Patent Application: US-9612606-A

Abstract:
the invention is concerned with a method and an apparatus for automatic comparison of at least two data sequences characterized in — an evaluation of a local relationship between any pair of subsequences in two or more sequences ; — an evaluation of a global relationship by means of aggregation of the evaluations of said local relationships .

Description:
detection of unknown attacks is a long - standing issue on a wish - list of security practitioners . while it is often claimed that current applications and infrastructures for tracking vulnerabilities and their exploits provide adequate protection by means of attack signatures , there exist numerous examples of unknown attacks , notably worms [ e . g . 38 ] and zero - day exploits [ e . g . 1 ], that have defeated signature - based defenses . furthermore , it often does not suffice for a signature to be available — deployed signatures must be kept up - to - date by security administrators in order to keep their systems safe . discussion about unknown attacks has been carried out in various parts of the intrusion detection community . for misuse detection , it centers around the issues of making signatures more generic — and capable of at least not to be fooled by mutations of known attacks [ 37 , 22 , 15 , 30 , 7 , 33 ]. there is , however , a growing consensus that genuinely novel attacks can be only detected by anomaly detection tools , at a cost of having to deal with false positives which may also be valid anomalies . a large amount of previous work has been done on anomaly detection in network traffic [ e . g . 41 , 42 , 16 , 26 , 25 , 9 ]. the main hurdle on the way to its acceptance in practice is a high rate of false - positives . most of the previous approaches do not deliver sufficient accuracy in the promille range of false - positive rates , which is what practitioners need ( and which may still be too high ). hence further improvements of anomaly - based intrusion detection techniques are highly desirable . apart from methodical differences , the main issue underlying various anomaly detection approaches is the features they operate on . some early approaches considered only packet header information or statistical properties of sets of packets or connections [ 25 , 19 ]. this information has proved to be useful for detection of certain kinds of malicious activity , e . g . probes and port scans , yet it usually does not suffice to detect attacks that exploit semantic vulnerabilities of application - layer protocols and their implementations . in this paper we present a general technique for detection of unknown network attacks which uses similarity measures over language models , such as n - grams and words , for analysis of byte streams in tcp connections . the n - gram representation has been long known in the literature on host - based ids [ e . g . 10 , 14 , 43 , 27 , 12 ]. recently , some techniques of network intrusion detection have been proposed in which n - gram models are applied for anomaly detection over packet payloads or connection contents [ 16 , 42 , 41 ]. it has been demonstrated that such models can be quite effective in detecting attacks that do not manifest themselves in packet headers . the reason why n - grain models are successful in description of content - based discriminative features can be seen by comparing protocols and natural languages . the content of both is characterized by rich syntax and semantics , and discrimination between different categories is only possible in terms of syntactic and semantic constructs . for both protocols and natural languages , extensive effort has been made to describe important concepts by means of rules , only to find out that rules can hardly encompass the full generality of underlying content . protocols and natural languages possess grammatic structure , yet recovery of this structure is stymied by uncertainty and ambiguity . in view of the linguistic analogy , one can see that identification of ( unknown ) misuse patterns amounts to learning ( unknown ) concepts in an underlying protocol language . hence it is clearly promising to apply the machinery of natural language processing to network intrusion detection . while doing so one must , however , beware a technical challenge of network - based ids : high - speed and high - volume data . for all previously reported experimental results with n - gram models of network traffic n = 1 was used , which indirectly points out the main technical problem with applying this model : how can statistical features of n - grams , the number of which can be large , be efficiently computed and compared ? to address this problem we propose a novel representation of n - grams based on tries . this representation allows one to compute , in linear time , a large variety of similarity measures on n - grams , e . g . manhattan , euclidean and canberra distances , kulczynski and czekanowski similarity coefficients , as well as various kernel functions . using these similarity measures , one can apply unsupervised anomaly detection algorithms to detect unusual events . as a result , anomaly detection using our technique is extremely easy to deploy in practice : once connected to a network , our system performs anomaly detection without any training or extensive configuration , converging to a stable regime after a short period of learning a profile of normal data . as a proof of concept , we experimentally evaluate our methods on the darpa 1999 ids dataset and on our own dataset created by a penetration testing expert . unlike previous work using the darpa 1999 dataset , in which usually the whole spectrum of attacks is considered , we focus on attacks against application - layer protocols whose increasing complexity breeds a large amount of vulnerabilities . exploits of such vulnerabilities often enable attackers to obtain privileges sufficient for severe abuse of network services ; therefore , attacks against application - layer protocols are most dangerous in the sense of practical security . the list of attacks present in our experiments is given in tables 1 and 2 . the results of our experiments demonstrate that n - grams can convey a valuable information for detection of unknown attacks . as a distinction from previous work , we have observed that for some attacks important discriminative features are contained in n - grams of length n & gt ; 1 . on the other hand , our experiments show that it may be difficult to determine an optimal length of n - gram models in advance , an effect known from research in natural language processing . to remedy this problem , we extend our models beyond n - grams to words , and show that such models yield accuracy that is only marginally lower than the accuracy of experimentally optimal n - gram models . finally , we establish that the proposed methods significantly outperform a recent version of an open - source ids snort with a standard signature set . quite naturally , language models have been first developed by researchers in the fields of information retrieval and natural language processing — several decades before their relevance for intrusion detection was discovered . as early as mid - sixties , character n - grams were used for error correction in optical character recognition [ 32 ]. application of n - grams to text categorization was pioneered by suen [ 40 ] and was followed by a large body of subsequent research [ e . g . 