# Naive Bayesian Classifier on transactions

For a long time I have the idea to enhance my BudgetApp application with machine learning techniques. I would like to use these techniques to categorize my transactions. Let me first explain how my current solution works. I have a set of rules that are used to assign a category to a transaction. In principle there are two kind of rules: Rules based on the description of a transaction and rules based on the contra account number of the transaction. The first rule that matches the transaction is used to categorize the transaction. The rules engine works quite well. About 90% of all transactions are recurring so these can be categorized automatically. But on the moment you get a new kind of transaction that will be recurring you have to create a new rule so in the near future this will be categorized automatically. My total ruleset now contains about 100 rules. In a few years I collected about 1400 transactions that are categorized with the above mechanism. After trying a implementation of the K-nearest-neighbor algorithm. I finally use a bayesian classifier implementation which works quite well.

So 2 weeks ago I finally decided to try using machine learning techniques. With all the categorized transactions I have a great set of data that I can use for supervised learning, also this can be used to validate my solution. There are a few basic assumptions for my solution. I don’t mind that the chosen solution is not able to classify a transaction but it should have very little incorrect classifications. The tool is used to create a budget and if too many transactions are incorrectly classified, the budget might be incorrect.

One of the easiest classification algoritms to implement is K nearest neigbour. The algoritm might be slow if you have many data points. But my total data set seems to be small (only 1400 entries). The main part of this algorithm is to construct a distance function that determines how similar the new transaction to categorize is compared to all other transactions. Looking at the previous solution I recon that there are two major features of a transaction that are used to categorize a transaction: Description and Contra account. So probably the distance function should use these two things to categorize a transaction. I think that the contra account is a good place to start. Basically each different contra account should indicate another category. While running this on the real data I notice that I got a lot of incorrect categorizations in my set, and more importantly that it takes a few minutes to calculate the category of 10 transactions based on the ‘learned’ input of about 1000 transactions. So the solution is actually pretty slow even on my small data set. Another problem I have is that I can’t think of a way to construct a description distance function. I don’t find it acceptable that a categorization of a dozen transactions takes minutes as the old way only takes seconds. After checking if I could improve my calculations I found I didn’t make any major mistakes. Now I have an extra requirement: the solution should be about as fast as the rules solution.

Back to the drawing board it is. I need to select a different classification algoritm. After spending some time on the wikipedia pages I think a naive bayesian classifier might help me. It is pretty straightforward to implement. Furthermore it seems to be quite effective and efficient for similar problems (like spam filtering). A naive bayesian classifier assumes that an absence or presence of a feature is independent of the presence or absence of another feature. This assumption is often wrong, but in practice it seems to work pretty well. Let’s implement this thing.

Starting with the contra account number. What is the probability that a new transaction has contra account 123 and belongs to category x? I think it should be the number of transactions with contra account 123 and category x in the training set divided by the number of all transactions with contra account 123 I can’t think of a better way to find the probabilities on this feature. After implementing this thing I use about 10% of all known transactions as training set and try to categorize the remaining transactions to validate my solution. The results are really promising: 533 transactions are categorized correctly, 697 couldn’t be categorized based on the contra account number (basically the contra account number for these transactions is zero or not in my training set), and only 11 transactions are classified incorrectly. After some investigation on these incorrect transactions I notice that 10 of them fall in the category “salary” while it should be “expense claim”. As my probability only takes the account number as feature this makes sense. I have far more salary payments than expense claim payments. This problem should be resolved if I add more features to my probability calculations. Probably if I add description the distinction can be made. I might include the transaction amount as well as these amounts are quite far apart.

Implementing the probability of the descriptions is similar to the contra account number: the number of transactions with word y in the description and category x in the training set divided by the number of all transactions with word y in the description. This works only for a single word in the description. To combine multiple words these probabilities should be multiplied. Ok implemented, time to validate again: 912 transaction classified successfully, 208 can’t be classified and 121 classified incorrectly. The incorrect classifications worry me. If I look into the details I see that most of them are classified as groceries but the actual category can be many things e.g. gifts. The problem here is that most incorrect transactions are “pin” transactions as we call that in the Netherlands, transactions paid with my debit card. The transactions are categorized as groceries due to similarities in the description field. They all contain the same words.

At this moment the solution cannot replace the ruleset mainly due to the high number of incorrect classifications. However I want to include other features as well. The amount should fix some problems.

P.S. As a proof that the old system is not ideal as well I found 1 transaction that was incorrectly classified in the old system!

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