TY - JOUR
AU1 - Yin, Penghang
AU2 - Pham, Minh
AU3 - Oberman, Adam
AU4 - Osher, Stanley
AB - In this paper, we propose an implicit gradient descent algorithm for the classic k-means problem. The implicit gradient step or backward Euler is solved via stochastic fixed-point iteration, in which we randomly sample a mini-batch gradient in every iteration. It is the average of the fixed-point trajectory that is carried over to the next gradient step. We draw connections between the proposed stochastic backward Euler and the recent entropy stochastic gradient descent for improving the training of deep neural networks. Numerical experiments on various synthetic and real datasets show that the proposed algorithm provides better clustering results compared to k-means algorithms in the sense that it decreased the objective function (the cluster) and is much more robust to initialization.
TI - Stochastic Backward Euler: An Implicit Gradient Descent Algorithm for k-Means Clustering
JF - Journal of Scientific Computing
DO - 10.1007/s10915-018-0744-4
DA - 2018-05-31
UR - https://www.deepdyve.com/lp/springer-journals/stochastic-backward-euler-an-implicit-gradient-descent-algorithm-for-k-KH505woBm1
SP - 1133
EP - 1146
VL - 77
IS - 2
DP - DeepDyve
ER -