TY - JOUR
T1 - Parzen windows for multi-class classification
AU - Pan, Zhi-Wei
AU - Xiang, Dao-Hong
AU - Xiao, Quan-Wu
AU - Zhou, Ding-Xuan
PY - 2008/10
Y1 - 2008/10
N2 - We consider the multi-class classification problem in learning theory. A learning algorithm by means of Parzen windows is introduced. Under some regularity conditions on the conditional probability for each class and some decay condition of the marginal distribution near the boundary of the input space, we derive learning rates in terms of the sample size, window width and the decay of the basic window. The choice of the window width follows from bounds for the sample error and approximation error. A novelly defined splitting function for the multi-class classification and a comparison theorem, bounding the excess misclassification error by the norm of the difference of function vectors, play an important role. © 2008 Elsevier Inc. All rights reserved.
AB - We consider the multi-class classification problem in learning theory. A learning algorithm by means of Parzen windows is introduced. Under some regularity conditions on the conditional probability for each class and some decay condition of the marginal distribution near the boundary of the input space, we derive learning rates in terms of the sample size, window width and the decay of the basic window. The choice of the window width follows from bounds for the sample error and approximation error. A novelly defined splitting function for the multi-class classification and a comparison theorem, bounding the excess misclassification error by the norm of the difference of function vectors, play an important role. © 2008 Elsevier Inc. All rights reserved.
KW - Approximation
KW - Excess misclassification error
KW - Multi-class classification
KW - Parzen windows
KW - Reproducing kernel Hilbert space
UR - http://www.scopus.com/inward/record.url?scp=54849441621&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-54849441621&origin=recordpage
U2 - 10.1016/j.jco.2008.07.001
DO - 10.1016/j.jco.2008.07.001
M3 - 21_Publication in refereed journal
VL - 24
SP - 606
EP - 618
JO - Journal of Complexity
JF - Journal of Complexity
SN - 0885-064X
IS - 5-6
ER -