Multinational corporations have multiple databases distributed throughout their branches, which store millions of transactions per day. For business applications, identifying disjoint clusters of similar and relevant databases contributes to learning the common buying patterns among customers and also increases the profits by targeting potential clients in the future. This process is called clustering, which is an important unsupervised technique for big data mining. In this article, we present an effective approach to search for the optimal clustering of multiple transaction databases in a weighted undirected similarity graph. To assess the clustering quality, we use dual gradient descent to minimize a constrained quasi-convex loss function whose parameters will determine the edges needed to form the optimal database clusters in the graph. Therefore, finding the global minimum is guaranteed in a finite and short time compared with the existing non-convex objectives where all possible candidate clusterings are generated to find the ideal clustering. Moreover, our algorithm does not require specifying the number of clusters a priori and uses a disjoint-set forest data structure to maintain and keep track of the clusters as they are updated. Through a series of experiments on public data samples and precomputed similarity matrices, we show that our algorithm is more accurate and faster in practice than the existing clustering algorithms for multi-database mining.

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Clustering algorithms for multi-database mining (MDM) rely on computing (n2−n)/2 pairwise similarities between n multiple databases to generate and evaluate m∈[1,(n2−n)/2] candidate clusterings in order to select the ideal partitioning that optimizes a predefined goodness measure. However, when these pairwise similarities are distributed around the mean value, the clustering algorithm becomes indecisive when choosing what database pairs are considered eligible to be grouped together. Consequently, a trivial result is produced by putting all the n databases in one cluster or by returning n singleton clusters. To tackle the latter problem, we propose a learning algorithm to reduce the fuzziness of the similarity matrix by minimizing a weighted binary entropy loss function via gradient descent and back-propagation. As a result, the learned model will improve the certainty of the clustering algorithm by correctly identifying the optimal database clusters. Additionally, in contrast to gradient-based clustering algorithms, which are sensitive to the choice of the learning rate and require more iterations to converge, we propose a learning-rate-free algorithm to assess the candidate clusterings generated on the fly in fewer upper-bounded iterations. To achieve our goal, we use coordinate descent (CD) and back-propagation to search for the optimal clustering of the n multiple database in a way that minimizes a convex clustering quality measure L(θ) in less than (n2−n)/2 iterations. By using a max-heap data structure within our CD algorithm, we optimally choose the largest weight variable θp,q(i) at each iteration i such that taking the partial derivative of L(θ) with respect to θp,q(i) allows us to attain the next steepest descent minimizing L(θ) without using a learning rate. Through a series of experiments on multiple database samples, we show that our algorithm outperforms the existing clustering algorithms for MDM.

Clustering algorithms for multi-database mining (MDM) rely on computing $(n^2-n)/2$ pairwise similarities between $n$ multiple databases to generate and evaluate $m\in[1, (n^2-n)/2]$ candidate clusterings in order to select the ideal partitioning which optimizes a predefined goodness measure. However, when these pairwise similarities are distributed around the mean value, the clustering algorithm becomes indecisive when choosing what database pairs are considered eligible to be grouped together. Consequently, a trivial result is produced by putting all the $n$ databases in one cluster or by returning $n$ singleton clusters. To tackle the latter problem, we propose a learning algorithm to reduce the fuzziness in the similarity matrix by minimizing a weighted binary entropy loss function via gradient descent and back-propagation. As a result, the learned model will improve the certainty of the clustering algorithm by correctly identifying the optimal database clusters. Additionally, in contrast to gradient-based clustering algorithms which are sensitive to the choice of the learning rate and require more iterations to converge, we propose a learning-rate-free algorithm to assess the candidate clusterings generated on the fly in a fewer upper-bounded iterations. Through a series of experiments on multiple database samples, we show that our algorithm outperforms the existing clustering algorithms for MDM.