Are there frequent itemsets mining algorithms based on linear algebra?

Question

Matrix equations of some sort or matrix decompositions often lie in foundation of many algorithms not only in data analysis but in many other fields. The wealth of already written libraries makes it tempting to formulate frequent itemsets mining problems in terms of said matrix equations and/or decompositions, yet after some search I haven't found any algorithms which would rely on linear algebra. Could some please show me if such algorithms exist or explain their absence?

Answer 1

To elaborate on Vijay's answer

Firstly, it's not frequent itemset analysis, but you can use correlations to analyse the "shopping basket". This is amenable to linear algebra analysis. So you could do PCA, where you would first sphere the data- to remove the frequency effect of each item ( eg milk, bread being most frequently bought). Then pca would identify items that have high positive or negative correlation. another linear algebra option would be non negative matrix factorisation ( to try to decompose the shopping basket as a sum of a 'minibasket' of few positive amounts of each item).

frequent item set analysis does not limit itself to linear relations ( correlations).Eg in Wikipedia's example, you consider: $\text{onion}\cap \text{potatoes} \rightarrow \text{burger}$. Now just as with linear regression, you could augment your dataset by creating cross terms and looking at the correlation between onion x potato and burger (represented as eg dummy variables ), however this quickly becomes impractical... which is why frequent item set mining is used. One might argue however that there are few nonlinear relations that can be effectively estimated and correlations dominate - I haven't worked on that data so i can't answer...