KR20120101925A - Apparatus for discovering sequential patterns over data stream using dual tree and method thereof - Google Patents

Abstract

PURPOSE: A device for discovering sequential patterns in a data stream using a dual tree structure and a method thereof are provided to find sequential patterns through MTeISeq structure capable of sequence pattern mining of a 1-item sets sequence, thereby effectively perform a data analysis. CONSTITUTION: A first extracting unit extracts sequence candidate item sets by using a monitoring tree from a data stream(110). A mapping unit maps the sequence candidate item sets in a 1-item set sequence format. A second extract unit extracts a 1-item set frequent sequence from the 1-item set sequence by using the monitoring tree. A generating unit generates an extended sequence composing item sets. A restoring unit restores the 1-item set frequent sequence added the extended sequence to a n-item set frequent sequence. [Reference numerals] (110) Data stream; (150) Generating an extended sequence; (170) n-item set frequent sequence; (AA) Input; (BB) Output; (CC) Mapping table; (DD) n-item set ▶ 1-item set; (EE,160) 1-item set frequent sequence; (FF) Extracting a sequence candidate item set

Description

Apparatus and method for exploring sequential patterns in a data stream using a dual tree structure {APPARATUS FOR DISCOVERING SEQUENTIAL PATTERNS OVER DATA STREAM USING DUAL TREE and method}

The present invention relates to a sequential pattern exploration method, and more particularly, to find a sequence candidate item set, which is a frequent item in each transaction by using an MTestDec structure, and to map these items to a specific ID by using a mapping table. The present invention relates to an apparatus and method for exploring a sequential pattern in a data stream using a dual tree structure that allows a sequential pattern to be found using a MTeISeq structure capable of mining a sequential pattern of a 1-item set sequence.

Data streams that are constantly input by various input methods cannot be processed in limited memory space by the mining method of existing finite data sets. Therefore, in order to extract knowledge from a data stream, it must be possible to obtain meaningful knowledge in a short time with a single data search, to be able to process in limited storage space, and to extract meaningful knowledge extracted from the data stream. There is a condition that needs to be available at any time when user wants. Thus, the mining method in the data stream, unlike the mining method in a finite data set, includes an error in the result.

In the data stream environment, the sequential pattern exploration method considers the time sequence between multiple transactions in comparison to the frequent pattern exploration method for finding frequent items among items in a single transaction or the association rule exploration method for finding frequent items by considering the correlation between items. Find frequent patterns. Therefore, not only whether the itemsets of the frequent sequence constituting the sequential pattern are frequent, but also the order information between these itemsets must be taken into consideration, which requires a lot of computation and requires a large amount of memory. Due to these difficulties, many studies have not been conducted worldwide on sequential pattern mining algorithms in data stream environments.

In the case of sequential pattern mining algorithms targeting 1-item set sequences among the sequential pattern mining methods in the data stream environment that have been studied previously, it is impossible to process a sequence composed of various items which are original definitions of the sequence. For example, it is not possible to handle the case where a customer buys more than one item each time he visits a store. As such, research has begun to enable such treatments.

Recently, sequential pattern mining algorithms targeting n-itemset sequences still need improvement in terms of memory usage and accuracy.

The sliding window IncSPAM algorithm and the time-tilted window method can reduce memory usage, but they are not accurate because they do not maintain consistent information for all sequences. There is a disadvantage that the processing of the sequence is impossible.

In the case of the landmark method, all pattern information generated up to now is managed to have high accuracy, but there are disadvantages of high memory usage and long execution time. The SPAMS algorithm is a landmark algorithm that has this feature, but because it does not manage the potentially frequent data separately and removes infrequent items for the entire SPA (Sequential Patterns Automaton) structure, it is not accurate. Also has problems falling. In addition, since additional information for maintaining the SPA structure must be maintained for each state, more memory is required than the number of nodes.

Accordingly, an object of the present invention is to find a sequence candidate item set, which is a frequent item in each transaction, using an MTestDec structure, and map these items to a specific ID using a mapping table. An apparatus and method for exploring a sequential pattern in a data stream using a dual tree structure that allows the sequential pattern to be found using an MTeISeq structure capable of mining the sequential pattern of a 1-item set sequence after item set sequencing. To provide.

However, the objects of the present invention are not limited to those mentioned above, and other objects not mentioned can be clearly understood by those skilled in the art from the following description.

In order to achieve the above objects, an apparatus for exploring a sequential pattern in a data stream according to an aspect of the present invention, upon receiving a data stream that is an infinite data set consisting of continuously occurring transactions, the monitoring tree from the data stream. A first extracting unit which extracts a sequence candidate item set which is a frequent item in each transaction using an MTestDec structure; A mapping unit for mapping the sequence candidate item sets in the form of a 1-item set sequence; A second extracting unit for extracting a 1-item set frequent sequence from the 1-item set sequence by using a MTeISeq structure which is a monitoring tree; a generating unit for generating an enlarged sequence composed of item sets having k or more items; And a reconstruction unit for restoring the 1-item set frequent sequence to which the enlarged sequence is added to the original n-item set frequent sequence.

Preferably, the first extracting unit extracts a sequence candidate item set that is greater than or equal to a support value set as a user-defined value, wherein the support ratio is a ratio of the number of customers including the corresponding sequence to the total number of customers. The sequence is characterized in that the list is a list of the transactions that occur continuously occur in order of the time the transaction occurred based on the customer identifier.

If necessary, the support is characterized in that the weight is maintained differently for each item according to the passage of time in order to extract a frequent pattern centered on a recent frequent item set.

Preferably, the mapping unit maps each of the sequence candidate item sets to a single ID to map the sequence candidate item sets having less than k items to convert the sequence candidate item sets into a 1-item set sequence. It features.

Preferably, the generation unit generates an enlarged sequence consisting of sequence candidate item sets having k items in which sequence candidate item sets having all k-1 items that are partial item sets exist.

According to another aspect of the present invention, a method for exploring a sequential pattern in a data stream includes (a) an MTestDec structure that is a monitoring tree from the data stream when the data stream is an infinite data set composed of continuously occurring transactions. Extracting sequence candidate item sets that are frequent items in each transaction by using; (b) mapping the sequence candidate item sets in the form of a 1-item set sequence; (c) extracting a 1-item set frequent sequence from the 1-item set sequence by using a MTeISeq structure which is a monitoring tree; (d) generating an enlargement sequence composed of item sets having k or more items; And (e) restoring the 1-item set frequent sequence to which the enlargement sequence is added to the original n-item set frequent sequence.

