Constraint-based substructure mining

According to the request of the user, the constraints described changes in the mining process. But, if we generalize and categorize them into specific constraints, the mining process would be handled easily by pushing them into the given frameworks.  constraint-pushing strategy is used in pattern growth mining tasks. Let’s see some important constraint categories.

• Subgraph containment constraint: When a user requests a pattern with specified subgraphs, this constraint is used. This constraint is also called a set containment constraint. The given set of subgraphs is taken as a query and then mining is done based on the chosen data by extending the patterns from the subgraph sets. This technique can be used to mine when the user requests patterns with specific sets of edges or vertices.
• Value- sum constraint: Here, the constraint is the sum of weights on the edges. There are two ranges high and low. The two constraints are designated as and  The first condition is called monotonic constraint because once the condition is satisfied, still the extension can take place by adding edges until the next condition is satisfied. But the latter condition is called anti-monotonic constraint because once the condition becomes satisfied, further no more extension can be made. By this method, the constraint-pushing technique will work out well.
• Geometric Constraint: In this constraint, the angle between pair of edges within a given range that is connected is taken. Let us consider a graph h, such that where E₁, E₂ are the edges connected at the vertex V and connected to the other two vertices at the other two ends V₁, V₂. A_h is called the anti-monotonic constraint because if any one of the angles formed by combining two edges didn’t satisfy, it does not move to the next level and it will never satisfy A_h. It can be pushed to the edge extension process and eliminate any extension that doesn’t satisfy A_h.

Data mining is the process of collecting and processing data from a heap of unprocessed data. When the patterns are established, various relationships between the datasets can be identified and they can be presented in a summarized format which helps in statistical analysis in various industries. Among the other data structures, the graph is widely used in modeling advanced structures and patterns. In data mining, the graph is used to find subgraph patterns for discrimination, classification, clustering of data, etc. The graph is used in network analysis. By linking the various nodes, graphs form network-like communications, web and computer networks, social networks, etc. In multi-relational data mining, graphs or networks is used because of the varied interconnected relationship between the datasets in a relational database.