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In this paper, we introduce the homological de-noising algorithm whose purpose is preparing point cloud data (PCD) sets that are noisy to analyze topological data. We essentially, base this method on the homological persistence whose using avoids choosing a parameter ε. Alternatively, the interval of ε must be defined for which the topological feather occurs. In computational, this algorithm is an efficient. We can run it easily. We improve and generalize the topological de-noising algorithm. We can apply this algorithm to noisy sampling, for example, the circle and sphere in the Euclidean space. Finally, we apply the new algorithm to the noisy sampling of the torusℝ3 in and the Klein bottle in ℝ4 .
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