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Download file# A New Interpolation Approach and Corresponding Instance-Based Learning

Starting from finding
approximate value of a function, introduces the measure of approximation-degree
between two numerical
values, proposes the concepts of “strict approximation” and “strict approximation region”, then, derives the
corresponding one-dimensional interpolation methods and formulas, and then
presents a calculation model called “sum-times-difference formula” for
high-dimensional interpolation, thus develops a new interpolation approach, that is, ADB interpolation. ADB interpolation is applied to the interpolation of
actual functions with satisfactory results. Viewed from principle and effect, the interpolation approach is of novel idea, and has
the advantages of simple calculation, stable accuracy, facilitating parallel processing, very suiting for
high-dimensional interpolation,
and easy to be extended to the interpolation of vector valued functions. Applying
the approach to instance-based learning, a new instance-based learning method,
learning using ADB interpolation, is obtained. The learning method is of unique technique, which has also the advantages of definite mathematical basis, implicit distance weights, avoiding
misclassification, high efficiency, and wide range of applications, as well as being interpretable, etc. In principle, this method
is a kind of learning by analogy, which and the deep learning that belongs to inductive learning can
complement each other, and for some problems, the two can even have an effect
of “different approaches but
equal results” in big data and cloud
computing environment.
Thus, the learning using ADB
interpolation can also be regarded as a kind of “wide learning” that is dual to deep learning.