Itemset mining has been an active area of research due to its successful application in various data mining scenarios including finding association rules. Though most of the past work has been on finding frequent itemsets, infrequent itemset mining has demonstrated its utility in web mining, bioinformatics and other fields. In this paper, we propose a new algorithm based on the pattern-growth paradigm to find minimally infrequent itemsets. A minimally infrequent itemset has no subset which is also infrequent. We also introduce the novel concept of residual trees. We further utilize the residual trees to mine multiple level minimum support itemsets where different thresholds are used for finding frequent itemsets for different lengths of the itemset. Finally, we analyze the behavior of our algorithm with respect to different parameters and show through experiments that it outperforms the competing ones.
To the best of our knowledge there has been only one other work that discusses the mining of MIIs. @cite_9 , proposed the algorithm which is based upon the algorithm developed for finding unique itemsets (itemsets with no unique proper subsets) @cite_10 @cite_6 . The authors also showed that the minimal infrequent itemset problem is NP-complete @cite_9 .
@cite_9 @cite_10 @cite_6
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A new algorithm for minimal infrequent itemset mining is presented. Potential applications of finding infrequent itemsets include statistical disclosure risk assessment, bioinformatics, and fraud detection. This is the first algorithm designed specifically for finding these rare itemsets. Many itemset properties used implicitly in the algorithm are proved. The problem is shown to be NP-complete. Experimental results are then presented. In this paper, we examine the issue of mining association rules among items in a large database of sales transactions. The mining of association rules can be mapped into the problem of discovering large itemsets where a large itemset is a group of items which appear in a sufficient number of transactions. The problem of discovering large itemsets can be solved by constructing a candidate set of itemsets first and then, identifying, within this candidate set, those itemsets that meet the large itemset requirement. Generally this is done iteratively for each large k-itemset in increasing order of k where a large k-itemset is a large itemset with k items. To determine large itemsets from a huge number of candidate large itemsets in early iterations is usually the dominating factor for the overall data mining performance. To address this issue, we propose an effective hash-based algorithm for the candidate set generation. Explicitly, the number of candidate 2-itemsets generated by the proposed algorithm is, in orders of magnitude, smaller than that by previous methods, thus resolving the performance bottleneck. Note that the generation of smaller candidate sets enables us to effectively trim the transaction database size at a much earlier stage of the iterations, thereby reducing the computational cost for later iterations significantly. Extensive simulation study is conducted to evaluate performance of the proposed algorithm. Recent work has highlighted the importance of the constraint based mining paradigm in the context of frequent itemsets, associations, correlations, sequential patterns, and many other interesting patterns in large databases. The authors study constraints which cannot be handled with existing theory and techniques. For example, avg(S) spl theta spl nu , median(S) spl theta spl nu , sum(S) spl theta spl nu (S can contain items of arbitrary values) ( spl theta spl isin spl ges , spl les ), are customarily regarded as "tough" constraints in that they cannot be pushed inside an algorithm such as a priori. We develop a notion of convertible constraints and systematically analyze, classify, and characterize this class. We also develop techniques which enable them to be readily pushed deep inside the recently developed FP-growth algorithm for frequent itemset mining. Results from our detailed experiments show the effectiveness of the techniques developed. In the period 1991–2015, algorithmic advances in Mixed Integer Optimization (MIO) coupled with hardware improvements have resulted in an astonishing 450 billion factor speedup in solving MIO problems. We present a MIO approach for solving the classical best subset selection problem of choosing k out of p features in linear regression given n observations. We develop a discrete extension of modern first-order continuous optimization methods to find high quality feasible solutions that we use as warm starts to a MIO solver that finds provably optimal solutions. The resulting algorithm (a) provides a solution with a guarantee on its suboptimality even if we terminate the algorithm early, (b) can accommodate side constraints on the coefficients of the linear regression and (c) extends to finding best subset solutions for the least absolute deviation loss function. Using a wide variety of synthetic and real datasets, we demonstrate that our approach solves problems with n in the 1000s and p in the 100s in minutes to provable optimality, and finds near optimal solutions for n in the 100s and p in the 1000s in minutes. We also establish via numerical experiments that the MIO approach performs better than Lasso and other popularly used sparse learning procedures, in terms of achieving sparse solutions with good predictive power.