CN109935277B - Abnormal motif query method based on meta-path in heterogeneous network - Google Patents
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Abstract
The invention provides an abnormal motif query method based on a meta path in a heterogeneous network, and belongs to the field of network abnormal query. The method includes the steps that for a data extraction network containing various kinds of information, a set of all motifs meeting conditions is found out by setting initial conditions required by query, normalized path similarity is used, the similarity between each motif and a reference motif set is compared, and for motifs with low similarity, the motifs are considered to be abnormal motif parts in a target motif. The method can be used as an abnormal motif query method in the heterogeneous network to be stably used, so that a new visual angle is provided for abnormal motif query.
Description
Technical Field
The invention belongs to the field of network anomaly query, and is mainly applied to query abnormal small motifs in a target motif set in a heterogeneous network. The method mainly comprises the steps of calculating the number of meta-paths of a specific type between the motifs as similarity, normalizing the number of the meta-paths from the motif to obtain the similarity between a target motif in a network and an expected motif, analyzing and determining the least similar partial motif, and further judging the abnormal motif in the given network.
Background
With the arrival of the big data era and the great improvement of the computer performance caused by the development of the science and technology, a lot of data which needs to consume a large amount of manpower and material resources for analysis and a lot of data which is difficult to be analyzed simply from the data angle can be analyzed efficiently and accurately by means of the computer, so that people can be liberated from complicated physical labor and focus on mining hidden relations in the network theoretically. Meanwhile, the anomalies in the network are also parts which are frequently contacted in the research process, and how to define the anomalies in the network is undoubtedly one of important parts in the network research. In the existing abnormal query methods, most abnormal points in the network are queried through methods such as numerical analysis and cluster analysis, and an effective query means is lacked for abnormal motifs in the network, so that a method is expected to be provided for accurately querying the abnormal motifs in the network, and the influence of some abnormal motifs in the network on the network is conveniently researched.
Disclosure of Invention
The invention aims to solve the problem that an effective means for inquiring abnormal motifs in a network is lacked in the existing research, based on the concept of meta-paths, and in combination with the idea of using a method for inquiring abnormal nodes in a meta-path inquiry network, the similarity between a target motif and a standard motif is measured by calculating the number of meta-paths existing between the target motif and a certain type of standard motif specified by a user, meanwhile, the similarity is normalized by using the number of meta-paths from the motif to the self as a standard, and the result is used as a basis for measuring the relative similarity. By means of the concept of meta-path, similarity between the motifs in the network is measured and compared structurally, an index for measuring whether a target motif is similar to a standard motif set given by a user or not is obtained, and experiments show that the method can better depict the abnormal degree of the motifs in the network.
The technical scheme of the invention is as follows:
a meta-path-based abnormal motif query method in a heterogeneous network comprises the following steps:
step 1) processing a data set and determining query conditions
The method can be divided into the following steps according to the data types contained in the data set:
1.1) extracting the network from the data set according to the type of the motif formed by the concerned different node types. The motif refers to a small network structure which appears at high frequency in the network, and generally refers to a high-frequency network substructure which comprises more than three nodes and less than eight nodes in research.
1.2) determining the node query condition. The method carries out motif query aiming at the heterogeneous network, so that edges of different types can be generated according to different node types of the heterogeneous network. A meta path is defined as a path connecting two classes of objects, and a formalized definition can be written as:
wherein A isiIndicates the node type, RiRepresenting the type of relationship. For example, in a collaborating network, an author-paper-author meta-path indicates that there is a collaborating relationship between two authors. For different networks, different types of meta-paths have different meanings, and different types of motifs have different values in research. By determining an initial motif to be queried, a meta-path for querying a target motif and a node type and a topological structure of the motif to be queried, a target motif set meeting requirements can be obtained. Although it is also possible to perform such queries over several unorthodox points, the results obtained from such queries are often of little or no significance. Meanwhile, it is also necessary to determine the initial motif of the standard motif set that is referred to by the query, the meta-path used for the query, and the type of the query motif, for calculating the number of meta-paths between the candidate motif set and the standard motif set.