4 , 3 , 35 ]. the main idea of n - gram - based approaches is to compute frequencies of all subsequences containing n consecutive characters ( n - grams ) and to define similarity measures based on these frequencies . despite the exponential number of n - grams in an alphabet , only a linear number of them is present in a given character string . efficient comparison of n - grams can be done by means of hashing . various similarity measures were used to compare n - gram frequencies , e . g . the inner product between frequency vectors [ 4 ] or manhattan and canberra distances [ 3 ]. recent approaches to text categorization advocate the use of kernel functions as similarity measures , which allow one to incorporate contextual information [ 44 , 21 , 24 ]. re - discovery of n - gram models in the realm of host - based ids began in the mid - nineties with the seemingly ad - hoc “ sliding window ” approach of forrest et al . [ 10 ]. in modern terminology this approach can be classified as n - gram - based supervised anomaly detection . the main idea of forrest et al . was to create a database of all possible n - grams in system call traces resulting from normal operation of a program . traces with a large degree of binary mismatch to the database were flagged as anomalous . in the ensuing work these ideas were extended through application of hidden markov models [ 43 ], feed - forward and recursive neural networks [ 12 ] and rule induction algorithms [ 20 ]. a comprehensive evaluation of these approaches showed that all of the above methods could effectively detect anomalous behavior of intrusions in the datasets they were tested on [ 43 ]. application of n - gram models for network - based ids originated in the idea of using a limited form of a byte histogram of packet payloads for statistical tests of anomality [ 16 ]. a more advanced model was proposed by wang and stolfo , in which histograms of packet payloads are used to detect anomalous packets whose payload histograms have large mahalanobis distance to histograms learned from normal data [ 42 ]. this approach can be easily seen as a particular case of an n - gram approach with n = 1 . the peculiarity of the method of wang and stolfo is that packet payload distributions are conditioned on packet lengths ; merging of adjacent models is used to reduce an overall model size . the anomalous payload detection sensor payl using this method has been successfully applied to detect worms in network traffic [ 41 ]. as a reader can easily see from a brief review of related work , different intuitions lead to a simple language model — namely , n - grams — which captures a coarse syntax of an underlying language in a way sufficient to discriminate between normal and anomalous events . a key to utilizing such models in anomaly detection algorithms is to provide a set of similarity measures that possess desirable discriminating properties . it should be noted that a large variety of similarity ( and dissimilarity ) measures is available from literature , some of which are reviewed in a . 2 . therefore it is highly desirable to be able to draw upon these measures without alteration of data structures and algorithms for computation of n - gram histograms . to see why an underlying data structure is crucial for an efficient implementation of similarity measures , some technical issues must be discussed . a classical scheme of storing and comparing n - gram histograms makes use of a hash table [ e . g . 4 ]. it allows to store l − n + 1 ( in the worst - case ) distinct n - grams present in a character stream in an hash table of size k , the relation between l and k depending on parameters of a hash function . insertion into a hash table takes constant time , and a simple comparison of two hash tables takes o ( k ), again , provided that a hash function is good enough to avoid too many collisions . since the hash table elements are not ordered , computation of any similarity measure necessitates a loop over all k table elements . we propose to store the n - grams collected from a byte stream in a trie [ 5 , 11 ]. insertion into a trie takes o ( n log | σ |) where | σ | is the size of the alphabet ( in our case 256 ). an example of storing a set of words {“ bank ”, “ band ”, “ card ”} is shown in fig1 . each node of a trie is augmented to contain a counter which is incremented every time a node is hit during insertion of an n - gram into the trie . the counts in fig1 correspond to the presence of 3 “ band ” s , 5 “ bank ” s and 2 “ card ” s in an input stream . computation of similarity measures over n - gram tries can be done by expressing a target measure as an operator over matching functions : d ( x , y )=⊕ s , t triex , y m ( s , t ), where a matching function can be a match m + ( s , t ), a local mismatch m − ( s ) and a global mismatch m *( s ) function . using a suitable definition of m + , m − and m *, a variety of measures can be defined . for example , the manhattan distance between two tries is obtained with m + ( s , t )=| c s − c t |, m − ( s )= m *( s )=| c s |, where c i is a count of a respective node in the trie . a decisive advantage of tries - over hash tables takes place when comparing two byte streams of different lengths , say l 1 & lt ;& lt ; l 2 . for a trie representation a match can be performed in o ( min ( l 1 , l 2 )); for a hash table a match always requires o ( k )≈ o ( max ( l 1 , l 2 )) operations . in the application of a trie data structure to n - gram analysis of network traffic we consider streams of incoming bytes of assembled tcp connections . for every connection , a trie is built which contains a compressed representation of all n - grams in the incoming byte stream . we then feed tries into an unsupervised learning algorithm which performs detection using a given similarity measure . thus our approach is similar to the “ per connection ” model of wang and stolfo [ 42 ], except that we do not perform conditioning over payload length and clustering of adjacent bins . the way n - grams can characterize network attacks in tcp connections can be best illustrated by an example . fig2 shows the differences between 3 gram frequencies of an iis unicode attack and normal http traffic . due to the large possible space of 3 - grams the plot is limited to 3 grams present in the iis unicode attack . several positive peaks indicate a high deviation from normal traffic and correspond to typical 3 - grams of the attack , e . g . “ 35c ”, “/..” and “% 35 ”. these 3 - grams manifest an essential pattern of the unicode attack “%% 35c ” which is converted by a vulnerable iis server to “% 5c ” ( ascii code 0x35 corresponds to “ 5 ”) and finally interpreted as backslash ( ascii code 0x5c ). the corresponding fragment of the attack is shown below . unsupervised anomaly detection is particularly suitable to the practical needs of intrusion detection , as it spares an administrator from the task of collecting data representative of normal activity . an unsupervised anomaly detection algorithm can be directly applied to a stream of data and is supposed to effectively discriminate between normal and anomalous patterns “ on - the - fly ”. furthermore , no extensive configuration of the algorithm or training using manually labeled data is required . because of its favorable properties , unsupervised anomaly detection has gained significant interest in recent work on intrusion detection [ e . g . 34 , 9 , 18 ]. the algorithms for unsupervised anomaly detection exploit differences in geometric features of anomalies and normal data . these algorithms can explore local properties , e . g . single - linkage clustering [ 34 ] and our new k - nearest neighbor method zeta [ citation omitted ], or global properties , e . g . simplified mahalanobis distance [ 42 ] and quarter - sphere svm [ 17 ]. ( a brief summary of these four algorithms used in our work is presented in a . 