A Frequent Pattern Mining Method Based on Spatial Index

Abstract

The present invention belongs to the field of computer application technology, and discloses a frequent pattern mining method based on spatial index, including step 1: data preprocessing of geographic social network; step 2: constructing a tree-like spatial index NaR‑Tree; step 3: frequent pattern mining; step 4: returning a result set containing k patterns. The present invention constructs a spatial index of a geographic social network and uses a tree-like index structure to store the geographic location information of the network and the structural information within the regional range. After constructing the index structure, the target search area can be efficiently located and the subgraph information within the area can be obtained. Through the spatial index structure, the present invention refines the scope of frequent pattern mining work from the complete graph to a certain area in the graph. By comparing the frequent patterns of different areas, it can help analyze the differences in characteristics such as user behavior patterns and social preferences between regions.

Description

Technical Field

[0001] The present invention belongs to the technical field of computer applications, and in particular relates to a frequent pattern mining method based on spatial indexing. Background Art

[0002] In recent years, with the widespread adoption of smart mobile devices and the internet, massive amounts of user data have been generated. To make these applications more intelligent, uncovering behavioral patterns and underlying relationships between users is crucial. Frequent pattern mining is a key branch of data mining and forms the foundation for other pattern mining methods. However, the tens of thousands of candidate patterns generated during the mining process make efficient mining extremely difficult. Furthermore, traditional frequent pattern mining methods often treat social networks as a whole, failing to leverage users' geographic location information and, consequently, unable to perform fine-grained mining of the network. Summary of the Invention

[0003] The present invention aims to provide a frequent pattern mining method based on spatial indexing to solve the above technical problems.

[0004] To solve the above technical problems, the specific technical solution of the frequent pattern mining method based on spatial indexing of the present invention is as follows:

[0005] A frequent pattern mining method based on spatial indexing includes the following steps:

[0006] Step 1: Data preprocessing of geosocial network;

[0007] Integrate the geographic location information in the geo-social network and assign a location label to each node, which will serve as the basis for building a tree-like spatial index and mining frequent patterns in the subsequent steps;

[0008] Step 2: Construct the tree-like spatial index NaR-Tree;

[0009] Based on the geographical location attributes of nodes and the coverage relationship between regions, a NaR-Tree index structure is constructed. This spatial index transforms the region retrieval problem into a tree search problem, that is, searching for nodes representing the target region starting from the root node.

[0010] Step 3: Frequent pattern mining;

[0011] Given the target search area, result set size k, and sample pattern c, return the k most frequent patterns extending from c in the target area;

[0012] Step 4: Return a result set containing k patterns.

[0013] Furthermore, the step 2 includes the following specific steps:

[0014] Each node of the geographic social network graph G(V, E, L) contains the geographic location information of the current node. The data file consists of r rectangles, and each NaR-Tree node contains n rectangles. The specific construction process is as follows:

[0015] Step 2.1: Preprocess the data file;

[0016] Step 2.2: Construct leaf nodes;

[0017] Step 2.3: Merge nodes at the same level;

[0018] Step 2.4: Generate the root node.

[0019] Furthermore, the step 2.1 includes the following specific steps:

[0020] Preprocess the data file so that the r rectangles are located at The rectangles record all the nodes contained in the network graph, as well as all the edge types and the number of edge types.

[0021] Furthermore, the step 2.2 includes the following specific steps:

[0022] Convert each rectangle group generated in step 2.1 into a leaf node, where each leaf node contains at most n rectangles.

[0023] Furthermore, the step 2.3 includes the following specific steps:

[0024] Merge tree nodes that are close to each other in the same layer, and use the minimum bounding rectangle corresponding to the tree node as one of the rectangles within the tree node of the previous layer. When merging tree nodes, the graph information contained in the nodes needs to be merged as well.

[0025] Furthermore, the step 2.4 includes the following specific steps:

[0026] Iterate the operation of step 2.3 starting from the layer where the leaf node is located until the root node is generated, that is, all rectangles are covered.