Preferably, the step (a) extracts the sequence candidate item sets that are greater than or equal to a support value set to a user-defined value, wherein the support is the number of customers including the corresponding sequence for the total number of customers. The sequence is characterized in that the sequence is a list of continuously occurring transactions grouped in order of the time the transaction occurred based on the customer identifier.

If necessary, the support is characterized in that the weight is maintained differently for each item according to the passage of time in order to extract a frequent pattern centered on a recent frequent item set.

Preferably, the step (b) maps each of the sequence candidate item sets to a single ID in order to convert the sequence candidate item sets into a 1-item set sequence, and includes sequence candidate item sets having less than k items. It is characterized in that the mapping.

Preferably, the step (d) is characterized by generating an enlarged sequence consisting of sequence candidate item sets having k items in which sequence candidate item sets having all k-1 items that are partial item sets exist. .

Through this, the present invention finds the sequence candidate item sets, which are frequent items in each transaction by using the MTestDec structure, and maps these items to specific IDs using the mapping table to sequence 1-item sets, and then 1-item sets. By using the MTeISeq structure, which enables the sequential pattern mining of the sequence, the sequential pattern can be found, thereby making it possible to analyze data such as customer-specific usage patterns more quickly and effectively.

In addition, the present invention uses the MTestDec structure to find the sequence candidate item sets, which are frequent items in each transaction, and map these items to specific IDs using a mapping table to sequence the 1-item set and then 1-item set sequence. By using the MTelSeq structure capable of mining the sequential pattern, the sequential pattern is found, but the mining operation is performed by excluding candidate sequences composed of item sets having a length of k or more among the item sets, thereby reducing memory usage.

In addition, the present invention performs a mining operation by excluding candidate sequences consisting of item sets having a length of k or more among the item sets, and performing a reconstruction process using an enlarged sequence, thereby reducing the accuracy lost due to the limitation of the length of the item sets. There is a complementary effect.

1 is an exemplary view showing an apparatus for exploring a sequential pattern according to an embodiment of the present invention.
2 is an exemplary view for explaining a preprocessing process of a sequence transaction according to an embodiment of the present invention.
3 is an exemplary diagram illustrating a mapping table of estDuT according to an embodiment of the present invention.
4 is an exemplary diagram for describing a mapping process of a sequence candidate item set according to an embodiment of the present invention.
5 is an exemplary diagram for explaining a 1-itemset sequence mapping technique according to an embodiment of the present invention.
6 is a first exemplary diagram for explaining a 1-itemset sequence transformation technique according to an embodiment of the present invention.
FIG. 7 is a second exemplary view for explaining a 1-itemset sequence transformation technique according to an embodiment of the present invention. FIG.
8 is an exemplary diagram for explaining a principle of generating an enlarged sequence according to an embodiment of the present invention.
9 is a graph showing memory usage according to a change in the length limit value k of a sequence candidate item set according to an embodiment of the present invention.
10 is a graph showing execution time according to a change in the length limit value k of a sequence candidate item set according to an embodiment of the present invention.
11 is a graph showing precision and recall according to a change in the sequence candidate item set length limit value k according to an embodiment of the present invention.
12 is a graph illustrating an ASE according to a change in the sequence candidate item set length limit value k according to an embodiment of the present invention.
13 is a graph showing the performance according to the Ssig value change of the estDuT according to an embodiment of the present invention.
14 is a graph showing the performance according to the application (decay) according to an embodiment of the present invention.
FIG. 15 is a graph showing the results of experiments comparing the accuracy (Precision, Recall) of estDuT and SPAMS according to an embodiment of the present invention. FIG.
16 is a graph showing the results of experiments comparing the accuracy (ASE) of estDuT and SPAMS according to an embodiment of the present invention.
17 is a graph showing performance evaluation results in a long sequence according to an embodiment of the present invention.
18 is an exemplary view showing a method for exploring a sequential pattern according to an embodiment of the present invention.

Hereinafter, an apparatus and method for exploring a sequential pattern in a data stream using a dual tree structure according to an embodiment of the present invention will be described with reference to FIGS. 1 to 18. It will be described in detail focusing on the parts necessary to understand the operation and action according to the present invention. Like reference numerals in the drawings denote like elements throughout the specification.

The present invention proposes a new sequential pattern mining structure, estDuT (estmation Dual Trees for sequential pattern mining), to improve the problem of existing SPAMS. Here, estDuT is MTestDec, which is a monitoring tree of the estDec algorithm for detecting frequent itemsets of a sequence, a mapping table used for converting n-itemsets to 1-itemsets, and a frequent sequence from 1-itemsets. This structure consists of MTeISeq, which is a monitoring tree of the eISeq algorithm for discovery.It reduces the memory usage by performing mining operations by excluding candidate sequences composed of item sets having lengths of k or more among the item sets, and generates items by generating enlarged sequences. This method compensates for the accuracy that is lost due to the length limitation of the set.

1 is an exemplary view showing an apparatus for exploring a sequential pattern according to an embodiment of the present invention.

As shown in FIG. 1, an apparatus for exploring a sequential pattern according to the present invention includes an input unit 110, a first extractor 120, a mapping unit 130, a second extractor 140, and a generator ( 150, the restoration unit 160, the output unit 170, and the like.

The input unit 110 may receive a data stream, which is an infinite data set composed of continuously occurring transactions. Here, in the data set that is the subject of data mining, all unit information appearing in the application domain is defined as a unit item, and the unit information having semantic concurrency (that is, semantically occurring together) in the application domain is defined. A meeting is defined as a transaction.

In this case, the data stream for finding frequent item information includes a transaction ID (TID) and item information, and may be defined as follows.

i) item set I = {i ₁ , i ₂ ,... , i _n } is a set of items generated through transactions up to now, and the item may represent unit information in an application domain.

ii) When P (I) is the set of itemsets I, e ∈ {P (I) ?? The e satisfying {??}} is called an item set, and the length of the item set | e | means the number of items constituting the item set e, and the arbitrary item set e is the length of the item set. Can be defined as | e | -itemset. In general, the 3-item set {a, b, c} can be simply expressed as abc.

iii) A transaction is a subset of I, not an empty set, and each transaction can have a transaction identifier TID and a customer identifier CID. A transaction added to the data set in the k-th order is denoted by T _k , and the TID of T _k may denote k.

iv) When a new transaction T _k is added, the current data set D _k occurs so far that all of the added transactions, that is, D _k = <T ₁ , T ₂ ,. , T _k >. Therefore, | D _k | may refer to the total number of transactions included in the current data set Dk.

v) When T _k is the current transaction, the current frequency of occurrence for any set of items e is defined as C _k (e), which can represent the number of transactions that contain e in the k transaction to date. Similarly, the support of a set of items, S _k (e), is the total number of transactions so far | D _k | It can be defined as the ratio of the frequency of occurrence C _k (e) to the set of items e.

