In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. International Nuclear Information System (INIS) Histogram bin width selection for time-dependent Poisson processes The experimental results on synthetic data sets show the robustness of the BRDs to partial matching, and the experiments on seven benchmark data sets demonstrate promising results of the BRDs for image classification.

The BRDs and logistic regression-based histogram fusion are applied to image classification. We propose a method for assessing the robustness of histogram distances to partial matching.

These combinations exploit and benefit from the robustness of the BRD under partial matching and the robustness of the â„“1 and Ï‡(2) distances to small noise. We combine the BRD with the â„“1 histogram distance and the Ï‡(2) histogram distance to generate the â„“1 BRD and the Ï‡(2) BRD, respectively. The BRD is robust to partial matching and histogram normalization, and captures correlations between bins with only a linear computational complexity. We propose a bin ratio-based histogram distance (BRD), which is an intra-cross- bin distance, in contrast with previous bin-to-bin distances and cross- bin distances. In this paper, we deal with this problem by using the ratios between bin values of histograms, rather than bin values' differences which are used in the traditional histogram distances. Large variations in image background may cause partial matching and normalization problems for histogram-based representations, i.e., the histograms of the same category may have bins which are significantly different, and normalization may produce large changes in the differences between corresponding bins. Hu, Weiming Xie, Nianhua Hu, Ruiguang Ling, Haibin Chen, Qiang Yan, Shuicheng Maybank, Stephen The interplay between these opposing factors effectively implements Occam's razor by selecting the most simple model that best describes the data.īin Ratio-Based Histogram Distances and Their Application to Image Classification. The maximum of the posterior probability occurs at a point where the prior probability and the the joint likelihood are balanced. Opt BINS (optimal binning) determines the optimal number of bins in a uniform bin-width histogram by deriving the posterior probability for the number of bins in a piecewise-constant density model after assigning a multinomial likelihood and a non-informative prior.

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