[0027] Furthermore, the step 3 includes the following specific steps:

[0028] Step 3.1: Access the NaR-Tree and determine the node where the target search area is located;

[0029] The process of searching for the node where the target area is located in the NaR-Tree is similar to the tree search process: Step 3.1.1: Check whether the current node covers the target search area;

[0030] Step 3.1.2: If it is covered, access the child nodes of the current node and execute step 3.1.1;

[0031] If not covered, return the current node;

[0032] Starting from the root node, perform steps 3.1.1 to 3.1.2 until the result is obtained, which is the minimum bounding rectangle that contains the target search area.

[0033] Step 3.2: Subgraph retrieval;

[0034] After obtaining the NaR-Tree node corresponding to the target search area, the subgraph corresponding to the target area is retrieved and generated in G according to the subgraph information stored in the tree node. The specific steps are as follows:

[0035] Step 3.2.1: Get all graph nodes (v1, v2, …, vn) stored in the NaR-Tree node;

[0036] Step 3.2.2: Retrieve the edges connecting the above nodes from G;

[0037] Construct the corresponding subgraph S based on the node and edge information obtained in steps 3.2.1 and 3.2.2;

[0038] Step 3.3: Initialize the priority queue;

[0039] Initialize the two priority queues required for the mining mode. The specific steps are as follows:

[0040] Step 3.3.1: Generate a maximum priority queue q1 and a minimum priority queue q2. The sorting criterion of the priority queue is the support of the pattern in the queue. The size of q2 is set to k.

[0041] Step 3.3.2: Calculate the support of the initial pattern c and put c into q1;

[0042] Step 3.4: The first element p1 of q1 is removed from the queue and its support is compared with the first element p2 of q2;

[0043] Step 3.5: If the support of p1 is greater than that of p2, perform the following steps:

[0044] Step 3.5.1: Perform lazy retrieval based on the node and edge information of p1 to speed up support calculation.

[0045] Step 3.5.2: Calculate the true support of p1. If it is still greater than p2, then p2 is removed from the queue and p1 is expanded, and finally p1 is added to the queue.

[0046] Repeat steps 3.4:~3.5 until the queue q1 is empty. At this time, the k elements in q2 are the k frequent patterns required.

[0047] Furthermore, the step 3.3.2 includes the following specific steps:

[0048] The support of pattern c is calculated based on the side information of c's instances in subgraph S. The specific steps are as follows:

[0049] a1: Get all instances of c {I1, I2, …, Im} in subgraph S;

[0050] a2: Get all edge information of all instances and generate edge sets;

[0051] a3: Count and return the number of unique edges in the edge set;

[0052] Step a3: The returned value is the support of pattern c;

[0053] After the initialization step is completed, the mining work officially begins.

[0054] Furthermore, the lazy search operation steps of step 3.5.1 are as follows:

[0055] b1: If the node and edge types of p1 are all included in S, there is no need to re-search;

[0056] b2: Otherwise, re-search S.

[0057] Furthermore, the steps of the expansion operation of p1 in step 3.5.2 are as follows:

[0058] c1: Generate all possible sub-patterns of p1 based on the edge information stored in the NaR-Tree node;

[0059] c2: The support of the sub-pattern is temporarily set to the true support of p1;

[0060] c3: Add all generated sub-patterns to q1.

[0061] The present invention's spatial index-based frequent pattern mining method has the following advantages: By constructing a spatial index for a geographic social network, the method uses a tree-like index structure to store the network's geographic location information and regional structural information. Once the index structure is constructed, the target search area can be efficiently located and subgraph information within the area can be retrieved.

[0062] Through the spatial index structure, the present invention refines the scope of frequent pattern mining from the complete graph to a certain area in the graph. By comparing the frequent patterns of different areas, it can help analyze the differences in user behavior patterns, social preferences and other characteristics between regions. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1(a) is a schematic diagram of a graph G containing 12 vertices;

[0064] Figure 1(b) Schematic diagram of the initial mode P;

[0065] Figure 2 Schematic diagram of the minimum circumscribed rectangle division of graph G;

[0066] Figure 3 Schematic diagram of the tree-like spatial index structure of graph G;

[0067] Figure 4 Schematic diagram of an example of index structure search; DETAILED DESCRIPTION

[0068] In order to better understand the purpose, structure and function of the present invention, the frequent pattern mining method based on spatial indexing of the present invention is further described in detail below with reference to the accompanying drawings.

