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Functional Curve Fitting Algorithm via Multi-Heterogeneous Data Curve


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Abstract


Complex computing based on multi-heterogeneous parameters can utilize the Lebesgue measure to measure their linear and non-linear relations in innite dimensional Hilbert space, which can characterize those different dimensional characteristics in a set of autonomous learning base. The temporal-spatial micro-scalemildew indices can be tted by using four heterogeneous parameters, including temperature, humidity, wind force, and water vapor pressure. This paper proposes a tting process of heterogeneous parameter curves, which is based on a common reference coordinate base. The multi-scale functional tting tree is constructed by R  -tree and the Lebesgue similarity measure algorithm. When the similarity of two tree nodes representative of similar environmental sub-space exceeds a given threshold, these nodes can be combined into a parent node, which represents the environmental characteristic of combined bigger-space and its mildew curve is the tted result of all the son-node mildew curves. The curve similaritymeasurement based on the Lebesguemulti-dimensional matrix and the functional curve generating process of multi-heterogeneous data curves are proposed in the micro-space mildew index tting example. The boundary nding of tting curves can be realized by envelop curve algorithm. Based on two years environmental measurement parameters of ancient dwellings, the mildew index comparison of indoor and outdoor can be obtained. The experimental results show that the multi-heterogeneous curve tting algorithm is effective and the mildew indices of indoor and outdoor have cyclical differences

KeyWords
Lebesgue measure, Hilbert space, mildew index, curve tting, R  -tree



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