and states that it catches 60%-90% of all incoming sam. Another disadvantage is the time taken for the network looku. 3.8 Money stams The idea of stams is not new, having been discussed since 99, but it is not until recently that major comanies have considered using it to combat sam. The sender would have to ay a small fee for the stam. This fee could be minor for legitimate senders, while it could destroy business for sammers that send millions of s daily. There are two stam tyes; money stams and roof-of-work stams (discussed later). GoodmailSystems is develoing a system for money stams. The basic idea is to insert a unique encryted id to the header of each sent . If the reciient ISP is also articiating in the system, the id is sent to Goodmail where it is decryted. Goodmail will now be able to identify and charge the sender of the . Today there are many issues requiring solutions before such a system can be deloyed. Who receives the money? Where is tax aid? Who are allowed to sell stams? Since this is a centralized solution, what about scalability? It would also be the end of many legitimate newsletters. 3.9 Proof-of-work stams At the beginning of 004, Bill Gates, Microsoft s chairman, suggested that the sam roblem could be solved within two years by adding a roof-of-work stam to each . Camram 3 is a system that uses roof-of-work stams. Instead of taking a micro fee from the sender, a cheat-roof mathematical uzzle is sent. The uzzle requires a certain amount of comutational ower to be 8 Mail Abuse Prevention System LLC (MAPSSM), htt://mailabuse.com/ 9 Oen Relay DataBase (ORDB), htt://ordb.org/ 0 Samco, htt:// Viul s Razor, htt://razor.sourceforge.net/ Goodmail, htt:// 3 Camram, htt:// 7

20 solved (matter of seconds). When a solution is found, it is sent back to the receiver and the is allowed to ass to the receiver. The uzzle Camram is using is called Hashcash 4. Whether it is money or roof-of-work stams, many oose the idea, not only because e- mailing should be free, but also because it will not solve the sam roblem. To make this aroach effective, most ISP s would have to join the stam rogram. As long as there are ISP s that are not integrated into the stam system, sammers could use their servers for mass ing. It could then still be ossible for the legitimate ers to ay to send s, while sam is still flooding into the inboxes of users. Many non-rofit legitimate mass ers will robably have to abandon their newsletters due to the sending cost. Historically, sammers have been able to deceive most of the other anti sam filters and this could also be the case with the stam system. 3.0 Legal measures In recent years many nations have introduced anti-sam laws, in December 003, resident George W. Bush signed the CAN-SPAM 5 act, the Controlling the Assault of Non-Solicited Pornograhy and Marketing Act. The law rohibits the use of forged header information in bulk commercial e- mail. It also requires sam to include ot-out instructions. Violations can result in fines of $50 er , caed at $6 million. In Aril 004 the first four sammers were charged under the CAN- SPAM law. The trial is still on, but if the court manages to send out a strong message, this could deter some sammers. The Euroean Union introduced an anti-sam law on the 3st of October 003 called The Directive on Privacy and Electronic Communications. This new law requires that comanies gain consent before they send out commercial s. Many argue that this law is toothless since most of the sam comes from the outside of EU. In the long-run legislation can be used to slowdown the sam flood to some extent, but it will require an international movement. Legislation will not be able to solve the sam roblem by itself, at least not in the near future. 3. Conclusion The most commonly used methods for eliminating sam were described in this chater. Perhas legislation is the best otion in the long run. However, it requires a world wide effort and this rocess could be slow. Presently users need to rotect themselves and for the moment statistical filters are the most romising method for this urose. They have suerior erformance, can adat automatically as sam changes and in many cases are comutationally efficient. 4 Hashcash, htt:// 5 Information about sam laws can be found here htt:// 8

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