[0069] The present invention provides a geosocial network G(V,E,L), where V represents the set of all user nodes in the network, E represents the connections between users, and L represents the label constraints on the nodes in the graph. Each node in V contains a geographic location attribute, namely the latitude and longitude of the user's location. G(V,E,L) contains multiple frequent patterns that need to be mined.

[0070] The pattern referred to in the present invention refers to a weakly connected subgraph obtained from the pattern space, in which each node contains a label and all edges in the pattern exist in the graph G.

[0071] The instance referred to in the present invention refers to the isomorphic subgraph corresponding to the pattern in the graph G.

[0072] The frequent pattern mining involved in the present invention refers to inputting a sample pattern and an integer k and mining the k patterns with the highest support in a graph G.

[0073] The support index in the present invention is evaluated using a method based on the minimum edge mapping support, that is, the number of different edges in all instances corresponding to the pattern.

[0074] When mining frequent patterns, dividing the search area requires traversing all nodes in the graph and comparing their geographic locations. This process is time-consuming in large networks, so there is an urgent need to develop an efficient spatial index to accelerate regional search. To ensure the accuracy of search results, it is also necessary to generate all potential frequent patterns and compare their support. Reducing the number of candidate patterns is also a key concern of this invention.

[0075] The innovation of this invention is to utilize the user's geographic location information during frequent pattern mining, enabling the mining process to be refined to specific areas within the network, such as cities, communities, and schools. A suitable spatial index is designed to accelerate the regional search process. Secondly, the information stored in the spatial index is used to optimize the pattern expansion process, thereby reducing the number of candidate patterns.

[0076] Specifically, a frequent pattern mining method based on spatial indexing of the present invention comprises the following steps:

[0077] Step 1: Data preprocessing of geosocial network;

[0078] The geographic location information in the geographic social network is integrated and a location label is assigned to each node, which serves as the basis for constructing a tree-like spatial index and mining frequent patterns in the subsequent steps.

[0079] Step 2: Construct the tree-like spatial index NaR-Tree;

[0080] Based on the geographical location attributes of nodes and the coverage relationship between regions, a NaR-Tree index structure is constructed. This spatial index transforms the region retrieval problem into a tree search problem, that is, searching for nodes representing the target region starting from the root node.

[0081] Each node in the geographic social network graph G(V,E,L) contains the geographic location information of the current node. The construction process of NaR-Tree includes: preprocessing data files, constructing leaf nodes, merging nodes at the same level, and generating root nodes.

[0082] Assume that the data file consists of r rectangles and each node of the NaR-Tree can accommodate n rectangles.

[0083] The specific construction process is as follows:

[0084] Step 2.1: Preprocess the data file;

[0085] Preprocess the data file so that the r rectangles are located at The network is constructed by dividing the network into continuous rectangular groups and arranging them in an orderly manner. The rectangles record all the nodes contained in the network graph, as well as all the edge types and the number of edge types.

[0086] Step 2.2: Construct leaf nodes;

[0087] Convert each rectangle group generated in the previous step into a leaf node, and each leaf node contains at most n rectangles.

[0088] Step 2.3: Merge nodes at the same level;

[0089] Merge tree nodes that are close to each other on the same layer, and use the minimum bounding rectangle of the tree node as one of the rectangles within the tree node on the previous layer. When merging tree nodes, the graph information contained in the nodes needs to be merged as well.

[0090] Step 2.4: Generate the root node;

[0091] Iterate the previous step starting from the layer where the leaf node is located until the root node is generated, that is, all rectangles are covered.

[0092] Step 3: Frequent pattern mining;

[0093] Given the target search area, result set size k, and sample pattern c, return the k most frequent patterns that extend from c in the target area.

[0094] The specific steps of frequent pattern mining are as follows:

[0095] Step 3.1: Access the NaR-Tree and determine the node where the target search area is located;

[0096] The process of searching for the node where the target area is located in the NaR-Tree is similar to a tree search process:

[0097] Step 3.1.1: Check whether the current node covers the target search area;

[0098] Step 3.1.2: If it is covered, access the child nodes of the current node and execute step 3.1.1;

[0099] If not covered, return the current node;

[0100] Start from the root node and perform steps 3.1.1 to 3.1.2 until the return result is obtained, that is, the minimum bounding rectangle containing the target search area.