Step 2) determining a candidate motif set and a standard motif set (determined by a user and referred to as a reference motif set hereinafter) as a reference according to the query conditions given in the step 1), and dividing the method into the following two steps:
2.1) calculating a candidate motif set. For the starting point of each type, a plurality of meta-paths can be defined for query, the starting node type of the meta-path should be any node type contained in the starting motif, and the ending node type of the meta-path should be one of the node types contained in the target motif. Starting from the initial motif, using the defined meta-path, and querying by adopting the corresponding meta-path according to the node type of the initial motif, wherein the result obtained by querying the meta-path is a point set meeting the requirement. According to the difference of the types of the nodes in the point set, searching the motif meeting the conditions from different positions of the type of the nodes in the target motif as starting points. For the queried motif, if the motif has an isomorphic motif, the same motif is calculated for multiple times due to different positions of the same node in the motif, and therefore repeated motifs need to be removed from the result. All generated motifs that meet the conditions are finally stored in one set.
2.2) calculating a reference motif set. In step 1), the query condition of the candidate motif is given, and the query condition of the reference motif is also given, and with reference to the query step of 2.1, a reference motif set can be obtained through query. It should be noted that this step may also be omitted in the algorithm, and the reference motif set in the result obtained after this step is omitted is the candidate motif set, and the query result of the algorithm is the partial motif that is the least "non-matched" compared with all the candidate motifs.
And 3) calculating the similarity between each motif in the candidate motif set and the whole reference motifs according to the candidate motif set and the reference motif set obtained in the step 2).
3.1) calculating the similarity of each motif to the reference motif set. Here, with the concept of symmetric meta-path, if two nodes of the same type query a same node through a same meta-path, we call this combined path as a symmetric path. In the query, one half of the symmetric path can be given, and two start nodes are enabled to perform bidirectional query through the meta path, so that the number of the queried meta path is as follows:
wherein m represents a motif, PsymRepresenting a path of a symmetric element, P representing a half of the paths constituting the path of the symmetric element, Num () function representing the number of paths, VabIndicating the die body maAnd a mold body mbThe point in (1) is a set of nodes that can be reached by a certain meta-path, the value is taken as the similarity between two points, and under the condition that a plurality of query meta-paths exist, different weights of each path can be defined, so that a weighted similarity value is obtained. The weight defaults to 1.
3.2) calculating the number of paths of each motif returning to the motif through the symmetrical element path, and normalizing the similarity. In this step, the influence of the same type of nodes and isomorphic factors on the calculation result still needs to be considered, and in the result, the number of meta-paths of each node returning to itself and the same type of nodes in the same motif is counted as a standard for normalizing the similarity, that is, the similarity is normalized by:
the number of paths from each motif in the candidate set and the reference set to the motif is calculated through the formula, and the similarity is obtained. Likewise, in the case where there are a plurality of meta paths, if the weight is defined in 3.1), the same weight is also used for calculation in this step.
3.3) using the similarity of the motif and the motif as a measurement standard to carry out standardization operation on the similarity. For different motifs, because the positions of the motifs in the network are different, the topological structures of the motifs are different, and the magnitude relation of the similarity between the two motifs and the candidate set cannot be accurately measured by simply comparing the similarity. For example, in the case of the same similarity, if there are more symmetric paths in a motif that connect to motifs outside the reference motif set, it is obvious that the similarity should be smaller than that of motifs in which all symmetric paths connect to the reference set, but the feature cannot be directly expressed by using the similarity alone. We therefore address this problem with normalized similarity. According to the definition and calculation method of different similarities, different normalized similarity calculation methods may be adopted, where path similarity (PathSim) is used for calculation, and other optional similarities further include cosine similarity and the like. Defining the normalized path similarity between the motifs as:
where PathSim represents path similarity. By defining the similarity between motifs, a definition of similarity between a motif and a set of reference motifs can be obtained:
wherein m isjRepresenting any of a set of standard motifs, SRRepresenting a set of reference motifs, Ω being the total path similarity. Through normalization, a uniform standard can be used for comparing the similarity between two motifs with the same similarity and a reference set, so that a reasonable result is obtained.