In addition, the data stream for sequential pattern mining is composed of a customer ID (CID), the occurrence time of the transaction, item information can be defined as an infinite set of transactions that occur continuously as follows.

i) sequence s = <s ₁ , s ₂ ,... , s _m > may refer to a list of continuously occurring transactions in chronological order based on the customer identifier CID. s _j represents one set of items e, and one customer cannot have more than one transaction within the same transaction unit time.

ii) The length | s | of the sequence means the number of itemsets e constituting the sequence, and any sequence s can be defined as | s | -sequence according to the length of the sequence. In general, the 3-sequence can be expressed simply as <(a, b), (b), (a, c, d)> as <(ab) (b) (acd)>.

iii) For the k sequences that have occurred so far, the count C _k (s) of the sequence so far may represent the number of customers containing s. The sequence support S _k (s) may represent the ratio of C _k (s) in the total number of customers generated so far.

iv) the sequence s _a = <a ₁ , a ₂ ,. , a _n > and s _b = <b ₁ , b ₂ ,.. , b _m >, 1 ≦ j ₁ <j ₂ <. s _a is called a sub-sequence of s _b if <j _n ≤ m satisfies the relationship a _n ⊆ b _jn . For example, the sequence of <(1 2) (3) (4 5)> is a partial sequence of <(1 2 5) (3 4) (4 5)>, while <(1) (2)> is <(1 2)> is not a partial sequence. In contrast, sb becomes the supersequence of sa. For example, <(1 2 5) (3 4) (4 5)> is an enlarged set of <(1 2) (3) (4 5)>.

Further, according to the above definitions, when the support S _k (e) of the item set e has a value equal to or more than a predefined minimum support S _min , e is called a frequent item set in the current data stream D _k , and the sequence s When s of support S _k (s) has a value equal to or more than a predefined minimum support S _min , s may be defined as a frequent sequence in the current data stream D _k .

The first extractor 120 may extract sequence candidate item sets, which are frequent items in each transaction, using the MTestDec structure, which is a monitoring tree of the estDec algorithm, from the received data stream. Here, MTestDec plays a role of finding the sequence candidate item set e _c of the currently occurring transaction by exploring this tree with a monitoring prefix tree generated using the estDec algorithm to maintain the frequent item set information of the sequence transaction. Can be.

The process of extracting the sequence candidate item sets will be described in detail as follows.

First, the present invention performs a preprocessing process for converting a sequence transaction into a unit sequence transaction type since a frequent sequence appearing within a specific period is searched for an unspecified number of customers.

2 is an exemplary view for explaining a preprocessing process of a sequence transaction according to an embodiment of the present invention.

As shown in FIG. 2, when a transaction occurs, after a user-defined collection activity for a predetermined time, the transactions having the same customer identifier ID (CID) are grouped together to sort the transactions occurring from one customer in the order in which the transaction occurs. Can be. The sorted customer-specific transaction information can be used to create a sequence for that customer.

The sequential pattern mining process is performed by the estDuT method proposed by the present invention using a sequence obtained after the preprocessing of the sequence transaction.

It is not necessary to check the frequency of sequences for every set of items to find the frequent sequences. If one of the items in the sequence does not occur frequently, the sequence cannot be seen as a frequent sequence. In this paper, we tried to reduce the cost of sequential pattern exploration by eliminating these infrequent items. The MTestDec structure is used to monitor the information of the set of items that will make up the sequence in real time, allowing you to perform sequential pattern exploration only on the frequently occurring itemsets. In the present invention, a frequently occurring item set is referred to as a sequence candidate item set e _c and defined as follows.

Definition 1. Sequence candidate item set e _c

} 와 S_k(e_c) ≥ S_sig 을 만족하는 e_c를 시퀀스 후보항목집합이라고 한다. 시퀀스후보항목집합의 길이 |e_c|는 e_c를 구성하는 항목의 수를 의미하며, 임의의 시퀀스후보항목집합 e_c는 해당 항목집합의 길이에 따라 |e_c|-시퀀스 후보항목집합이라 정의할 수 있다.When P (e) is the set of item set e, e _c ∈ {P (e)-

} And _k is referred to as S (e _c) ≥ S _c e _sig set a sequence of candidate entries satisfying. The length of the sequence candidate item set | e _c | means the number of items constituting e _c , and the arbitrary sequence candidate item set e _c is defined as the | e _c | -sequence candidate item set according to the length of the corresponding item set. can do.

For example, if {1}, {2}, and {1,2} of the subsets of the {1,2,3} subset have a value greater than or equal to the minimum map, the sequence of the {1,2,3} subset Candidate item sets are {{1}, {2}, {1,2}}.

As mentioned above, the present invention finds the sequence candidate item set e _c using MTestDec, which is a monitoring tree of the estDec algorithm, which is a frequent pattern mining method in a data stream environment. However, since the definition of support for a sequence is different from the definition of support used in the existing frequent pattern mining method, if a frequent item is found using Tid of a transaction that has not been preprocessed, the sequence candidate item set that will be the item set of the frequent sequence e _c cannot be found. Therefore, we want to define a new transaction as follows.

Definition 2. Transaction T _F

For sequence s _k , which occurs when CID is k, s _k is n transactions <T _k1 , T _k2,. , T _kn >, the definition of transaction T _F to find the sequence candidate item set e _c with a value equal to or greater than the critical support S _sig can be expressed as:

T _F = <T _F1.tid , T _F2.tid ,.. , T _Fn.tid >

T _F1.tid = k, T _F1.itemset = T _k1.itemset

T _F2.tid = k, T _F2.itemset = T _k2.itemset

...

T _Fn.tid = k, T _Fn.itemset = T _kn.itemset

The T _F obtained through definition 2 is composed of MTestDec, which is a potential tree for T _F , using the estDec method, which is a frequent pattern exploration method. Using the MTestDec configured as described above, all the candidate candidate sets greater than or equal to the critical support S _sing ∈ (0, S _min ) previously set to the user-defined value of estDec can be obtained.

