We propose an optimization of Dr. Ross Quinlan's C4.5 decision tree algorithm, used for data mining and classification. We will show that by discretizing and binning a data set's continuous attributes into four groups using our novel technique called MSD-Splitting, we can significantly improve both the algorithm's accuracy and efficiency, especially when applied to large data sets. We applied both the standard C4.5 algorithm and our optimized C4.5 algorithm to two data sets obtained from UC Irvine's Machine Learning Repository: Census Income and Heart Disease. In our initial model, we discretized continuous attributes by splitting them into two groups at the point with the minimum expected information requirement, in accordance with the standard C4.5 algorithm. Using five-fold cross-validation, we calculated the average accuracy of our initial model for each data set. Our initial model yielded a 75.72% average accuracy across both data sets. The average execution time of our initial model was 1,541.57 s for the Census Income data set and 50.54 s for the Heart Disease data set. We then optimized our model by applying MSD-Splitting, which discretizes continuous attributes by splitting them into four groups using the mean and the two values one standard deviation away from the mean as split points. The accuracy of our model improved by an average of 5.11% across both data sets, while the average execution time reduced by an average of 96.72% for the larger Census Income data set and 46.38% for the Heart Disease data set.
We perform an extensive analysis of optical counterparts of Planck PSZ2 clusters, considering matches with three recent catalogs built from Sloan Digital Sky Survey (SDSS) data: AMF DR9, redMaPPer (v6.3) and Wen et al (WHL). We significantly extend the number of optical counterparts of detected Planck clusters, and characterize the optical properties when multiple identifications in different catalogs exist. For Planck clusters which already possess an external validation, we analyze the redshift assignment for both optical and X-ray determinations. We then analyze the Planck Cosmology sample and comment on redshift determination and potential mass misdeterminations due to alignment issues. Finally, we inspect the reconstructed y map from Planck and reason on the detectability of optical clusters. Overall, AMF DR9 main (extended) finds 485 (511) optical matches, with 45 (55) previously unmatched PSZ2 clusters, to be compared with the 374 optical matches already present in PSZ2. 29 of the 55 previously unmatched clusters do not yet have a followup in the literature. 18 of these are found in more than one SDSS catalog with consistent redshifts. We provide redshift and mass estimates for the newly matched clusters, and discuss the comparison with the follow-ups, when present. We find good agreement between the redMaPPer and AMF DR9 redshift determinations. AMF DR9 tends to predict lower redshifts for a few PSZ2 high-redshift clusters which were previously validated by an optical counterpart. From the Planck Cosmology sample, optical matches are found for 204 of the 278 objects in the observed area. We find 14 clusters which merit further investigation, and discuss possible alignment issues for 9 of these clusters. After inspecting the y map, we provide a list of 229 optical clusters not included in the Planck PSZ2 catalog but showing a prominent y signal. We have further investigated the 86 clusters with Planck S/N> 4.5, 73 of which are unmasked by a nearby point source. From these potential clusters, using
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