1 ). anomaly detection algorithms usually require a similarity measure between pairs of objects which essentially defines a geometric representation of data . as it was shown in section 3 a variety of similarity measures can be defined on n - gram tries . in particular , we have examined the following measures : the canberra distance [ 8 ], the “ binarized ” manhattan distance , the czekanowski coefficient [ 6 ] and the ( second ) kulczynski coefficient [ 39 ]. ( a brief description of these measures is given in a . 2 .) in order to evaluate the proposed n - gram trie representation of network connections with respect to detection performance , and to gain insights into the nature of recovered syntactic information , we conducted experiments on two network traffic datasets . specifically we are interested to clarify the following open questions : 1 . does increased length of n - grams ( n & gt ; 1 ) improve detection performance ? 2 . at what false - positive rate do we detect all instances of attacks present in our data ? we limit our experiments to the popular application - layer protocols http , ftp and smtp , which constitute a steady target of network attacks in the last decade . this well - known dataset from an ids evaluation conducted by the darpa in 1999 [ 23 ] has been used in numerous publications and can be considered a standard benchmark for evaluation of ids . as a preprocessing step , we randomly extracted 1000 tcp connections for each protocol from the first and third weeks of the data corpus representing normal data . we then selected all remote - to - local attacks present in the fourth and fifth weeks of the dataset . table 1 lists these remote - to - local attacks . even though the darpa 1999 dataset is known to suffer from several flaws and artifacts [ 26 , 28 , 29 ], especially the selection of attacks can be considered antiquated in comparison to modern security threats , it remains the only major dataset on which results can be reproduced . in order to overcome the problems of the darpa 1999 dataset , we generated a second evaluation dataset named pesim 2005 . we deployed a combination of 5 servers using a virtual machine environment . the systems ran two windows , two linux and one solaris operating systems and offered http , ftp and smtp services . normal network traffic for these systems was generated by members of our laboratory . to achieve realistic traffic characteristics we transparently mirrored news sites on the http servers and offered file sharing facility on the ftp servers . smtp traffic was artificially injected containing 70 % mails from personal communication and mailing lists , and 30 % spam mails received by 5 individuals . the normal data was preprocessed similarly to the darpa 1999 dataset by random selection of 1000 tcp connections for each protocol from the data corpus . attachments were removed from the smtp traffic . attacks against the simulated services were generated by a penetration testing expert using modern penetration testing tools . multiple instances of 27 different attacks were launched against the http , ftp and smtp services . the attacks are listed in table 2 . the majority of these attacks is part of the comprehensive collection of recent exploits in the metasploit framework [ 31 ]. additional attacks were obtained from common security mailing lists and archives , such as bugtraq and packetstorm security . the “ php script attack ” was introduced by the penetration testing expert and exploits insecure input processing in a php script . as previously mentioned , similarity measures induce various geometric properties which , in turn , are explored in different ways by anomaly detection methods . hence , as a first step , we need to roughly establish what combinations of similarity measures and anomaly detectors perform best on n - gram tries for each protocol in question . the candidate similarity measures for this experiment are the canberra and the “ binarized ” manhattan distances , the czekanowski and the kulczynski similarity coefficients . the anomaly detectors under consideration are the simplified mahalanobis distance , the quarter - sphere svm , the single - linkage clustering and the zeta anomaly detector . the following experimental - protocol is implemented . for each measure / detector configuration 10 independent datasets are generated from the corpus . each dataset is split into a validation partition , used for finding optimal detector parameters , and an independent test partition , used for evaluation of detector accuracy . the evaluation criterion is the so called area under curve ( auc ) which integrates true - positive rates over a certain interval of false - positive rate , in our case [ 0 , 0 . 1 ]. the procedure is repeated for values of n from 1 to 8 , and the results are averaged over 10 runs and all values of n . table 3 lists the best three measure / detector configurations for the http , ftp and smtp protocols on both datasets . for all protocols the configuration with similarity coefficient kulczynski and local anomaly detector zeta yields the best overall performance for varying length of n . in the remaining experiments we fix the measure / detector configuration to this setup . previous results in natural language processing and host - based ids indicate that the optimal n - gram length may vary for different applications [ 24 , 10 ]. we now investigate if the same observation holds for n - gram models of tcp connections . we follow the same setup as in the selection of the optimal measure / detector configuration , except that results of individual values of n are reported using a fixed configuration . the results are shown in fig3 ( for the darpa 1999 dataset ) and fig4 ( for pesim 2005 dataset ), which display the roc graphs for selected values of n . it can be clearly seen that detection performance varies significantly among the values of n for different protocols . in fact , it turns out that each of the three values considered in this experiment is optimal for some protocol — and for a different one in two datasets . apart from that , the overall accuracy of our approach is very encouraging , especially on the more recent pesim 2005 dataset . for the best value of n , a detection rate between 80 % and 100 % was observed at a false - positive rate of 0 . 