And 4) sequencing the motifs with the normalized similarity calculated according to the normal score similarity to obtain a similarity list result set from small to large, wherein the similarity list result set is used for representing the similarity degree with the reference motif set, and the smaller the value is, the more different the corresponding motif is from the reference motif set, and otherwise, the more similar the corresponding motif is to the reference motif set.
The invention has the beneficial effects that: the invention can use a data set containing various data information to extract the concerned heterogeneous network, according to different concerned motif types, the motif set meeting the requirements is inquired in a meta-path inquiry mode according to different inquiry conditions given by a user, and the normalized similarity is finally obtained to measure the relative similarity between the motif and the reference set by calculating the similarity between the motif in the candidate motif set and the motif in the reference motif set. Compared with most of the prior algorithms which focus on inquiring abnormal points in the network, a more complete solution for inquiring abnormal motifs in the network is provided. The experimental result shows that for the heterogeneous network extracted from the data set, the scheme can better identify the abnormal motif part in the network. From the experimental results, it can also be found that the found abnormal motif has a larger difference from the standard motif in the practical sense, and the motif with higher similarity to the reference motif set often has the similar property to the reference motif in the real sense.
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FIG. 1 is an experimental flow of the present invention, which extracts a network according to a TFG-Ohmnet data set in a BIOSNAP project, and calculates an abnormal motif in a heterogeneous network by a meta-path query method.
Detailed Description
The embodiment of the invention provides an abnormal motif inquiring method based on a meta-path, which comprises the following four steps:
step 1: a network is constructed by extracting data of the type we are interested in from the data set, and determining query conditions.
The invention selects a TFG-Ohmnet data set in the BIOSNAP project, and the data set records the ternary relationship among biological tissues (tissue), functions (ontology) and genes (gene). The node comprises 2000 nodes of the three types, wherein 18000 edges are formed, and the information is complete. In the experiment, the similarity among the motifs of the three nodes contained in the ternary relationship is concerned, so that all the ternary relationships in the data set are directly extracted to form a network. The three-point motifs in the network thus formed will contain edges that belong to different triads, and the network that is ultimately formed will therefore contain far greater triads than those contained in the previous data set.
Aiming at the data set, setting the initial query condition of the candidate set as a ternary relationship of ymphocyte-GO:0050871-100, wherein the ymphocyte represents biological tissues (lymphocytes), GO:0050871 is a function number, 100 is a gene number, starting from the model, a heterogeneous three-point model with a tissue-ontology-gene type is queried, and the structure is a triangle. And (3) setting the query path as a tissue-ontology-gene, namely starting from a tissue type point, finally reaching a gene type node through an ontology type node, and counting three-point motifs including the gene type nodes as a candidate motif set. In the experiment, the query condition of the reference motif set is not set, which means that the reference set is a candidate set, each queried motif is compared with the whole candidate motif set, and the similarity is calculated to obtain a result. The path for calculating the similarity is set as the tissue-gene, that is, the similarity between two motifs is calculated by counting the symmetric meta-path of the tissue-gene-tissue.
Step 2: and inquiring the candidate motif set according to the obtained network and the determined inquiry condition.
2.1) according to the query conditions given in the step 1, carrying out breadth-first search from the initial three-point die body to obtain a point set meeting the requirement of the meta-path. For each point in the set of points, all motifs are found using a depth-first search. In the experiment, the target die body does not have any isomorphic die body, so that an isomorphic die body structure is not required to be given, but under the condition that the target die body structure has isomorphism, the isomorphic structure of the target die body is given in the step 1, namely, each point is numbered, the conventional die body is a list numbered in sequence, and the isomorphic die body is a node list which is obtained after the node sequence is adjusted and is completely the same as the original die body in structure. If the found motif is added into the candidate motif set after being adjusted according to the isomorphic motif list, the motif is proved to be found, and the motif is not added into the candidate motif set.
2.2) for the reference motif set, no query condition is given in the experiment, the default reference motif set is equal to the candidate motif set, but a user can also give a group of initial query conditions with the same format as the candidate motif set, and the reference motif set is obtained according to the meta-path query method of the candidate motif set.