In static databases, the count for a transaction does not change and the number of transactions is constant. Therefore, the frequent item set can be kept constant because there is no change in transaction support in the database. However, in the data stream environment, since the total number of transactions is constantly changing, the support of the transaction is not always maintained but always changes. Therefore, even if a frequent item set results in a longer appearance period of a transaction including the item set, the count of the item set is not counted, but only the count of the entire transaction is increased. At this time, the support of the item set temporarily does not satisfy the minimum map, and thus is excluded from the frequent candidate item set. In this case, because the item set is missing from the sequence candidate item set, the sequence transaction is not generated in the step of generating a candidate sequence which is a transaction of MTeISeq. Therefore, in the present invention, in order to handle such potentially frequent item sets, not only frequent items of MTestDec but also important item sets are defined as sequence candidate item sets.

The mapping unit 130 may map or convert the sequence candidate item sets into a 1-item set sequence using a mapping table.

The process of mapping in the form of such a 1-item set sequence will be described in detail as follows.

In order to find a frequent sequence using the MTeISeq structure in a sequence composed of n-item sets, a conversion to a 1-item set sequence is required. Accordingly, in the present invention, each sequence candidate item set obtained by using the frequent items of the MTestDec structure is mapped to a unique ID representing the item set of the original transaction, and the candidate sequence is mapped using the mapped ID. Create Through this process, the n-itemset sequence may be converted into a 1-itemset sequence.

i) Sequence candidate set mapping

3 is an exemplary diagram illustrating a mapping table of estDuT according to an embodiment of the present invention.

As shown in Fig. 3, the sequence candidate item sets of the previous step, that is, the sequence candidate item sets in Fig. 2, represent the respective item sets in order to change the n-item set sequence into the form of the 1-item set sequence. Can be mapped to a unique ID. Therefore, the sequence candidate item sets stored in the mapping table are all frequent item sets.

4 is an exemplary diagram for describing a mapping process of a sequence candidate item set according to an embodiment of the present invention.

As shown in FIG. 4, whenever a new sequence candidate item set occurs, a mapping ID is sequentially assigned, and if the sequence candidate item set already exists in the mapping table, a corresponding mapping ID is assigned to the sequence candidate item set. Can be. As the number of sequence candidate item sets increases, the cost of searching for the sequence candidate item sets in the mapping table increases, so the search cost can be reduced by using a hash table data structure.

ii) length limited sequence candidate items

In the case of an item set having n items as elements, the maximum number of candidate item sets that can be assumed when all candidate item sets are frequent is 2 ⁿ at most. Therefore, in the case of a sequence having ^m itemsets, there is (2 ⁿ ) ^{m possible} combinations of candidate sequences. Therefore, the number of candidate sequences to be processed for one sequence increases exponentially, requiring a large processing cost. In this paper, we want to reduce the number of sequence candidate item sets created by limiting the number of items in the sequence candidate item set to reduce the processing cost.

Definition 3. k-sequence candidate item set e _c.k

When the number of items that the user wants to limit is k, the sequence candidate item set e _c having less than k items is called k-sequence candidate item set e _ck . The number of k-sequence candidate item sets | e _ck | is defined as follows according to the method of obtaining the number of 멱 sets.

For a sequence that owns m itemsets according to definition 3, the maximum possible combination of candidate sequences is | e _ck | ^{m will} be. As a result, limiting the number of items in the number of items to k (k <n) yields 2-(nCk-1 + nCk-2 +…) rather than generating subitems for all items (k = n). Since + nC1) subsets are not generated, the number of candidate sequences to be processed by the algorithm can be effectively reduced. However, in this method, the mining operation for the entire sequence candidate item set is not performed, which may cause an error in terms of accuracy.

Definition 4. Potentially frequent k-item set PLI _k

For the k-item set I _k , if I _k is frequent according to the Apriori principle, then the subitem sets I _(k-1) of this set are also frequent. Thus, if all I _(k-1) are frequent inversely, then I _k may be a frequent or non-frequent item set. Thus, I _k is a potentially frequent set of items. Therefore, all I _(k-1) define the frequent I _k as PLI _k , a potentially frequent k-item set.

According to definition 4, the PLI _k can be found using the (k-1) -item sets. However, as defined, just because all (k-1) -itemsets are frequent, a k-itemset is not necessarily a frequent itemset. In other words, since PLI _k is assumed to be a frequent set of items by inference, there is a possibility that it is not frequent. Therefore, there is a possibility that a false positive error occurs in the frequent sequence finally obtained through the algorithm of the present invention.

In the algorithm of the present invention, by using the k-sequence candidate set, the processing cost can be reduced instead of generating an error for the frequent items. In the case of a sequence candidate item set having a length of k or more, after the algorithms are all performed, the sequence candidate item sets can be recovered through a simple post-processing process using a method of obtaining PLI _k of the _k -sequence candidate item sets. This restoration process will be described in detail later.

5 is an exemplary diagram for explaining a 1-itemset sequence mapping technique according to an embodiment of the present invention.

As shown in FIG. 5, the 1-itemset sequence mapping technique according to the present invention is represented by an algorithm. Since MTestDec is a prefix tree, it attempts to match all subsets of the current transaction using depth-first search, as shown in Figure (a), and checks whether the existing k-sequence candidate sets are shown in Figure (b). Check it.

iii) 1-itemset sequence transformation

Since MTeIseq can only detect frequent sequences for 1-item sets, a method of converting n-item set sequences to 1-item set sequences is required. Accordingly, in the present invention, the k-sequence candidate sets found in MTestDec are mapped to a single ID, and the combinations thereof are converted into a 1-item set sequence.

The mapping ID does not exist for these sequence candidate item sets because the sequence candidate item sets or the length candidate k lengths greater than k that are not frequent in MTestDec are excluded in ii). Therefore, it is possible to convert to the form of 1-item set sequence by using only the k-sequence candidate item set in which mapping IDs except these exist. An example of such a 1-itemset sequence transformation technique is as follows.

FIG. 6 is a first exemplary diagram for explaining a one-item set sequence transformation technique according to an embodiment of the present invention, and FIG. 7 is a second illustration for explaining a one-item set sequence transformation technique according to an embodiment of the present invention. It is an illustration.