2 % for the http , ftp and smtp protocols . one is always interested to know how well an ids detects specific attacks in a dataset . the results of the previous experiment suggest that , in addition , the optimal n - gram length for each attack might be insightful . as criterion for this experiment we considered the minimum false - positive rate at which all instances of an attack are detected . the results are shown in table 4 . most of the network attacks from the pesim 2005 data set are detected with false - positive rates below 1 %. only one attack , the proftpd exploit , is poorly recognized . this exploit uploads a malicious file to an ftp server . since the file content is transferred over a data channel which is not monitored by our system , this attack can only be detected by chance in our setup . distribution of optimal n - gram lengths across the attacks reveals two aspects . for several attacks , which are particularly easy to detect , the n - gram length is irrelevant . there exists , however , attacks ( easy as well as difficult to detect ) for which detection accuracy is significantly better for certain n - gram lengths . the message from the experiments in the previous section may be somewhat confusing for a practitioner . one can see that longer n - grams bring improvement in detection performance in some cases , on the other hand , no consistency can be found across various attacks and protocols . how should one choose the right n beforehand if attacks are unknown ? the following extension of the n - gram model addresses this concern . note that the semantics of natural languages is , in fact , defined in terms of words rather than n - grams . words in a natural language are defined as consecutive character sequences separated by white - space symbols . we conjecture that semantics of application - layer protocols such http , ftp and smtp can likewise be captured by appropriately defined words . as word separators , the following bytes are proposed : we are now about to discover another remarkable property of the trie representation of n - grams proposed in this paper : it can handle variable - length “ grams ” without any alteration ! we repeat the experiments under the same setup as the experiments on varying n - gram length using the stream of words instead of n - grams . similarity measures are computed over word frequencies , and the same optimal measure / detector configuration is used . to emphasize the practical focus of this experiment , we compare the results of our - models with the performance of the open - source signature - based ids snort [ 36 ] ( snort version 2 . 4 . 2 , released on 28 . 09 . 2005 and configured with the default set of rules ). the results are shown in fig5 ( for the darpa 1999 dataset ) and fig6 ( for the pesim 2005 dataset ). it can be seen that our word - based detector yields the same accuracy on the pesim 2005 dataset as the best n - gram - based detector . unfortunately , no consistency can be observed on the darpa 1999 dataset , which can be attributed to the artificial nature of some attacks present in this dataset . to our surprise , the n - gram and word models significantly outperformed snort on the pesim 2005 dataset even though all included attacks except for the “ php script ” were known months before the release date of our snort distribution . this result confirms a misgiving that signature - based ids may fail to discover “ fresh ” attacks despite a major effort in the security community to maintain up - to - date signature repositories . noteworthy is the fact that snort failed in our experiments due to two reasons . some attacks were not detected because no appropriate signature was present , which is manifested by flat roc graphs that never reach the 100 % level . other failures occurred due to minor variations in attack syntax . for example , one of the smtp attacks was not discovered when an attacker replaced the initial “ helo ” command with “ ehlo ”, which is allowed by protocol specification and frequently used in practice . we have proposed a novel representation of language models for network intrusion detection that uses tries for efficient storage of n - grams and words extracted from tcp connections . our representation allows one to compute a variety of similarity and dissimilarity measures over these models in linear time . being able to compute similarity between tcp connections , we can apply unsupervised anomaly detection algorithms suitable for detection of previously unknown attacks . results of experiments conducted on the darpa 1999 dataset and on our own dataset pesim 2005 demonstrate the importance of higher - order n - grams ( as opposed to l - grams ) for detection of recent network attacks . it is nonetheless difficult to determine the optimal length of n - gram models for particular attacks and protocols . this problem can be alleviated by considering language models based on words , using “ white - space ” separators appropriate for protocol syntax . the accuracy of unsupervised anomaly detectors based on word models , as investigated in our experiments , is almost identical to the accuracy of the best n - gram models . furthermore , the system based on our language model significantly outperformed a recent version of the open - 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172 , april 1979 . k . wang , g . cretu , and s . j . stolfo . anomalous payload - based worm detection and signature generation . in proc . raid , 2005 . k . wang and s . j . stolfo . anomalous payload - based network intrusion detection . in proc . raid , pages 203 - 222 , 2004 . c . warrender , s . forrest , and b . perlmutter . detecting intrusions using system calls : alternative data methods . in proc . ieee symposium on security and privacy , pages 133 - 145 , 1999 . c . watkins . dynamic alignment kernels . in a . j . smola , p . l . bartlett , b . schölkopf , and d . schuurmans , editors , advances in large margin classifiers , pages 39 - 50 , cambridge , ma , 2000 . mit press . the simplified mahalanobis distance [ 42 ] determines the center of mass of data μ and the variance of each dimension σ i in input space . the anomaly score is defined as the variance - scaled distance from x to μ : the quarter - sphere svm [ 17 ] is a kernel - based learning method that determines the center of mass of input data φ ( μ ) in a high - dimensional feature space using a non - linear mapping function φ : the anomaly score is defined as the distance from φ ( x ) to φ ( μ ) in feature space : simplified single - linkage clustering [ 34 ] is a common clustering algorithm . given a cluster assignment , the anomaly score is defined as the size of the cluster x : is assigned to : our new method zeta is an anomaly score based on the concept of k - nearest neighbors . the score is calculated as the mean distance of x to its k - nearest neighbors normalized by the mean inner - clique distance : ζ k ⁡ ( x ) = 1 k ⁢ ∑ i = 1 k ⁢ d ⁡ ( x , nn i ⁡ ( x ) ) - 1 k 2 ⁢ ∑ i = 1 k ⁢ ∑ j = 1 k ⁢ d ⁡ ( nn i ⁡ ( x ) , nn j ⁡ ( x ) ) a ( dis ) similarity measure is a binary function that maps x and y with component values x i and y i to a singular ( dis ) similarity score . the canberra distance d c is a normalized form of the manhattan distance . it expresses metric characteristics and distance scores lie within the range [ 0 , 1 ]. the distance is suitable for histograms containing quantities and frequencies : the “ binarized ” manhattan distance d b is similar to the hamming distance [ 13 ]. it is metric and maps the input vectors z and y to a binary space using the function b which returns 1 for non - zero values : d b ⁡ ( x , y ) = ∑ i = 1 n ⁢  b ⁡ ( x i ) - b ⁡ ( y i )  similarity coefficients are often applied to binary data and express non - metric properties [ 2 ]. these coefficients are constructed over four summation variables a , b , c and d . the variable a defines the number of positive matching components ( 1 - 1 ), b the number of left mismatches ( 0 - 1 ), c the number of right mismatches ( 1 - 0 ) and d the number of negative matches ( 0 - 0 ). the coefficients can be extended to non - binary data by modification of these summation variables . the degree of matching between two components can be defined as min ( x i , y i ) and accordingly mismatches as differences from min ( x i , y i ): the czekanowski coefficient s c measures the ratio between positive matching components and the sum of all components [ 6 ]. in the extended form it can be expressed as following : the second kulczynski coefficient s k measures the ratio between positive matching components against the left - and right - hand side of mismatches [ 39 ]. in the extended form the second kulczynski coefficient is defined as following : kernel functions as similarity measures for sequential data have been extensively studied in previous research . this contribution addresses the efficient computation of distance functions and similarity coefficients for sequential data . two proposed algorithms utilize different data structures for efficient computation and yield a runtime linear in the sequence length . experiments on network data for intrusion detection suggest the importance of distances and even non - metric similarity measures for sequential data . sequences are a common non - vectorial data representation used in various machine learning and pattern recognition applications , e . g . textual documents in information retrieval , dna sequences in bioinformatics or packet payloads in intrusion detection . an essential procedure for analysis of such data is the efficient computation of pairwise similarity between sequences . beside specialized string distances [ e . g . 