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Considering the creation of persistence landscape on a parametrized curve andstructure of sampling, there exists a random process for which a finite mixturemodel of persistence landscape (FMMPL) can provide a better description for agiven dataset. In this paper, a nonparametric approach for computing integratedmean of square error (IMSE) in persistence landscape has been presented. As aresult, FMMPL is more accurate than the another way. Also, the samplingimportance resampling (SIR) has been presented a better description ofimportant landmark from parametrized curve. The result, provides more accuracyand less space complexity than the landmarks selected with simple sampling.

Finite Mixture Model of Nonparametric Density Estimation using Sampling Importance Resampling for Persistence Landscape