As shown in FIG. 6 to FIG. 7, a process of converting an original sequence having a k-sequence candidate item set into a 1-item set sequence form in order to be used in MTeISeq using the mapping ID of the mapping table is shown. . This process begins when one sequence occurs, and is repeated until all k-sequence candidate sets of the sequence are mapped and combined to convert them into the form of all possible candidate 1-item set sequences.

In FIG. 7, an algorithm is used to convert a 1-item set sequence.

The second extractor 140 may extract the 1-item set frequent sequence from the 1-item set sequence using the MTeISeq structure which is a monitoring tree.

A process of extracting the 1-item set frequent sequence will be described in detail as follows.

In order to find the frequent sequences using the candidate sequences transformed in the form of 1-item sequence in the previous step, the eISeq method is used to find the frequent sequences of the 1-item set sequence in the data stream. Since the k-sequence candidate item sets are mapped in the form of ID, the nodes present in the MTeISeq represent the k-sequence candidate item sets corresponding to the mapping IDs, and can be searched along the path of the MTeISeq to find frequent sequences. That is, MTeISeq in estDuT contains time order information between k-sequence candidate itemsets.

At this time, even if the number of items in the item set is limited, the number of items to be monitored is still large, and thus still requires a lot of memory and execution time. However, recently frequent items in a data stream environment may have more important values than frequent items in the past. In such a case, space of the memory is unnecessarily consumed in order to keep the information of the frequent items in the past. In general, the mining method of the landmark type maintains the same support as the recently generated items, even if the items have passed for a long time and cannot be distinguished from the items that were frequently used in the past.

In order to solve this problem, the estDec method or the eISeq method has applied attenuation rate to maintain the weight of item support differently over time, thereby making it possible to extract the frequent pattern centered on the frequent itemsets. Therefore, by applying the decay rate to each tree of estDuT, it is possible to optimize the algorithm around recently frequent items, so that a frequent sequence can be obtained using a small amount of memory at a faster time.

In this case, items that occurred only frequently in the past are often lost in the monitoring tree due to the decay rate, thereby saving memory. In the present invention, by applying the attenuation rate to both MTestDec and MTeISeq, it is possible to minimize the memory usage by reducing the support rate for a certain period of time.

The generation unit 150 may generate an enlargement sequence composed of item sets having a length of k or more and add the generated enlargement sequence to the 1-item set frequent sequence.

The process of creating and adding such an enlarged sequence will now be described in detail.

Using a method of inferring PLI _k according to definition 4, it consists of a set of k-sequence candidates that are potentially PLI _k with only the results of frequent sequences consisting of (k-1) -sequence candidate sets. Infer the expansion sequence es. Obtain a PLI _k from the first (k-1) -sequence candidate set that constitutes the frequent sequence to form a new magnification sequence, and for each subsequent (k-1) -sequence candidate set, add a new Configure. This same method can be repeated to restore all potentially frequent magnification sequences up to the magnification sequence consisting of n-sequence candidate sets in the same manner. The restoration procedure proceeds through the following steps.

i) A set of n frequent sequences FS = {f _s1 , f _s2 ,... found as a result of sequential pattern mining using the estDuT method. , f _sn } selects a random sequence f _si (1 ≦ i ≦ n).

ii) any sequence f _si = <s _i1 , s _i2 ,... For s _im >, select s _ia (1 ≦ a ≦ m).

iii) Compare the selected sequence f _si with the rest of the other sequences in the FS. According to definition 4, in order to become an enlargement sequence of f _si , all (k-1) -sequence candidate sets that are sub-items of the k-sequence candidate sets constituting the enlargement sequence must be frequent. Thus, _"when referred to, f _si, the sequence to be compared. F f _{si si} is _{s ij = s i'j (j ≠} a, 1 ≤ j ≤ m) of (k-1) - sequence of the candidate set of items Must consist of

iv) comparing all (k-1) _-sequence candidate sets f _sia with all f _si'a to see if all (k-1) _-sequence candidate sets exist to generate k-sequence candidate sets. If present, f _sia creates an expansion sequence whose k-sequence candidate set is added to FS.

v) Repeat steps ii) to iv) for all sequence candidate items in s _i .

vi) Repeat steps i) to v) to generate all possible magnification sequences. This is a candidate for a potentially frequent sequence.

8 is an exemplary diagram for explaining a principle of generating an enlarged sequence according to an embodiment of the present invention.

As shown in FIG. 8, it is shown that when k = 3, an enlarged sequence consisting of item sets having a length of k or more is generated using a (k-1) -sequence candidate item set.

Since the magnification sequence generated through this process is a potentially frequent sequence, it needs to be verified using MTestDec. Therefore, we check to see if all the sequences in the sequence actually exist in MTestDec.

i) Select any sequence s (s ∈ FS) and select a set of sequence candidate items with a length greater than or equal to k.

ii) Check if the corresponding sequence candidate item set exists in MTestDec.

iii) If it does not exist in MTestDec, the sequence is not a frequent sequence and thus false false error. Therefore, the sequence is deleted.

iv) Repeat steps i) to iii) to remove the magnification sequences that are false positive errors.

However, verification with MTestDec does not eliminate all false positive errors. For example, {23}, {24}, {34}, and {2} all exist in MTestDec as a sequence candidate set, and the sequence <(23) (2)>, <(34) (2)>, If <(24) (2)> exists in the MTeISeq as a frequent sequence, an enlargement sequence called <(234) (2)> may be generated. In this case, even if {234} is a frequent item set in MTestDec, it is not necessarily frequent that a sequence candidate item set called {2} occurs after a sequence candidate item set called {234}. That is, in a sequence, not only the frequent occurrence of a single item set but also the temporal order among the item sets must be frequent, such a factor may be a factor causing a false positive error.

Since the extended sequence does not directly count the frequency of occurrence of the sequence using MTeISeq, it is not possible to obtain an accurate support value.However, using the Apriori principle mentioned in definition 4, the range of support can be estimated.

Definition 5. Support for Magnification Sequence es

The support of the extended sequence es is the sequence s _i (s ∈ FS, 1 <i≤ n, n = _k with the (k-1) -sequence candidate set of PLI _k (∈ es) among the sequence candidate items of es). C _k-1 ) is determined by the minimum value of the support of the sequence candidate item set e _ck of the MTestDec tree corresponding to PLI _k .