And step 3: and (3) calculating the normalized similarity of each motif in the candidate motif set and the reference set according to the candidate motif set and the reference motif set obtained in the step (2).
3.1) for each motif in the candidate motif set and the reference motif set, calculating the set of nodes which can be reached by the candidate motif set and the reference motif set through the meta-path for query, and the number of different paths for reaching the node. Since we use symmetric meta-paths to perform path number statistics, here we should first determine the intersection of two sets after obtaining the reachable points of two sets of motifs via meta-path tissue-gene and the number of paths, namely:
S{vii gene on the symmetric path ═ S { v ═ v { (v) }jGene reachable in reference set | S { v } S { vkI the gene that the candidate set can reach }
Thus, the total number of symmetry-element paths between two motifs is:
wherein m isaBelongs to a candidate motif, mbBelongs to the reference motif. At this time, we obtain the total number of symmetric paths between two motifs, which can be regarded as the similarity between the two motifs.
3.2) calculating the number of paths of each motif in the candidate motif set and the reference motif set to reach the motif through the symmetry element path for normalization operation. Step 3.1) only calculates the number of element paths between two motifs, but cannot accurately compare the number with the similarity between the two motifs and other motifs, so that the normalization operation is performed by using the number of symmetrical element paths from the motif to the motif as a standard. The number of meta-paths between a motif and itself can be written as:
in this experiment, the number of paths representing the tissue node back to itself via a meta-path such as tissue-gene-tissue is shown. Similarly, although there are no nodes of the same type in this experiment, from a point viThe original path can only go back viBy itself, but if the same type of node is present in the target motif, then from one point viThe outgoing path of the symmetric element may eventually also go to another node v of the same typejThis should be taken into account in the experiments.
3.3) calculating the normalized similarity of each motif in the candidate motif set and the whole reference motif set. In this experiment, it is equivalent to calculate the similarity between each motif in the set and the entire set of motifs, and the normalized similarity used for calculation is:
wherein m isaBelongs to a candidate motif, mbBelongs to the reference motif. M belonging to two sets for each pairiAnd mjWe calculate the normalized path similarity for the two correspondences
For each motif m in the candidate motif setiAnd all reference motif sets SRThe normalized similarity between the motifs in (1) is summed to obtain miAnd SRThe similarity is recorded as omegaPathSim：
Through the calculation, a similarity list containing each motif and the reference set is obtained.
And 4, step 4: and (3) sorting by using a similarity list, wherein the obtained sorted list is algorithm output, and for our experiment, the motif with lower similarity represents that the difference with the whole candidate motif set is larger, in other words, the motif is the abnormal part in the motif meeting the requirements. For the case where the reference set and the candidate set are different, an abnormal motif is an abnormality with respect to the reference set. The results of the experiment are shown in tables 1(a) and 1 (b).
Table 1(a) ten abnormal motifs queried from the lymphoma-GO: 0050871-100 motif in TFG-Ohmnet
TABLE 1(b) the last ten abnormal motifs (the ten most similar to the candidate set of motifs)
While the invention has been described in connection with specific embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (1)
1. An abnormal motif query method based on meta-paths in a heterogeneous network is characterized by comprising the following steps:
step 1) processing a TFG-Ohmnet data set in a BIOSNAP project and determining query conditions, wherein the data set records the ternary relationship among biological tissues, functions and genes:
1.1) directly extracting all the ternary relations in the data set to form a network because the similarity among the motifs of the three nodes contained in the ternary relations is concerned;
1.2) determining a node query condition; the initial query condition is a ternary relationship of lymphoma-GO 0050871-100, wherein the lymphoma represents biological tissue lymphocytes, GO 0050871 is a function number, 100 is a gene number, and from the model, a heterogeneous three-point model with a tissue-interaction-gene type is queried, and the structure is triangular; according to different node types of the heterogeneous network, different types of edges can be generated; a meta path is defined as a path connecting two classes of objects, the formalized definition being written as:
wherein A isiIndicates the node type, RiRepresenting a relationship type;
step 2) determining a candidate motif set and a reference motif set according to the node query conditions given in the step 1.2), and dividing the steps into the following two steps:
