Title :
Principal curves: learning and convergence
Author :
Kegl, Balazs ; Krzyzak, Adam ; Linder, Tamas ; Zeger, Kenneth
Author_Institution :
Dept. of Comput. Sci., Concordia Univ., Montreal, Que., Canada
Abstract :
Principal curves have been defined as “self consistent” smooth curves which pass through the “middle” of a d-dimensional probability distribution or data cloud. We take a new approach by defining principal curves as continuous curves of a given length which minimize the expected squared distance between the curve and points of the space randomly chosen according to a given distribution. The new definition makes it possible to carry out a theoretical analysis of learning principal curves from training data and it also leads to a new practical construction
Keywords :
data analysis; learning (artificial intelligence); probability; statistical analysis; continuous curves; convergence; data cloud; learning; principal curves; probability distribution; self consistent smooth curves; squared distance; training data; Clouds; Computer science; Convergence; Mathematics; Statistics; Training data;
Conference_Titel :
Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
0-7803-5000-6
DOI :
10.1109/ISIT.1998.708992
