Using Advanced Maths for Inspection

A number of central banks are investing time and money to understand the life cycle and performance of banknotes based on tracking the changes in individual banknote detector scores over time. It does this by reading banknote serial numbers, and their detector data, and analysing the results. Given the number of detectors on a sorting machine, the volume of data generated reaches the realms of ‘big data’.

Keesing Technology posted a paper by Ramesh Paskarathas, ‘Big Banknote Data – Exploring the Challenges and Applications of Big Data Analysis to Banknote Data’, which discusses three mathematical techniques being used by the Bank of Canada, explaining how they work, why they are used and what they can deliver. The paper does not give an insight into the life of a banknote, but it does delve into the modelling techniques needed to get to those insights.

When data volumes are in the tens of millions, and that data is in a relatively simple format of integers and strings, conventional computing techniques, statistical tools, and sample statistics can be used. In 2017 the Bank of Canada published a study on their circulation trials using traditional regression techniques on single-CPU systems.

When the number of banknote records grows to a few billion, new tools and techniques are needed to make sense of these data. The three data analytic techniques in this paper are a correlogram analysis of wear categories, principal component analysis (PCA) to simplify the data, and data mining using Association Rules to understand the relationships between types of wear are presented.

Correlogram Analysis

Correlation is a statistical method that can show whether, and if so how strongly, pairs of variables are related. A correlogram is a visual representation of a correlation analysis that can make relationships between large sets of variables easy to see.

Unfortunately, this visual tool does not show how groups of pairwise correlations relate to one another. In addition, if the set of variables is large, it can be very hard, if not impossible, to see the structure of the relationships.

This is why the second tool, PCA, is relevant since it helps group variables together and is used as a data simplification tool.

Principal Component Analysis

PCA is a data compression technique that replaces a larger number of correlated variables with a smaller number of uncorrelated variables. In addition to simplifying the data, it allows for relationships among sets of variables, rather than just pairs. The resulting components from PCA are often inputs into other models such as regression, classification, and clustering.

Correlations and PCA can create spurious relationships when there are dominant categories that occur very frequently. To limit these, and to understand probabilities of occurrence for specific categories, such as wear on a banknote, Association Rules (market based) algorithms can be used.

Association Rules

Association rule analysis searches for connections among a very large number of variables; these include objects or attributes that frequently occur together. Examples of where this technique is used are, for example, understanding products that are often bought together during a shopping session, queries that tend to occur together during a session on a website’s search engine, etc.

Although we are capable of such insights intuitively, it takes expert-level knowledge, or a great deal of experience, to do what a rule-learning algorithm can do in minutes.