  The graph-based semi-supervised label propagation algorithm has delivered
impressive classification results. However, the estimated soft labels typically
contain mixed signs and noise, which cause inaccurate predictions due to the
lack of suitable constraints. Moreover, available methods typically calculate
the weights and estimate the labels in the original input space, which
typically contains noise and corruption. Thus, the en-coded similarities and
manifold smoothness may be inaccurate for label estimation. In this paper, we
present effective schemes for resolving these issues and propose a novel and
robust semi-supervised classification algorithm, namely, the
tri-ple-matrix-recovery-based robust auto-weighted label propa-gation framework
(ALP-TMR). Our ALP-TMR introduces a triple matrix recovery mechanism to remove
noise or mixed signs from the estimated soft labels and improve the robustness
to noise and outliers in the steps of assigning weights and pre-dicting the
labels simultaneously. Our method can jointly re-cover the underlying clean
data, clean labels and clean weighting spaces by decomposing the original data,
predicted soft labels or weights into a clean part plus an error part by
fitting noise. In addition, ALP-TMR integrates the au-to-weighting process by
minimizing reconstruction errors over the recovered clean data and clean soft
labels, which can en-code the weights more accurately to improve both data
rep-resentation and classification. By classifying samples in the recovered
clean label and weight spaces, one can potentially improve the label prediction
results. The results of extensive experiments demonstrated the satisfactory
performance of our ALP-TMR.