1 , 2 ] a large class of similarity measures for sequential data can be defined over contained subsequences by embedding them in a high - dimensional feature space . previous research focused on computation of kernel functions in such feature spaces . for example , the inner - product over n - gram or word frequencies has been widely used for analysis of textual documents [ e . g . 3 , 4 , 5 ] or host - based intrusion detection [ e . g . 6 ]. the challenge of uncovering information in dna has influenced further advancement of kernel functions , e . g . by exploring different sets of subsequences [ e . g . 7 , 8 , 9 , 10 ] or incorporating mismatches , gaps and wildcards [ e . g . 11 , 12 , 13 ]. there exist , however , a large amount of learning algorithms which are not directly suitable for kernel functions . in principle , any inner - product induces a euclidean distance in feature space [ 14 ], yet the richness of content in sequential data and the variability of its characteristics in feature spaces motivate application of other distance functions . a general technique for computation of similarity measures suitable for kernels , distances and similarity coefficients is proposed in this contribution . it is based on incremental accumulation of matches and mismatches between subsequences comprising a feature space . two algorithms are presented that utilize different data structures for efficient computation : hash tables and tries . both algorithms have linear runtime complexity in terms of sequence lengths . the rest of the paper is organized as follows : section 2 defines several similarity measures for sequential data including kernels , distances and similarity coefficients . comparison algorithms and corresponding data structures are introduced in section 3 . finally , experiments in section 4 compare the efficiency of the introduced algorithms and illustrate their application in network intrusion detection . given an alphabet σ of size n , a sequence x is defined as a concatenation of symbols from σ . the content of a sequence can be modeled as a set of possibly overlapping subsequences w taken from a finite language l ⊂ σ *. we refer to these extracted subsequences as words . the language l constitutes the basis for calculating similarity of sequences and typically corresponds to a bag of characters , words or n - grams . given a sequence z and a language l , an embedding into feature space is performed by calculating φ w ( x ) for every wεl appearing in x . usually the function φ w ( x ) returns the frequency of w in x , however , other definitions returning a count or a binary flag for w are possible . furthermore we define l to be the length of x . we assume that the total length of words in every sequence x is proportional to l . this assumption is valid , for example , for n - grams of fixed length n and non - overlapping words , and ensures linear runtime of the proposed algorithms . in context of kernels several approaches have been investigated that do not make such an assumption [ e . g . 9 , 10 , 11 , 12 , 13 ], however , some of them come at a cost of super - linear complexity . by utilizing the feature space induced through φ , one can adapt classical kernel and distance functions to operate on sequences . table 5 lists kernel functions and table 6 distance functions that are implemented using the algorithms presented in section 3 . yet another way of measuring similarity are so called similarity coefficients [ e . g . 15 , 16 ]. they are non - metric and have been primarily used on binary data . similarity coefficients are constructed using three summation variables a , b and c . the variable a contains the number of positive matches ( 1 - 1 ), b the number of left mismatches ( 0 - 1 ) and c the number of right mismatches ( 1 - 0 ). the most common similarity coefficients are given in table 7 . similarity coefficients can be extended to non - binary data by modification of the summation variables . the degree of match for a word wεl can be defined as min ( φ w ( x ), φ w ( y )) and the respective mismatches are defined as deviations thereof : a = ∑ w ∈ l ⁢ min ⁡ ( ϕ w ⁡ ( x ) , ϕ w ⁡ ( y ) ) b = ∑ w ∈ l ⁢ [ ϕ w ⁡ ( x ) - min ⁡ ( ϕ w ⁡ ( x ) , ϕ w ⁡ ( y ) ) ] c = ∑ w ∈ l ⁢ [ ϕ w ⁡ ( y ) - min ⁡ ( ϕ w ⁡ ( x ) , ϕ w ⁡ ( y ) ) ] in order to calculate the presented kernels , distances and similarity coefficients , one needs to establish a general model or similarity measures for sequential data . a key instrument for computation of kernel functions is finding words w εl present in two sequences x and y — we refer to these words as matches . for distances and similarity coefficients , we also need to consider words w εl present in x but not in y ( and vice versa )— we refer to these words as mismatches 1 . 1 the term “ mismatch ” herein corresponds to two sequences being unequal and not , as often used in bioinformatics , to inexact matching of sequences . furthermore we introduce an outer function ⊕ which corresponds to the global aggregation performed in many similarity measures , e . g . the summation in various kernel and distance functions . given these definitions , we can express a generic similarity measure s as we can now reformulate the set of distances given in table 6 using the functions ⊕, m + , m x − and m y − . the generalized formulations of some distances are presented in table 8 . adapting similarity coefficients to such a generic representation is even simpler , since only the three summation variables a , b and c need to be reformulated , as shown in table 9 . the classical scheme for computation of similarity measures over sequences utilizes indexed tables , or in the more general case hash tables [ e . g . 