Classifying Functional Data from Orthogonal Projections – Model, Properties and Fast Implementation
| Autor: | Ewa Skubalska-Rafajłowicz, Ewaryst Rafajłowicz |
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| Rok vydání: | 2021 |
| Předmět: |
Correctness
Basis (linear algebra) Computer science Data classification Random element 02 engineering and technology 01 natural sciences 010104 statistics & probability 0202 electrical engineering electronic engineering information engineering Discrete cosine transform 020201 artificial intelligence & image processing Equidistant Differentiable function 0101 mathematics Finite set Algorithm |
| Zdroj: | Computational Science – ICCS 2021 ISBN: 9783030779665 ICCS (3) |
| DOI: | 10.1007/978-3-030-77967-2_3 |
| Popis: | We consider the problem of functional, random data classification from equidistant samples. Such data are frequently not easy for classification when one has a large number of observations that bear low information for classification. We consider this problem using tools from the functional analysis. Therefore, a mathematical model of such data is proposed and its correctness is verified. Then, it is shown that any finite number of descriptors, obtained by orthogonal projections on any differentiable basis of \(L_2(0,\, T)\), can be consistently estimated within this model. |
| Databáze: | OpenAIRE |
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