S (es) = min (S (s ₁ ), S (s ₂ ),…, S (s _n ), S (e _ck ))

Definition 5 can be used to obtain the support of the magnification sequence es. According to the Apriori principle of definition 4, if the k-sequence candidate set PLI _k is frequent, then all (k-1) -sequence candidate sets that produce PLI _k must also be frequent. Thus, the sequence support composed of the (k-1) -sequence candidate sets should always be less than or equal to the support of the extended sequence es with PLI _k generated through them. In addition, the support of PLI _k must have the same value as the support of the sequence candidate item set e _ck of the MTestDec tree. Therefore, the support of the expansion sequence es composed of PLI _k cannot have a value larger than the support of e _ck . Therefore, the support of the extended sequence es can be inferred to the minimum value of the support of the e _ck and the support of the sequence consisting of the (k-1) -sequence candidate sets of PLI _k .

The restoration unit 160 may restore the 1-item set frequent sequence to which the enlargement sequence is added to the original n-item set frequent sequence.

The output unit 170 may output the restored original n-item set frequent sequence in real time.

Hereinafter, the results of verifying the performance of the estDuT method proposed by the present invention through various experiments will be described.

The data used in the experiment was generated using the IBM dataset generator. In each experiment, it is assumed that the data set occurs repeatedly, and preprocessing for the sequence is assumed to occur every time the data set is repeated once, and the preprocessing process is not reflected in the experimental data. In all experiments, the critical support Ssig is defined as the relative value of the minimum support Smin, and when the user-defined threshold Ssig is expressed in p%, the actual value of Ssig is Smin * (p / 100). In all experiments, the forced cell of the tree was performed when the CID was a multiple of 100, and the set values of minimum support Smin and critical support Ssig remain the same in MTestDec and MTeISeq unless otherwise indicated. All experiments were performed on quad-core 2.4GHz computers with 4GB of memory and the 2.6.26 Linux kernel, and the estDuT algorithm was all implemented in C. The memory usage and execution time of the algorithm are compared with SPAMS, which is a sequential pattern mining algorithm of landmark data stream environment such as estDuT, and the accuracy of the algorithm is the result of SPAM, a sequential pattern mining method in finite data set Measurement was based on the set. Mining methods on finite datasets, such as the SPAM algorithm, always have accurate results because the entire transaction is limited. Therefore, it is suitable for use as a correct answer for comparing the accuracy of data stream mining.

In the present invention, an experiment for evaluating the performance and accuracy of the algorithm was performed using the following data sets.

[Table 1]

Each data set was set to a parameter value for generating data suitable for the purpose of experiment, and each parameter value was defined as shown in [Table 2] below.

[Table 2]

In the data set D0.1C3T1S3I1N0.03, the number of customers is 100, the average number of transactions generated by one customer is three, and the average number of items in one transaction is three. In addition, this data set is composed of 30 different items. The average length of the frequent sequences is 3 and the size of the itemsets of the frequent sequences is 1.

The density of the generated data set is defined as follows.

Therefore, the density rho (R) of the data set R = D0.1C3T1S3I1N0.03 is ㅧ 100 = 3.33 (%).

9 is a graph showing memory usage according to a change in the length limit value k of a sequence candidate item set according to an embodiment of the present invention.

As shown in Figure 9, data sets of D0.1C3T1S3I1N0.03, D0.1C3T1.5S3I1.5N0.03, D0.1C3T2S3I2N0.03, D0.1C3T2.5S3I2.5N0.03, and D0.1C3T3S3I3N0.03 are used. Therefore, when Smin is 0.05 and Ssig is 90%, the maximum memory usage change and its effect according to the change of the length limit value k of the sequence candidate item set are shown. Figure (a) shows the maximum memory usage of MTestDec. MTestDec maintains all item sets above Ssig regardless of the length limit value k of the sequence candidate item set. Figure (b) shows the maximum memory usage of the MTeISeq. As the value of k is limited to a small value, the number of sequence candidate item sets decreases, thereby reducing the memory usage. Figure (c) shows the memory usage of the mapping table. The sequence candidate item set that is not created due to the k value restriction is not recorded in the mapping table. Therefore, the smaller the k value, the smaller the memory usage.

10 is a graph showing execution time according to a change in the length limit value k of a sequence candidate item set according to an embodiment of the present invention.

As shown in Figure 10, it is a comparison of the average execution time of the same experiment as in FIG. Figure (a) shows the average execution time of MTestDec. Unlike the memory usage of MTestDec, the execution time increases as the value of k increases. This cost is incurred in the matching process to find the k-sequence candidate itemsets, which reduces the execution time of the algorithm by not attempting matching when the lengths of the itemsets are larger than k. Figures (b) and (c) show the average execution time of the MTeISeq and the mapping table, which vary greatly depending on the value of k. Overall, the execution time increases with the value of k, but it can be seen that the execution time increases significantly, especially in dense data sets.

11 is a graph showing precision and recall according to a change in the sequence candidate item set length limit value k according to an embodiment of the present invention.

As shown in FIG. 11, when Smin is 0.05 and Ssig is 90% using the same data set as in FIG. 9, the length of the sequence candidate item set before and after the post-processing operation for restoring the frequent sequence using the enlarged sequence. It is a graph of precision and recall as the limit value k changes. As an algorithm to compare the accuracy, SPAM was used. As can be seen in Figures (a) and (b), the smaller the value of k, the lower the accuracy after post-processing. If the value of k is 1, since the generated magnification sequence is infinitely large, it is impossible to measure because the memory usage is exceeded. However, in this case, since a magnification sequence is generated for all frequent items of length 1, there is no frequent sequence that is missed according to definition 4. Therefore, the recall rate is always maintained at 100%, but the accuracy rate drops significantly because it generates a large number of false positive values. Therefore, the value of k must be selected to be greater than 1 because it is obvious that this is a very inefficient method.

Comparing Figures (c) and (d) shows that the reproducibility of k = 3 and k = 4 does not improve much for this dataset. The reason why the reproducibility is poor when k = 3 and k = 4 is an error that occurs in the data stream environment. That is, the post-processing restoration work through the magnification sequence may reduce the error in the data stream environment.

Therefore, the value of k in this data set is best suited to 2, which does not drop the accuracy rate significantly, uses less memory, and shows a short execution time. The reason for the lower accuracy after post-processing restoration is that the smaller the value of k, the greater the number of escalation sequences es that must be inferred using the potentially frequent item set PLIk. In this process, a false positive that is considered to be frequent even though it is not actually frequent is generated, which affects the accuracy rate.