4 ]. the words extracted from a sequence and corresponding frequencies or counts are stored in the bins of a hash table . fig8 ( a ) shows two hash tables carrying the words {“ bar ”, “ barn ”, “ card ”} and {“ car ”, “ bank ”, “ band ”, “ card ”} with corresponding counts . algorithm 1 defines the comparison of two hash tables x and y with fixed size m . the algorithm proceeds by looping over all m bins , checking for matching ( c . algorithm 1 : case 1 ) and mismatching words ( cf . algorithm 1 : case 2 & amp ; 3 ). fig8 ( b ) illustrates this process at the mismatches “ bar ” and “ bank ” which are stored in corresponding bins . since the size of the hash tables is fixed at m , the average runtime for a comparison is θ ( m ). to avoid possible hash collisions , a high value of m & gt ;& gt ; l must be chosen in advance , otherwise the chaining of bins ( case 2 ) results in o ( l 2 ) worst - case runtime for o ( l ) extracted words per sequence . a trie is an n - ary tree , whose nodes are n - place vectors with components corresponding to the elements of σ [ 17 ]. fig9 ( a ) shows two tries x and y containing the same words as the hash tables in fig8 ( a ). the nodes of the tries are augmented to carry a variable reflecting the count of the passing sequence . the end of each extracted word is indicated by a marked circle . application of tries to computation of kernel functions has been considered by [ 18 ]. depending on the applied similarity measure the trie nodes can be extended to store other aggregated values which speed up calculations involving subtrees , e . g . for the minkowski distance σ w φ w ( x ) k for all lower words w , comparison of two tries can be carried out as in algorithm 2 : starting at the root nodes , one traverses both tries in parallel , processing matching and mismatching nodes . if the traversal passes two equal and marked nodes , a matching word is discovered ( case 1 ), if only one node is marked a mismatch occurred ( case 2 ). the recursive traversal is stopped if two nodes do not match , and thus two sets of underlying mismatching words are discovered ( case 3 ). fig9 ( b ) shows a snapshot of such a traversal . the nodes x and y are not equal , and the words (“ bar ”, “ barn ”) and (“ band ”, “ bank ”) constitute mismatches . as an invariant , the nodes under consideration in both tries remain at the same depth and thus the worst - case runtime is o ( l ). an advantage of the trie data structure comes into play especially if the provided alphabet is large and a lot of mismatches occur . the traversal discovers mismatching words after passing the first few symbols and omits further unnecessary comparisons . algorithm ⁢ ⁢ 2 . ⁢ ⁢ trie ⁢ - ⁢ based ⁢ ⁢ sequence ⁢ ⁢ comparison 1 ⁢ : ⁢ ⁢ function ⁢ ⁢ compare ⁢ ⁢ ( x , y ) 2 ⁢ : ⁢ ⁢ s ← 0 3 ⁢ : ⁢ ⁢ for ⁢ ⁢ i ← 1 , n ⁢ ⁢ do 4 ⁢ : ⁢ ⁢ x ← child ⁡ [ x , i ] 5 ⁢ : ⁢ ⁢ y ← child ⁡ [ y , i ] 6 ⁢ : ⁢ ⁢ if ⁢ ⁢ x ≠ nil ⁢ ⁢ and ⁢ ⁢ y ≠ nil ⁢ ⁢ then 7 ⁢ : ⁢ ⁢ if ⁢ ⁢ end ⁡ [ x ] ⁢ ⁢ and ⁢ ⁢ end ⁡ [ y ] ⁢ ⁢ then 8 ⁢ : ⁢ ⁢ ⁢ s ← s ⊕ m + ⁡ ( x , y ) ⁢ ⊳ case ⁢ ⁢ 1 9 ⁢ : ⁢ ⁢ else ⁢ ⁢ if ⁢ ⁢ end ⁡ [ x ] ⁢ ⁢ then 10 ⁢ : ⁢ ⁢ ⁢ s ← s ⊕ m - ⁡ ( x ) ⁢ ⊳ case ⁢ ⁢ 2 11 ⁢ : ⁢ ⁢ else ⁢ ⁢ if ⁢ ⁢ end ⁡ [ y ] ⁢ ⁢ then 12 ⁢ : ⁢ ⁢ ⁢ s ← s ⊕ m - ⁡ ( y ) ⁢ ⊳ case ⁢ ⁢ 2 13 ⁢ : ⁢ ⁢ s ← s ⊕ compare ⁢ ⁢ ( x , y ) 14 ⁢ : ⁢ ⁢ else 15 ⁢ : ⁢ ⁢ if ⁢ ⁢ x ≠ nil ⁢ ⁢ then 16 ⁢ : ⁢ ⁢ ⁢ s ← s ⊕ m - ⁡ ( x ) ⁢ ⊳ case ⁢ ⁢ 3 17 ⁢ : ⁢ ⁢ if ⁢ ⁢ y ≠ nil ⁢ ⁢ then 18 ⁢ : ⁢ ⁢ ⁢ s ← s ⊕ m - ⁡ ( y ) ⁢ ⊳ case ⁢ ⁢ 3 19 ⁢ : ⁢ ⁢ return ⁢ ⁢ s efficiency of the two proposed algorithms has been evaluated on four benchmark data sets for sequential data : dna sequences of the human genome [ 19 ], system call traces and connection payloads from the darpa 1999 data set [ 20 ] and news articles from the reuters - 21578 data set [ 21 ]. table 10 gives an overview of the data sets and their specific properties . for each data set 100 sequences were randomly drawn and n - grams of lengths 3 , 5 and 7 extracted . the n - grams of each sequence were stored in tries and hash tables with varying size from 10 2 to 10 6 . subsequently the canberra distance was calculated pairwise over the tries and hash tables using the proposed algorithms , resulting in 5000 comparison operations per setup . the procedure was repeated 10 times and the runtime was averaged over all runs . the experimental results are given in table 11 . the average runtime of the hash - based algorithm strongly depends on the size of the hash table . the optimal value varies for different data sets and values of n . however , in 10 of 12 cases the trie - based algorithm performs equally well or better than the best hash table setup , being independent of a parameter . to demonstrate the proposed algorithms on realistic data , we conducted an experiment for unsupervised learning in network intrusion detection . the underlying network data was generated by the members of our laboratory using virtual network servers . recent network attacks were injected by a penetration - testing expert . a distance - based anomaly detection method [ 22 ] was applied on 5 - grams extracted from byte sequences of tcp connections using different similarity measures : a linear kernel ( euclidean distance ), the manhattan distance and the kulczynski coefficient . results for the common network protocols http , ftp and smtp are given in fig1 . application of the kulczynski coefficient yields the highest detection accuracy . over 78 % of attacks for each protocol are identified with no false - positives . in comparison the euclidean distances fails to uncover good geometric properties for discrimination of attacks in this particular setup . we have shown that , similarly to kernels , a large number of distances and similarity coefficients can be efficiently computed for sequential data . the use of such similarity measures allows one to investigate unusual metrics for application of machine learning in specialized problem domains . as an example , the best results in our experiments on unsupervised learning for network intrusion detection have been obtained with the kulczynski coefficient over n - 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( 2006 ) to appear . we propose a generic algorithm for computation of similarity measures for sequential data . the algorithm uses generalized suffix trees for efficient calculation of various kernel , distance and non - metric similarity functions . its worst - case run - time is linear in the length of sequences and independent of the underlying embedding language , which can cover words , k - grams or all contained subsequences . experiments with network intrusion detection . dna analysis and text processing applications demonstrate the utility of distances and similarity coefficients for sequences as alternatives to classical kernel functions . the ability to operate on sequential data is a vital prerequisite for application of machine learning techniques in many challenging domains . examples of such applications are natural language processing ( text documents ), bioinformatics ( dna and protein sequences ) and computer security ( byte streams or system call traces ). a key instrument for handling such data is the efficient computation of pairwise similarity between sequences . similarity measures can be seen as an abstraction between particular structure of data and learning theory . one of the most successful similarity measures thoroughly studied in recent years is the kernel function [ e . g . 1 - 3 ]. various kernels have been developed for sequential data , starting from the original ideas of watkins [ 4 ] and haussler [ 5 ] and extending to application - specific kernels such as the ones for text and natural language processing [ e . g . 6 - 8 ], bioinformatics [ e . g . 9 - 14 ], spam filtering [ 15 ] and computer security [ e . g . 16 ; 17 ]. although kernel - based learning has gained a major focus in machine learning research , a kernel function is obviously only one of various possibilities for measuring similarity between objects . the choice of a similarity measure is essentially determined by ( a ) understanding of a problem and ( b ) properties of the learning algorithm to be applied . some algorithms operate in vector spaces , others in inner product , metric or even non - metric feature - spaces . investigation of techniques for learning in spaces other than rkhs is currently one of the active research fields in machine learning [ e . g . 