Narrow Results

Topological data analysis is a relatively new branch of machine learning that excels in studying high-dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical attributes are ubiquitous in real-world applications. However, topological methods are usually applied to point cloud data, and to the best of our knowledge there is no available framework for the classification of mixed data using topological methods. In this paper, we propose a novel topological machine learning method for mixed data classification. In the proposed method, we use theory from topological data analysis such as persistent homology, persistence diagrams and Wasserstein distance to study mixed data. The performance of the proposed method is demonstrated by experiments on a real-world heart disease dataset. Experimental results show that our topological method outperforms several state-of-the-art algorithms in the prediction of heart disease.

For plate bending and stretching problems in piezoelectric materials, the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate mixed boundary conditions accurate to all order. The method developed by Gregory and Wan is used to establish necessary conditions which the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate; for the case of axisymmetric bending and stretching of a circular plate, these decaying state conditions are obtained explicitly for the first time when the mixed conditions are imposed on the plate edge. They are then used for the correct formulation of boundary conditions for the interior solution.

Efficient partitioning of large data sets into homogenous clusters is a fundamental problem in data mining. The standard hierarchical clustering methods provide no solution for this problem due to their computational inefficiency. The k-means based methods are promising for their efficiency in processing large data sets. However, their use is often limited to numeric data. But mixed data with numeric data and categorical data are extensive used. K-prototypes algorithm is based on the k-means paradigm but removes the numeric data limitation whilst preserving its efficiency. This paper researched the k-prototype algorithm and simulated it with mixed data .The simulation result express k-prototype algorithm is effective for clustering large data sets because it's time cost is linear increase by degrees.