2.1) calculating a candidate motif set; carrying out breadth-first search from the initial three-point die bodies to obtain a point set meeting the requirement of a meta path, and finding all the die bodies by using depth-first search; defining a plurality of meta-paths for querying the starting point of each type, wherein the starting node type of the meta-path is any node type contained in the starting motif, and the ending node type of the meta-path is one of the node types contained in the target motif; starting from an initial motif, using a defined meta-path, and querying by adopting a corresponding meta-path according to the node type of the initial motif, wherein the result obtained by querying the meta-path is a point set meeting the requirement; according to different types of the point concentration nodes, inquiring the motif meeting the conditions from different positions of the type nodes in the target motif as starting points; for the inquired motif, when the motif has an isomorphic motif, the same motif is calculated for multiple times due to different positions of the same node in the motif, so that the repeated motif needs to be removed from the result; finally, all generated motifs meeting the conditions are stored in a set, namely a candidate motif set;
2.2) calculating a reference motif set; in step 1.2), the query condition of the reference motif is given while the query condition of the candidate motif is given, wherein when the query condition of the reference motif set exists: obtaining a candidate motif set and a reference motif set according to the initial query condition and the query step of 2.1); the user may also present a set of initial query conditions in the same format as the candidate motif set: obtaining a candidate motif set according to the initial query condition and the query step of 2.1), and making the reference motif set equal to the candidate motif set to obtain a reference motif set;
step 3) calculating the similarity between each motif in the candidate motif set and the whole reference motifs according to the candidate motif set and the reference motif set obtained in the step 2);
3.1) calculating the similarity of each motif to the reference motif set; for each motif in the candidate motif set and the reference motif set, calculating a set of nodes which can be reached by the candidate motif set and the reference motif set through a meta-path for query and the number of different paths which pass through the nodes; since we use symmetric meta-paths to perform path number statistics, here we should first determine the intersection of two sets and then query the number of meta-paths after obtaining the reachable points and the number of paths of two motif sets via meta-path tissue-gene:
wherein m isaAnd represents a candidate motif, mbRepresents a reference motif, PsymRepresenting a path of a symmetric element, P representing a half of the paths constituting the path of the symmetric element, Num () function representing the number of paths, VabIndicating the die body maAnd a mold body mbA set of nodes that a point in (b) can go to via a certain meta-path, in VabThe value of (2) is used as the similarity between two points, and different weights of each path are defined under the condition that a plurality of query meta paths exist simultaneously, so that a weighted similarity value is obtained; the weight value is default to 1;
3.2) calculating the number of paths of each motif returning to the motif through the symmetrical element path, and normalizing the similarity; in the process, the influence of the same type of nodes and isomorphic factors on the calculation result still needs to be considered, and in the result, the number of meta-paths of each node returning to the node and the same type of nodes in the same motif needs to be counted as a standard for normalizing the similarity, that is, the method comprises the following steps:
calculating the number of paths from each motif in the candidate motif set and the reference motif set to the motif through the formula, wherein the number of the paths is the similarity with the motif; similarly, in the case where there are multiple meta paths and the weight is defined in 3.1), the same weight is also used for calculation in this step;
3.3) carrying out standardized operation on the similarity obtained in the step 3.1) by using the similarity of each motif obtained in the step 3.2) and the motif as a measurement standard; performing standardization operation by adopting different normalization similarities, wherein the normalization operation comprises a path similarity PathSim method and a cosine similarity method; the normalized path similarity between the defined motifs in the path similarity PathSim method is as follows:
wherein PathSim represents path similarity;
and obtaining the definition of the similarity between a motif and a reference motif set according to the definition of the similarity between the motifs:
wherein m isjRepresenting any of a set of standard motifs, SRRepresenting a reference motif set, wherein omega is the total path similarity;
and 4) sequencing each standardized die body according to the normal division similarity to obtain a similarity list result set from small to large, wherein the die bodies with lower similarity represent the abnormal parts in the die bodies meeting the requirements, and the differences between the die bodies with lower similarity and the whole candidate die body set are larger.
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