  Learning a classifier from ambiguously labeled face images is challenging
since training images are not always explicitly-labeled. For instance, face
images of two persons in a news photo are not explicitly labeled by their names
in the caption. We propose a Matrix Completion for Ambiguity Resolution (MCar)
method for predicting the actual labels from ambiguously labeled images. This
step is followed by learning a standard supervised classifier from the
disambiguated labels to classify new images. To prevent the majority labels
from dominating the result of MCar, we generalize MCar to a weighted MCar
(WMCar) that handles label imbalance. Since WMCar outputs a soft labeling
vector of reduced ambiguity for each instance, we can iteratively refine it by
feeding it as the input to WMCar. Nevertheless, such an iterative
implementation can be affected by the noisy soft labeling vectors, and thus the
performance may degrade. Our proposed Iterative Candidate Elimination (ICE)
procedure makes the iterative ambiguity resolution possible by gradually
eliminating a portion of least likely candidates in ambiguously labeled face.
We further extend MCar to incorporate the labeling constraints between
instances when such prior knowledge is available. Compared to existing methods,
our approach demonstrates improvement on several ambiguously labeled datasets.
