20,796 research outputs found
Knowledge reduction of dynamic covering decision information systems with varying attribute values
Knowledge reduction of dynamic covering information systems involves with the
time in practical situations. In this paper, we provide incremental approaches
to computing the type-1 and type-2 characteristic matrices of dynamic coverings
because of varying attribute values. Then we present incremental algorithms of
constructing the second and sixth approximations of sets by using
characteristic matrices. We employ experimental results to illustrate that the
incremental approaches are effective to calculate approximations of sets in
dynamic covering information systems. Finally, we perform knowledge reduction
of dynamic covering information systems with the incremental approaches
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Combining numeric and symbolic learning techniques
Incremental learning from examples in a noisy domain is a difficult problem in Machine Learning. In this paper we divide the task into two subproblems and present a combination of numeric and symbolic approaches that yields robust learning of boolean characterizations. Our method has been implemented in a computer program, and we plot its empirical learning performance in the presence of varying amounts of noise
A DEIM Induced CUR Factorization
We derive a CUR matrix factorization based on the Discrete Empirical
Interpolation Method (DEIM). For a given matrix , such a factorization
provides a low rank approximate decomposition of the form ,
where and are subsets of the columns and rows of , and is
constructed to make a good approximation. Given a low-rank singular value
decomposition , the DEIM procedure uses and to
select the columns and rows of that form and . Through an error
analysis applicable to a general class of CUR factorizations, we show that the
accuracy tracks the optimal approximation error within a factor that depends on
the conditioning of submatrices of and . For large-scale problems,
and can be approximated using an incremental QR algorithm that makes one
pass through . Numerical examples illustrate the favorable performance of
the DEIM-CUR method, compared to CUR approximations based on leverage scores
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