An effective discretization method for disposing high-dimensional data

A deep network embedded with rough fuzzy discretization for OCT fundus image segmentation

The noise and redundant information are the main reasons for the performance bottleneck of medical image segmentation algorithms based on the deep learning. To this end, we propose a deep network embedded with rough fuzzy discretization (RFDDN) for OCT fundus image segmentation. Firstly, we establish the information decision table of OCT fundus image segmentation, and regard each category of segmentation region as a fuzzy set. Then, we use the fuzzy c-means clustering to get the membership degrees of pixels to each segmentation region. According to membership functions and the equivalence relation generated by the brightness attribute, we design the individual fitness function based on the rough fuzzy set, and use a genetic algorithm to search for the best breakpoints to discretize the features of OCT fundus images. Finally, we take the feature discretization based on the rough fuzzy set as the pre-module of the deep neural network, and introduce the deep supervised attention mechanism to obtain the important multi-scale information. We compare RFDDN with U-Net, ReLayNet, CE-Net, MultiResUNet, and ISCLNet on the two groups of 3D retinal OCT data. RFDDN is superior to the other five methods on all evaluation indicators. The results obtained by ISCLNet are the second only inferior to those obtained by RFDDN. DSC, sensitivity, and specificity of RFDDN are evenly 3.3%, 2.6%, and 7.1% higher than those of ISCLNet, respectively. HD95 and ASD of RFDDN are evenly 6.6% and 19.7% lower than those of ISCLNet, respectively. The experimental results show that our method can effectively eliminate the noise and redundant information in Oct fundus images, and greatly improve the accuracy of OCT fundus image segmentation while taking into account the interpretability and computational efficiency.

Merging of Numerical Intervals in Entropy-Based Discretization

As previous research indicates, a multiple-scanning methodology for discretization of numerical datasets, based on entropy, is very competitive. Discretization is a process of converting numerical values of the data records into discrete values associated with numerical intervals defined over the domains of the data records. In multiple-scanning discretization, the last step is the merging of neighboring intervals in discretized datasets as a kind of postprocessing. Our objective is to check how the error rate, measured by tenfold cross validation within the C4.5 system, is affected by such merging. We conducted experiments on 17 numerical datasets, using the same setup of multiple scanning, with three different options for merging: no merging at all, merging based on the smallest entropy, and merging based on the biggest entropy. As a result of the Friedman rank sum test (5% significance level) we concluded that the differences between all three approaches are statistically insignificant. There is no universally best approach. Then, we repeated all experiments 30 times, recording averages and standard deviations. The test of the difference between averages shows that, for a comparison of no merging with merging based on the smallest entropy, there are statistically highly significant differences (with a 1% significance level). In some cases, the smaller error rate is associated with no merging, in some cases the smaller error rate is associated with merging based on the smallest entropy. A comparison of no merging with merging based on the biggest entropy showed similar results. So, our final conclusion was that there are highly significant differences between no merging and merging, depending on the dataset. The best approach should be chosen by trying all three approaches.

Graph clustering-based discretization of splitting and merging methods (GraphS and GraphM)

Discretization plays a major role as a data preprocessing technique used in machine learning and data mining. Recent studies have focused on multivariate discretization that considers relations among attributes. The general goal of this method is to obtain the discrete data, which preserves most of the semantics exhibited by original continuous data. However, many techniques generate the final discrete data that may be less useful with natural groups of data not being maintained. This paper presents a novel graph clustering-based discretization algorithm that encodes different similarity measures into a graph representation of the examined data. The intuition allows more refined data-wise relations to be obtained and used with the effective graph clustering technique based on normalized association to discover nature graphs accurately. The goodness of this approach is empirically demonstrated over 30 standard datasets and 20 imbalanced datasets, compared with 11 well-known discretization algorithms using 4 classifiers. The results suggest the new approach is able to preserve the natural groups and usually achieve the efficiency in terms of classifier performance, and the desired number of intervals than the comparative methods.