Unsupervised Entity Resolution using Graphs
By: Karan Sindwani
Tags: Graph, Optimization, Data Science, Unsupervised Learning

What is Entity Resolution ?

Entity Resolution refers to the task of finding all mentions of same -real world entity within a knowledge base or across multiple knowledge bases. This can be achieved through linking and grouping.For example, there could be different ways of addressing the same person in text, different addresses for businesses, or photos of a particular object.

Motivation for Entity Resolution

In the modern world, the speed and volume of data has increased exponentially. Thus making inference across networks and semantic relationships between entities a greater challenge to overcome. Entity resolution can reduce the complexity by proposing canonicalised references to entities and deduplicating and linking entities. The applications of entity resolution are tremendous, particularly for public sector and federal datasets related to health, transportation, finance, law enforcement, and antiterrorism

Tasks in Entity Resolution

Entity Resolution Tasks

Deduplication: The process of clustering/grouping records or mentions that represent the same real world entity .

Record Linkage: The process of matching records from one deduplicated knowledge base to another.

Canonicalisation: The process of converting data with more than one possible representation into a standard form.

Reference Matching: The process of matching noisy records to clean ones in a deduplicated reference table.

Challenges For Entity Resolution

One might face many challenges while performing entity resolution on a data set. The first one being due to poor quality of data available. This is mostly to presence of unstructured data or human maintained data such as such as different spellings (cancel and cancelling), missing values (e.g., missing price ) and ambiguity . The traditional pair-wise distance approaches are less effective on noisy datasets.

Additionally, the presence of one-to-many and many-to-many relation between entities creates a challenge. For instance, a product might be associated with many prices (normal or discount), and each manufacturer is associated with many products. The heterogeneous nature of relationships brings in an additional challenge when performing collective entity resolution : to determine which kind of relationship is best suited for resolving a particular type of entity.

Graphical Approach to Entity Resolution

In this section an unsupervised graphical solution is proposed to solve entity resolution.

Illustration

Problem Formulation

Firstly, The original dataset is transformed into multiple K-type graphs , with nodes representing fields of the row entries of the dataset. Nodes are connected by weighted edges representing relationships between entities themselves as well as between entities and their attributes. The weights on edges within layer represent the similarity scores while edges between two layers are calculated using TFIDF score.

The goal is to reduce the entity resolution problem to a graph summarisation problem where the nodes representing different mentions of the same hidden entity are summarised

k sets of super nodes , where each super node denotes a cluster of same type of vertices in the original graph (S)

, where each super node denotes a cluster of same type of vertices in the original graph (S) (k C 2 ) sets of links where each weighted edge denotes the expected probability that one type of super node is connected with another type of super node (L)

k sets of “zoom-in” mappings such that each mapping denotes probabilistic mapping between vertices and super nodes.( C )

One can postulate that super nodes in summary graph need to be coherent, in other words the nodes which are clustered in a super node should be similar to each other. The explanation behind this assumption is that different mentions of the same hidden entity needs to share some similarities otherwise the problem is infeasible.

Inherent Similarity : Similarity between content of nodes

Structural Similarity : Similar connectivity patterns in the multi-type graph

To accommodate for the first type of similarity, we define the following optimisation:

equation_1

This objective function ensures that any summary graph in which two highly similar vertices (x; y) are not mapped to the same super node, incurs a penalty.

To accommodate for structural similarity, we define the following optimisation:

equation_2

Next step would be to combine equation 1 and 2 to form equation 3

equation_3

Equation 3 tends to produce more super nodes. The first term becomes irrelevant if two nodes are very dissimilar (sim(x; y) 0), whereas the second term will tend to assign structurally dissimilar nodes to different super nodes. Furthermore, the second term favours a larger number of super nodes, whereas the first term tends to condense similar nodes as much as possible. These differences introduce some nontrivial tradeoffs in the optimisation process, which allow us to arrive at good summary graphs

Methodology

Solution Overview

In this section , a solution to equation 3 is introduced. The overview of the solution is as follows :

Start with a random summary graph

Search for an improved summary graph with fewer super nodes, by crossing out one or many super nodes

The next step is to fix the number of super nodes and compute the vertex-to-clustering mapping C(Equation 4) and super links L (Equation 5)

These two procedures are performed alternately, until they reach a locally optimal summary graph

Graphs Summarisation with super nodes

We assume that the number of super nodes in the summary graph is given. With this assumption, the vertex to super nodes mapping C and the connections among super nodes L can be computed with a standard multiplicative update.The intuition of the multiplicative rule is that whenever the solution is smaller than the local optimum, it multiplies with a larger value; otherwise, it multiplies with a smaller value.

Equation_4

Equation 4 calculates the vertex to super nodes mapping.

Similarly equation 5 calculates connections among super nodes

Equation 5

Searching for Optimal Number of Super Nodes

A greedy local search algorithm is proposed that can automatically determine the number of super nodes. The intuition of the approach is to use a backward search procedure : starting with an initialisation of a summary graph, where each type of vertices is assigned to a maximum number of clusters, it repeatedly removes one or many super nodes from a summary graph with the lowest information.

Limitations

In this blog, a multi graph co-summarisation based method was proposed that simultaneously identifies entities and their connections.

The proposed method has some limitations. First, the quality of entity-resolution solution depends on the quality of the user-supplied same-type vertex similarity.

Second, if the same-type vertex similarity matrices and the observed graphs are very dense, the proposed algorithm is not scalable.

References

Unsupervised Entity Resolution on Multi-type Graphs. ISWC 2016–15th International Semantic Web Conference. 2016. Linhong Zhu and Majid Ghasemi-Gol and Pedro Szekely and Aram Galstyan and Knoblock, Craig A. http://usc-isi-i2.github.io/papers/zhu16-iswc.pdf