18 - 21 ]. the focus of this contribution lies on general similarity measures for sequential data , especially on efficient algorithms for their computation . a large number of such similarity measures can be expressed in a generic form so that a simple linear - time algorithm can be applied for computation of a wide class of similarity measures . this algorithm enables the investigation of alternative representations of problem domain knowledge other than kernel functions . as an example , two applications are presented for which replacement of a kernel — or equivalently , the euclidean distance — with a different similarity measure yields a significant improvement of accuracy in an unsupervised learning scenario . the rest of the paper is organized as follows . section 2 provides a brief review of common similarity measures for sequential data and introduces a generic form in which a large variety of them can be cast . the generalized suffix tree and a corresponding algorithm for linear - time computation of similarity measures are presented in section 3 . finally , the experiments in section 4 demonstrate efficiency and utility of the proposed algorithm on real - world applications : network intrusion detection . dna sequence analysis and text processing . a common way to define similarity measures for sequential data is via explicit embedding into a high - dimensional feature space . a sequence x is defined as concatenation of symbols from a finite alphabet σ . to model the content of a sequence , we consider a language l ⊂ σ * comprising subsequences wεl . we refer to these subsequences as words , even though they may not correspond to a natural language . typical examples for l are a “ bag of words ” [ e . g . 22 ], the set of all sequences of fixed length ( k - grams or k - mers ) [ e . g . 10 ; 23 ] or the set of all contained subsequences [ e . g . 8 ; 24 ]. given a language l , a sequence x can be mapped into an | l |- dimensional feature space by calculating an embedding function φ w ( x ) for every wεl appearing in x . the function φ w is defined as follows φ w : σ *→ r + ∪{ 0 }, φ w ( x ):= ψ ( occ ( w , x ))· w w ( 1 ) where occ ( w , x ) is the number of occurrences of w in x , ψ a numerical transformation , e . g . a conversion to frequencies , and w a weighting assigned to individual words , e . g . length - dependent or frequency - dependent ( tfidf ) weights [ cf . 3 ; 24 ]. by employing the feature space induced through l and φ , one can adapt many vectorial similarity measures to operate on sequences . the feature space defined via explicit embedding is sparse , since the number of non - zero dimensions for each feature vector is bounded by the sequence length . thus the essential parameter for measuring complexity of computation is the sequence length , denoted hereinafter as n . furthermore , the length of a word | w | or in case of a set of words the maximum length is denoted by k . several vectorial kernel and distance functions can be applied to the proposed embedding of sequential data . a list of common functions in terms of l and φ is given in table 12 . beside kernel and distance functions , a set of rather exotic similarity coefficients is also suitable for application to sequential data [ 25 ]. the coefficients are constructed using three summation variables a , b and c , which in the case of binary vectors correspond to the number of matching component pairs ( 1 - 1 ), left mismatching pairs ( 0 - 1 ) and right mismatching pairs ( 1 - 0 ) [ cf . 26 ; 27 ] common similarity coefficients are given in table 13 . for application to non - binary data these summation variables can be extended as proposed in [ 25 ]: a = ∑ w ∈ l ⁢ min ⁡ ( ϕ w ⁡ ( x ) , ϕ w ⁡ ( y ) ) b = ∑ w ∈ l ⁢ [ ϕ w ⁡ ( x ) - min ⁡ ( ϕ w ⁡ ( x ) , ϕ w ⁡ ( y ) ) ] c = ∑ w ∈ l ⁢ [ ϕ w ⁡ ( y ) - min ⁡ ( ϕ w ⁡ ( x ) , ϕ w ⁡ ( y ) ) ] one can easily see that the presented similarity measures can be cast in a generic form that consists of an outer function ⊕ and an inner function m : given this definition , the kernel and distance functions presented in table 1 can be re - formulated in terms of ⊕ and m . adaptation of similarity coefficients to the generic form ( 2 ) involves a reformulation of the summation variables a , b and c . the particular definitions of outer and inner functions for the presented similarity measures are given in table 14 . the polynomial and rbf kernels are not shown since they can be expressed in terms of a linear kernel or a distance respectively . the key to efficient comparison of two sequences lies in considering only the minimum of words necessary for computation of the generic form ( 2 ) of similarity measures . in the case of kernels only the intersection of words in both sequences needs w be considered , while the union of words is needed for calculating distances and non - metric similarity coefficients . a simple and well - known approach for such comparison is representing the words of each sequence in a sorted list . for words of maximum length k such a list can be constructed in o ( kn log n ) using general sorting or o ( kn ) using radix - sort . if the length of words k is unbounded , sorted lists are no longer an option as the sorting time becomes quadratic . thus , special data structures are needed for efficient comparison of sequences . two data structures previously used for computation of kernels are tries [ 28 ; 29 ] and suffix trees [ 30 ]. both have been applied for computation of a variety of kernel functions in o ( kn ) [ 3 , 10 ] and also in o ( n ) run - time using matching statistics [ 24 ]. in this contribution we will argue that a generalized suffix tree is suitable for computation of all similarity measures of the form ( 2 ) in o ( n ) run - time . a generalized suffix tree ( gst ) is a tree containing all suffixes of a set of strings x 1 , . . . , x i [ 31 ]. the simplest way to construct a generalized suffix tree is to extend each string x i with a delimiter $ i and to apply a suffix tree construction algorithm [ e . g . 32 ] to the concatenation of strings x 1 $ 1 . . . x l $ l . in the remaining part we will restrict ourselves to the case of two strings x and y delimited by # and $, computation of an entire similarity matrix using a single gst for a set of strings being a straightforward extension . an example of a generalized suffix tree for the strings “ aab #” and “ babab $” is shown in fig1 ( a ). once a generalized suffix tree is constructed , it remains to determine the number of occurrences occ ( w , x ) and occ ( w , y ) of each word w present in the sequences x and y . unlike the case for kernels for which only nodes corresponding to both sequences need to be considered [ 24 ], the contributions must be correctly computed for all nodes in the generalized suffix tree . the following simple recursive algorithm computes a generic similarity measure between the sequence x and y in one depth - first traversal of the generalized suffix tree ( cf . algorithm 1 ). the algorithm exploits the fact that a leaf in a gst representing a suffix of x contributes exactly 1 to occ ( w , x ) if w is the prefix of this suffix — and similarly for y and occ ( w , y ). as the gst contains all suffixes of x and y , every word w in x and y is represented by at least one leaf . whether a leaf contributes to x or y can be determined by considering the edge at the leaf . due to the uniqueness of the delimiter #, no branching nodes can occur below an edge containing #, thus a leaf node at an edge starting before the index of # must contain a suffix of x ; otherwise it contains a suffix of y . the contributions of all leaves are aggregated in two variables z and y during a post - order traversal . at each node the inner function m of ( 2 ) is calculated using ψ ( x ) and ψ ( y ) according to the embedding φ in ( 1 ). a snapshot of the traversal procedure is illustrated in fig1 ( b ). to account implicit nodes along the edges of the gst and to support weighted embeddings φ , the weighting function weight introduced in [ 24 ] is employed . at a node υ the function takes the beginning ( begin | υ |) and the end ( end | υ |) of the incoming edge and the depth of node ( depth | υ |) as arguments to determine how much the node and edge contribute to the similarity measure , e . g . for k - gram models only nodes up to a path depth of k need to be considered . similarly to the extension of string kernels proposed in [ 33 ], the gst traversal can be performed on an enhanced suffix array [ 34 ] for further run - time and space reduction . to prove correctness of our algorithm , a different approach must be taken than the one in [ 24 ]. we cannot claim that the computed similarity value is equivalent to the one returned by the matching statistic algorithm , since the latter is restricted to kernel functions . instead we show that at each recursive call to the m atch function correct numbers of occurrences are maintained . theorem 1 . a word w occurs occ ( wn , x ) and occ ( w , y ) times in x and y if and only if m atch ( w ) returns x = occ ( w , x ) and y = occ ( w , y ), where w is the node at the end of a path from the root reassembling w in the generalized suffix tree of x and y . proof . if w occurs m times in x , there exist exactly m suffixes of x with w as prefix . since w corresponds to a path from the toot of the gst to a node w all m suffixes must pass w . due to the unique delimiters # each suffix of x corresponds to one leaf node in the gst whose incoming edge contains #. hence m equals occ ( w , x ) and is exactly the aggregated quantity z returned by m atch ( w ). likewise , occ ( w , y ) is the number of suffixes beginning after # and having a prefix w . which is computed by y . in order to illustrate the efficiency of the proposed algorithm , we conducted run - time experiments on three benchmark data sets for sequential data : network connection payloads from the darpa 1999 ids evaluation [ 35 ], news articles from the reuters - 21579 data set [ 36 ] and dna sequences from the human genome [ 14 ]. table 15 gives an overview of the data sets and their specific properties . we compared the run - time of the generalized suffix tree algorithm with a recent trie - based method supporting computation of distances . tries yield better or equal run - time complexity for computation of similarity measures over k - grams than algorithms using indexed arrays and hash tables . a detailed description of the trie - based approach is given in [ 25 ]. note that in all of the following experiments tries were generated in a pre - processing step and the reported run - time corresponds to the comparison procedure only . for each of the three data sets , we implemented the following experimental protocol : the manhauan distances were calculated for 1000 pairs of randomly selected sequences using k - grams as an embedding language . the procedure was repeated 10 times for various values of k , and the run - lime was averaged over all runs . fig1 compares the run - time of sequence comparison algorithms using the generalized suffix trees and tries . on all three data sets the trie - based comparison has a low run - time for small values of n but grows linearly with k . the algorithm using a generalized suffix tree is independent from complexity of the embedding language , although this comes at a price of higher constants due to a more complex data structure . it is obvious that a generalized suffix tree is the algorithm of choice for higher values of k . as a second part of our evaluation , we show that generality of our approach allowing to compute diverse similarity measures pays off when it comes to real applications , especially in an unsupervised learning scenario . the experiments were performed for ( a ) intrusion detection in real network traffic and ( b ) transcription start site ( tss ) recognition in dna sequences . for the first application , network data was generated by members of our laboratory using virtual network servers . recent attacks were injected by a penetration - testing expert . the distance - based anomaly detection method zeta [ 17 ] was applied to 5 - grams extracted from byte sequences of tcp connections using different similarity measures : then linear kernel , the manhattan distance and the kulczynski coefficient the results on network data from the http protocol are shown in fig1 ( a ). application of the kulczynski coefficient yields the highest detection accuracy . over 78 % of all attacks are identified with no false - positives in an unsupervised setup . in comparison , the linear kernel yields roughly 30 % lower detection rates . the second application focused on tss recognition in dna sequences . the data set comprises fixed length dna sequences that either cover the tss of protein coding genes or have been extracted randomly from the interior of genes [ 14 ]. we evaluated three methods on this data : an unsupervised k - nearest neighbor ( knn ) classifier , a supervised and bagged knn classifier and a support vector machine ( svm ). each method was trained and tested using a linear kernel and the manhattan distance as a similarity measure over 4 - grams . fig1 ( b ) shows the performance achieved by the unsupervised and supervised versions of the knn classifier 1 . even though the linear kernel and the manhattan distance yield similar accuracy in a supervised setup , their performance differs significantly in unsupervised application . in the absence of prior knowledge of labels the manhattan distance expresses better discriminative properties for tss recognition than the linear kernel . for the supervised application the classification performance is bounded for both similarity measures , since only some discriminative features for tss recognition are encapsulated in n - gram models [ 14 ]. 1 results for the svm are similar to the supervised knn and have been omitted . kernel functions for sequences have recently gained strong attention in many applications of machine learning , especially in bioinformatics and natural language processing . in this contribution we have shown that other similarity measures such as metric distances or non - metric similarity coefficients can be computed with the same run - time complexity as kernel functions . the proposed algorithm is based on a post - order traversal of a generalized suffix tree of two or more sequences . during the traversal , the counts of matching and mismatching words from an embedding language are computed in time linear in sequence length — regardless of the particular kind of chosen language : words , k - grams or even all consecutive subsequences . by using a generic representation of the considered similarity measures based on an outer and inner function , the same algorithm can be applied for various kernel , distance and similarity functions on sequential data . our experiments demonstrate that the use of general similarity measures can bring significant improvement to learning accuracy — in our case observed for unsupervised learning — and emphasize importance of further investigation of distance - and similarity - based teaming algorithms . the authors gratefully acknowledge the funding from bundesministerium forschung under the project mind ( fkz 01 - 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