84 research outputs found
Grafting for Combinatorial Boolean Model using Frequent Itemset Mining
This paper introduces the combinatorial Boolean model (CBM), which is defined
as the class of linear combinations of conjunctions of Boolean attributes. This
paper addresses the issue of learning CBM from labeled data. CBM is of high
knowledge interpretability but na\"{i}ve learning of it requires exponentially
large computation time with respect to data dimension and sample size. To
overcome this computational difficulty, we propose an algorithm GRAB (GRAfting
for Boolean datasets), which efficiently learns CBM within the
-regularized loss minimization framework. The key idea of GRAB is to
reduce the loss minimization problem to the weighted frequent itemset mining,
in which frequent patterns are efficiently computable. We employ benchmark
datasets to empirically demonstrate that GRAB is effective in terms of
computational efficiency, prediction accuracy and knowledge discovery
Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds
Machine learning for point clouds has been attracting much attention, with
many applications in various fields, such as shape recognition and material
science. To enhance the accuracy of such machine learning methods, it is known
to be effective to incorporate global topological features, which are typically
extracted by persistent homology. In the calculation of persistent homology for
a point cloud, we need to choose a filtration for the point clouds, an
increasing sequence of spaces. Because the performance of machine learning
methods combined with persistent homology is highly affected by the choice of a
filtration, we need to tune it depending on data and tasks. In this paper, we
propose a framework that learns a filtration adaptively with the use of neural
networks. In order to make the resulting persistent homology
isometry-invariant, we develop a neural network architecture with such
invariance. Additionally, we theoretically show a finite-dimensional
approximation result that justifies our architecture. Experimental results
demonstrated the efficacy of our framework in several classification tasks.Comment: 17 pages with 4 figure
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