12 is a graph illustrating an ASE according to a change in the sequence candidate item set length limit value k according to an embodiment of the present invention.

에 대해 다음과 같이 정의한다.As shown in FIG. 12, when Smin is 0.05 and Ssig is 90% for the same data set as in FIG. 9, it is a graph of the ASE value according to the change of the length limit value k of the sequence candidate item set. As an algorithm for comparing the accuracy, SPAM [7] was used. Average Support Error (ASE), as defined in [8], is used to measure the relative accuracy of the proposed method. It is used as a modified equation to compare sequences instead of comparing sets of items. Thus, two frequent sequence result sets = R1

For.

| R1 | represents the number of sequences of the result set R1. The smaller the ASE (R2 | R1), the closer the mining result set of R2 is to the result set of R1. In Figure 12, ASE (RestDuT | RSPAM) is used to represent the accuracy of the sequential pattern mining results. Here, RestDuT and RSPAM represent mining results obtained by the estDuT and SPAM algorithms, respectively. In Figure (b), the accuracy rate is reduced due to the creation of the PLIk magnification sequence, so when k = 2 in Figures (a) and (b), the ASE value compared to the mining result of SPAM is relatively large. . The reason why the ASE value of the data set D0.1C3T3S3I3N0.03 did not decrease significantly after post-processing is an error due to an exploration method that occurs because of the data stream environment. Therefore, the estDuT method has an effect on memory usage and algorithm execution time depending on the length limit of the sequence candidate item set. However, the accuracy of the estDuT method is poor.

13 is a graph showing the performance according to the Ssig value change of the estDuT according to an embodiment of the present invention.

As shown in FIG. 13, k = in D0.1C3T4S3I1.25N4, D0.1C3T4S3I1.25N0.8, D0.1C3T4S3I1.25N0.4, D0.1C3T4S3I1.25N0.08, D0.1C3T4S3I1.25N0.04 datasets. When 2 and Smin is 0.1, we show the performance of the estDuT algorithm as the Ssig changes. As you can see in Figure 13, as the dataset density increases, the memory usage increases and the execution time increases. The result is that as the density of the data set increases, more frequent item sets and frequent sequences appear, which increases the number of item sets that have greater support than Ssig. appear. Therefore, increasing the value of Ssig reduces the number of nodes maintained in MTestDec or MTeISeq and reduces the size of the mapping table, reducing memory usage and execution time as shown in Figure 13. Therefore, it is possible to control the memory usage and execution time by adjusting the Ssig value according to the characteristics of the data.

14 is a graph showing the performance according to the application (decay) according to an embodiment of the present invention.

As shown in FIG. 14, when Smin is 0.05 and Ssig is 90% for the same data sets as in FIG. 13, a performance comparison result of estDuT and SPAMS according to the data set is shown. In this experiment, the decay half-life parameters were set to 10000, 30000, and 50000 for further performance comparison with the optimized estDuT. estDuT uses less memory than SPAMS, but the denser the data set, the longer the execution time compared to SPAMS. This is because when the density of the data set is increased, the frequency of occurrence of each item increases and accordingly, the number of sequence candidate item sets that MTestDec should monitor increases. Similarly, SPAMS increases the number of frequent sequences that need to be managed according to density, so you can see that more memory uses more memory. However, since SPAMS has a lot of additional information to manage to maintain SPA structure, it uses more memory than estDuT as shown in Fig. (A). However, estDuT requires the process of generating a sequence candidate item set, so if the density increases and the item information to be maintained increases, it takes a long time to execute as shown in (b). Therefore, by applying the concept of decay mentioned above, as shown in FIG. 14, the memory usage and execution time of the algorithm can be partially reduced.

FIG. 15 is a graph showing the results of experiments comparing the accuracy (Precision, Recall) of estDuT and SPAMS according to an embodiment of the present invention. FIG.

As shown in FIG. 15, when Smin is 0.05 and Ssig is 90% using the data set as shown in FIG. 14, the accuracy rate according to the data set of estDuT and SPAMS which restores the frequent sequence using the enlarged sequence (Precision) ) And Recall. As an algorithm for comparing the accuracy, SPAM [7] was used. As Figure 15 shows, SPAMS tends to show irregularities in spite of the small size of datasets because of the lack of accurate management of frequent items. However, in the case of estDuT, the higher the density, the lower the accuracy, but the higher the reproducibility.

16 is a graph showing the results of experiments comparing the accuracy (ASE) of estDuT and SPAMS according to an embodiment of the present invention.

As shown in FIG. 16, when Smin is 0.05 and Ssig is 90% using the data set as shown in FIG. 14, a comparison of the ASE values according to the data set of estDuT and SPAMS, which restores the frequent sequence using the enlarged sequence, is performed. It is a graph. As an algorithm for comparing the accuracy, SPAM [7] was used. As shown in Figure 15, you can see that estDuT has a relatively high accuracy compared to SPAMS.

17 is a graph showing performance evaluation results in a long sequence according to an embodiment of the present invention.

As shown in FIG. 17, when Smin is 0.05 for the data set D1C10T1-1.3S10I1-1.3N1 having a relatively low density, the performance comparison of estDuT and SPAMS according to the change in transaction length is shown. estDuT had an important support of 0.05 and SPAMS used statistical support θ = θ-ε (θ = S) when δ = 0.01. In the case of a relatively low density data set, there is a characteristic that there are few frequent items because the distribution of items is widely spread. For estDuT, if the length of the set of items in the dataset is | e |, the maximum | e | = | | C + | Generate the C sequence candidate item set e. As the number of nodes of MTeISeq to be processed increases accordingly, as the length of item set | e | increases as shown in Figure 12, memory usage increases and algorithm execution time increases. In the case of SPAMS, unlike estDuT, SPA uses an autometa to manage the subset of the item set e only by transitions, not nodes, so that all subsequences of the sequence can be managed without maintaining many nodes. However, the SPA structure requires a lot of additional memory because there is a lot of information to be kept separately. Deletion of the entire node is not carried out, and since it is responsible for the nodes involved in the sequence that occurs, there is actually no frequent residual nodes, and a set of ingoing transitions that enter the current state, Additional information to be maintained, such as the set of generated customer identifier CIDs, must be maintained in each state, and there is also information that must be maintained in the SPA structure, such as the set of reachable states for the customer identifier. Therefore, as shown in FIG. 17, SPAMS has a higher memory usage and a slightly slower execution time than the estDuT algorithm.