[0101] Step 3.2: Subgraph retrieval;

[0102] After obtaining the NaR-Tree node corresponding to the target search area, the subgraph corresponding to the target area is retrieved and generated in G according to the subgraph information stored in the tree node. The specific steps are as follows:

[0103] Step 3.2.1: Get all graph nodes (v1, v2, …, vn) stored in the NaR-Tree node;

[0104] Step 3.2.2: Retrieve the edges connecting the above nodes from G;

[0105] According to the node and edge information obtained in steps 3.2.1 and 3.2.2, construct the corresponding subgraph S.

[0106] Step 3.3: Initialize the priority queue;

[0107] Initialize the two priority queues required for the mining mode. The specific steps are as follows:

[0108] Step 3.3.1: Generate a maximum priority queue q1 and a minimum priority queue q2. The sorting criterion of the priority queue is the support of the pattern in the queue. The size of q2 is set to k.

[0109] Step 3.3.2: Calculate the support of the initial pattern c and put c into q1;

[0110] The support of pattern c is calculated based on the side information of c's instances in subgraph S. The specific steps are as follows:

[0111] a1: Get all instances of c {I1, I2, …, Im} in subgraph S;

[0112] a2: Get all edge information of all instances and generate edge sets;

[0113] a3: Count and return the number of unique edges in the edge set;

[0114] Step a3: The returned value is the support of pattern c.

[0115] After the initialization steps are completed, mining can officially begin.

[0116] Step 3.4: The first element p1 of q1 is removed from the queue and its support is compared with the first element p2 of q2;

[0117] Step 3.5: If the support of p1 is greater than that of p2, perform the following steps:

[0118] Step 3.5.1: Perform lazy retrieval based on the node and edge information of p1 to speed up support calculation.

[0119] The lazy retrieval operation steps are as follows:

[0120] b1: If the node and edge types of p1 are all included in S, there is no need to re-search;

[0121] b2: Otherwise, S needs to be searched again;

[0122] Step 3.5.2: Calculate the true support of p1. If it is still greater than p2, then p2 is removed from the queue and p1 is expanded, and finally p1 is added to the queue.

[0123] The steps for expanding p1 are as follows:

[0124] c1: Generate all possible sub-patterns of p1 based on the edge information stored in the NaR-Tree node;

[0125] c2: The support of the sub-pattern is temporarily set to the true support of p1;

[0126] c3: add all generated sub-patterns to q1;

[0127] Repeat steps 3.4 to 3.5 until the queue q1 is empty. At this point, the k elements in q2 are the k frequent patterns we are looking for.

[0128] Step 4: Return a result set containing k patterns.

[0129] Example:

[0130] FIG1(a) is a graph G containing 12 vertices, and FIG1(b) is an initial pattern P. An embodiment of the present invention will be described below using this graph as an example.

[0131] The tree-like spatial index structure of graph G is as follows Figure 3 As shown, the construction of the spatial index is obtained by executing step 2 of the present invention, and we perform the following operations:

[0132] Divide each of the ten nodes of graph G into a minimum bounding rectangle and record these 12 nodes as the minimum area where the index can operate;

[0133] Figure 2 The minimum bounding rectangle partition of the graph G is obtained by executing step 2-1 of the present invention;

[0134] Grouping rectangles that are close together into the same group, the 12 nodes in graph G are divided into five groups: a1, a2, b1, b2, and b3. Specifically, the five groups are composed of (v1, v4), (v2, v3, v5), (v6, v7, v10), (v8, v9), and (v11, v12).

[0135] The five generated groups are used as the five leaf nodes of the tree-like spatial index, and the minimum enclosing rectangle is divided for each leaf node;

[0136] Merge the areas represented by the five leaf nodes and divide the minimum bounding rectangles of the two generated nodes. Specifically, merge a1 and a2 into A; merge b1, b2, and b3 into B;

[0137] The generated two nodes A and B are used as the nodes of the second layer of the tree space index;

[0138] Merge the areas represented by nodes A and B and generate a minimum bounding rectangle that covers the entire image;

[0139] The generated final node is used as the root node of the tree-like spatial index;

[0140] Figure 4 Represents the search results in the tree-like spatial index after the region is divided, obtained by executing steps 3-1-1 to 3-1-2 of the present invention;