18 is an exemplary view showing a method for exploring a sequential pattern according to an embodiment of the present invention.

As shown in FIG. 18, when the sequential pattern exploration apparatus according to the present invention receives a data stream, which is an infinite data set composed of continuously occurring transactions, each transaction is performed using an MTestDec structure, which is a monitoring tree of the estDec algorithm. In operation S1810, sequence candidate item sets that are frequent items may be extracted.

Next, the sequential pattern exploration apparatus may convert or map the extracted sequence candidate item sets into a 1-item set sequence using a mapping table (S1820). At this time, the sequential pattern exploration apparatus maps the k-sequence candidate item sets to a single ID, but does not map the sequence candidate item sets having a length of k or more.

Next, the sequential pattern exploration apparatus may extract the 1-item set frequent sequence from the transformed 1-item set sequence using the MTeISeq structure, which is a monitoring tree of the eISeq algorithm (S1830).

Next, the sequential pattern exploration apparatus may generate an enlarged sequence composed of item sets having k or more items (S1840), and add the generated enlarged sequence to the 1-item set frequent sequence (S1850).

Next, the sequential pattern exploration apparatus may restore the 1-item set frequent sequence to which the enlarged sequence is added to the original n-item set frequent sequence (S1860), and output the restored n-item set frequent sequence in real time. .

EstDuT according to the present invention is MTestDec for detecting in real-time k-sequence candidate itemsets, which are frequent itemsets having a length of k or less among the item sets constituting the sequence, and MTeISeq for detecting frequent 1-item sets sequences. It is an algorithm that finds frequent n-itemset sequences in the data stream environment using the structure. The estDuT method improves the algorithm's performance for detecting frequent sequences by limiting the length of frequent itemsets. When the user requests frequent sequences, the estDuT method uses a zoom sequence to generate a frequent sequence composed of items having a length greater than k. By reconstructing, we could show the results of frequent sequences with high accuracy.

Compared to the recently studied SPAMS algorithm, estDuT according to the present invention has the advantage of low memory usage and short execution time in relatively low density data. In addition, unlike SPAMS, it is possible to manage frequent items and sequences by estimating support for items that have not occurred for a long time, and efficiently manage items by periodically removing items and sequences that are not frequent through forced battery. In addition, the sequential pattern mining of the n-item set is possible even with relatively small memory usage by limiting the length of the sequence candidate item set.

Various modifications and variations may be made by those skilled in the art without departing from the essential features of the present invention, as well as an apparatus for exploring sequential patterns in a data stream using the dual tree structure according to the present invention. It will be possible. Therefore, the embodiments disclosed in the present invention are intended to illustrate rather than limit the scope of the present invention, and the scope of the technical idea of the present invention is not limited by these embodiments. The protection scope of the present invention should be interpreted by the following claims, and all technical ideas within the equivalent scope should be interpreted as being included in the scope of the present invention.

110: input unit
120: first extraction unit
130: mapping unit
140: second extraction unit
150: generator
160: restoration unit
170: output unit

Claims (10)

A first extracting unit extracts a sequence candidate item set, which is a frequent item in each transaction, by using an MTestDec structure, which is a monitoring tree, when the data stream is an infinite data set composed of continuously occurring transactions. ;
A mapping unit for mapping the sequence candidate item sets in the form of a 1-item set sequence;
A second extracting unit for extracting a 1-item set frequent sequence from the 1-item set sequence by using a MTeISeq structure which is a monitoring tree;
a generating unit for generating an enlarged sequence composed of item sets having k or more items; And
A restoration unit for restoring the 1-item set frequent sequence to which the enlarged sequence is added to the original n-item set frequent sequence
Apparatus for exploring the sequential pattern in a data stream comprising a. The method according to claim 1,
The first extraction unit,
Extract a set of candidate candidate sequences that are greater than or equal to a support value set to a user-defined value, where the support represents the ratio of the number of customers comprising the sequence to the total number of customers, and the sequence continues Apparatus for exploring a sequential pattern in a data stream, characterized in that the list of the generated transactions in the order of the time the transaction occurred based on the customer identifier. The method of claim 2,
The support degree,
Apparatus for exploring a sequential pattern in a data stream, characterized in that the weight is maintained for each item differently over time in order to extract a frequent pattern centered on a frequent item set. The method according to claim 1,
The mapping unit,
In order to convert the sequence candidate item sets into a 1-item set sequence, each of the sequence candidate item sets is mapped to a single ID and sequence candidate item sets having less than k items are mapped in the data stream. Device for exploring sequential patterns. The method according to claim 1,
The generation unit,
For generating a sequential pattern in a data stream, characterized by generating an enlarged sequence consisting of sequence candidate item sets with k items in which all the k-1 items that are subitems are present. Device. (a) receiving a data stream, which is an infinite data set consisting of continuously occurring transactions, extracting sequence candidate item sets, which are frequent items in each transaction, using the MTestDec structure, which is a monitoring tree, from the data stream ;
(b) mapping the sequence candidate item sets in the form of a 1-item set sequence;
(c) extracting a 1-item set frequent sequence from the 1-item set sequence by using a MTeISeq structure which is a monitoring tree;
(d) generating an enlargement sequence composed of item sets having k or more items; And
(e) restoring the 1-item set frequent sequence added with the enlarged sequence to the original n-item set frequent sequence
The method for exploring the sequential pattern in a data stream comprising a. The method of claim 6,
The step (a)
Extract a set of candidate candidate sequences that are greater than or equal to a support value set to a user-defined value, where the support represents the ratio of the number of customers comprising the sequence to the total number of customers, and the sequence continues A method for exploring a sequential pattern in a data stream, characterized in that the list of occurrences of the transactions is grouped in the order in which they occurred based on the customer identifier. The method of claim 7, wherein
The support degree,
A method for exploring a sequential pattern in a data stream, characterized in that the weight is maintained for each item differently over time in order to extract a frequent pattern centered on a frequent item set. The method of claim 6,
The step (b)
In order to convert the sequence candidate item sets into a 1-item set sequence, each of the sequence candidate item sets is mapped to a single ID and sequence candidate item sets having less than k items are mapped in the data stream. Device for exploring sequential patterns. The method of claim 6,
The step (d)
For generating a sequential pattern in a data stream, characterized by generating an enlarged sequence consisting of sequence candidate item sets with k items in which all the k-1 items that are subitems are present. Way.

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