[0141] For example, taking a1, a2, b1, and b2 as target search areas, perform the following operations on the tree-structured spatial index:

[0142] Starting from the root node, which covers the target search area, continue searching the two child nodes of the root node;

[0143] The area covered by node A is part of the target search area, and its leaf nodes are searched;

[0144] Update node A with the graph node information and edge information contained in leaf nodes a1 and a2;

[0145] Node B is not completely covered by the target search area, where b1 and b2 belong to the target search area but b3 does not, so no search is performed;

[0146] Search for leaf nodes b1 and b2, and update the information stored in node B;

[0147] Use nodes A and B to update the information stored in the root node. At this time, the tree-like spatial index has completed the search and update;

[0148] The pattern P(SP-KG) in Figure 1 is the initial pattern for frequent pattern mining, and k is the expected result set size, which is set to 3. Frequent pattern mining requires executing steps 3-3 to 3-5 of the present invention, and performing the following operations:

[0149] Initialize the maximum priority queue q1 and the minimum priority queue q2 with a size of 3;

[0150] Calculate the support of P. According to the number of unique edges, we can see that the support of (SP-KG) is 4;

[0151] Add P to queue q1;

[0152] The first element of team q1 (SP-KG) is out of the team;

[0153] At this time, q2 is empty, and p1 is expanded. The potential candidate patterns are (SP-KG-PM), (SP-SP-KG), (KG-SP-KG), (PM-SP-KG), and (SP-KG-PM-SP). 4 is used as the initial support of the candidate pattern.

[0154] Add the above five candidate nodes to queue q1;

[0155] The first element of q1 (SP-KG-PM) is removed from the queue;

[0156] Calculate the support of (SP-KG-PM), the result is 2. At this time, queue q2 is not full;

[0157] Expand the pattern (SP-KG-PM) to generate a series of candidate patterns, set the initial support to 2 and add them to queue q1;

[0158] Add (SP-KG-PM) to queue q2, which is not full at this time.

[0159] The first element of q1 (SP-SP-KG) is removed from the queue;

[0160] Calculate the support of (SP-SP-KG), the result is 1. At this time, queue q2 is not full;

[0161] Expand the pattern (SP-SP-KG) to generate a series of candidate patterns, set the initial support to 1 and add them to queue q1;

[0162] Add (SP-SP-KG) to queue q2, which is now full.

[0163] The remaining candidate patterns in q1 are dequeued one by one and their support is calculated;

[0164] The support of candidate patterns such as (KG-SP-KG), (PM-SP-KG), and (SP-KG-PM-SP) are all 1, which is less than or equal to the support of the first element of q2. Therefore, they cannot be added to q2 and no expansion operation is required;

[0165] Until q1 is empty, then the pattern in q2 is the result set {SP-KG, SP-KG-PM, (SP-SP-KG)};

[0166] Return the result.

[0167] It will be understood that the present invention is described by way of some embodiments, and it will be appreciated by those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are intended to be protected by the present invention.

Claims

1. A frequent pattern mining method based on spatial index, characterized in that: The steps include: Step 1: Data preprocessing of geosocial network; Integrate the geographic location information in the geo-social network and assign a location label to each node, which will serve as the basis for building a tree-like spatial index and mining frequent patterns in the subsequent steps; Step 2: Construct the tree-like spatial index NaR-Tree; Based on the geographic location attributes of nodes and the coverage relationship between regions, a NaR-Tree index structure is constructed. This spatial index transforms the regional retrieval problem into a tree search problem, that is, searching for nodes representing the target region from the root node. Each node in the geographic social network graph G(V, E, L) contains the geographic location information of the current node. Step 3: Frequent pattern mining; Given the target search area, result set size k, and sample pattern c, return the k most frequent patterns extending from c in the target area; Step 3.1: Access the NaR-Tree and determine the node where the target search area is located; The process of searching for the node where the target area is located in the NaR-Tree is similar to a tree search process: Step 3.1.1: Check whether the current node covers the target search area; Step 3.1.2: If it is covered, access the child nodes of the current node and execute step 3.1.1; If not covered, return the current node; Start from the root node and perform steps 3.1.1 to 3.1.2 until the result is obtained, which is the minimum bounding rectangle that contains the target search area. Step 3.2: Subgraph retrieval; After obtaining the NaR-Tree node corresponding to the target search area, the subgraph corresponding to the target area is retrieved and generated in G according to the subgraph information stored in the tree node. The specific steps are as follows: Step 3.2.1: Get all graph nodes (v1, v2, …, vn) stored in the NaR-Tree node; Step 3.2.2: Retrieve the edges connecting the above nodes from G; Construct the corresponding subgraph S based on the node and edge information obtained in steps 3.2.1 and 3.2.2; Step 3.3: Initialize the priority queue; Initialize the two priority queues required for the mining mode. The specific steps are as follows: Step 3.3.1: Generate a maximum priority queue q1 and a minimum priority queue q2. The sorting criterion of the priority queue is the support of the pattern in the queue. The size of q2 is set to k. Step 3.3.2: Calculate the support of the initial pattern c and put c into q1; Step 3.4: Remove the first element p1 of q1 from the queue and compare its support with the first element p2 of q2; Step 3.5: If the support of p1 is greater than that of p2, perform the following steps: Step 3.5.1: Perform lazy retrieval based on the node and edge information of p1 to speed up support calculation. Step 3.5.2: Calculate the true support of p1. If it is still greater than p2, then p2 is removed from the queue and p1 is expanded, and finally p1 is added to the queue. Repeat steps 3.4:~3.5 until the queue q1 is empty. At this point, the k elements in q2 are the k frequent patterns you are looking for. Step 4: Return a result set containing k patterns.

2. The frequent pattern mining method based on spatial index according to claim 1, characterized in that: The step 2 includes the following specific steps: Each node of the geographic social network graph G(V,E,L) contains the geographic location information of the current node. The data file consists of r rectangles, and each NaR-Tree node contains n rectangles. The specific construction process is as follows: Step 2.1: Preprocess the data file; Step 2.2: Construct leaf nodes; Step 2.3: Merge nodes at the same level; Step 2.4: Generate the root node.

3. The frequent pattern mining method based on spatial index according to claim 2, characterized in that: The step 2.1 includes the following specific steps: Preprocess the data file so that the r rectangles are in ⌈r / n⌉ consecutive rectangular groups, and arrange these rectangular groups in order. The rectangles record all the nodes contained in the network graph, as well as all the edge types and the number of edge types.

4. The frequent pattern mining method based on spatial index according to claim 2, characterized in that: The step 2.2 includes the following specific steps: Convert each rectangle group generated in step 2.1 into a leaf node, where each leaf node contains at most n rectangles.

5. The frequent pattern mining method based on spatial index according to claim 2, characterized in that: The step 2.3 includes the following specific steps: Merge tree nodes that are close to each other in the same layer, and use the minimum bounding rectangle corresponding to the tree node as one of the rectangles within the tree node of the previous layer. When merging tree nodes, the graph information contained in the nodes needs to be merged as well.

6. The frequent pattern mining method based on spatial index according to claim 2, characterized in that: The step 2.4 includes the following specific steps: Iterate the operation of step 2.3 starting from the layer where the leaf node is located until the root node is generated, that is, all rectangles are covered.

7. The frequent pattern mining method based on spatial index according to claim 1, characterized in that: The step 3.3.2 includes the following specific steps: The support of pattern c is calculated based on the side information of c's instances in subgraph S. The specific steps are as follows: Get all instances of c {I1,I2,…,Im} in subgraph S; Get all edge information of all instances and generate edge sets; Counts and returns the number of unique edges in an edge set; The value returned in step ③ is the support of pattern c; After the initialization step is completed, the mining work officially begins.

8. The frequent pattern mining method based on spatial index according to claim 1, characterized in that: The lazy retrieval operation steps of step 3.5.1 are as follows: If the node and edge types of p1 are both included in S, there is no need to re-search; Otherwise, S is searched again.

9. The frequent pattern mining method based on spatial index according to claim 1, characterized in that: The steps for expanding p1 in step 3.5.2 are as follows: Generate all possible sub-patterns of p1 based on the edge information stored in the NaR-Tree node; The support of the sub-pattern is temporarily set to the true support of p1; Add all generated subpatterns to q1.

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