Labelwalking nonnegative matrix factorization

Semi-supervised learning (SSL) utilizes plenty of unlabeled examples to boost the performance of learning from limited labeled examples. Due to its great discriminant power, SSL has been widely applied to various real-world tasks such as information retrieval, pattern recognition, and speech separa- tion. Label propagation (LP) is a popular SSL method which propagates labels through the dataset along high density areas defined by unlabeled examples, LP assumes nearby examples should share the same label, thus, it unavoidably pushes the labels to the wrong examples, especially when different la- beled examples are not strictly separated. Seed K-means uses labeled examples to initialize class centers, and avoid getting stuck in poor local optima comparing to traditional K-means, however the hard constraint of each example's membership makes Seed K-means failed in many real world applications. This paper proposes a novel label walking nonnegative matrix factorization method (LWNMF) to handle labeled examples in SSL based on the framework of NMF. LWNMF decomposes the whole dataset into the product of a basis matrix and a coefficient matrix, and to travel labels to unlabeled examples, LWNMF regards the class indicators of labeled examples as their coefficients and iteratively updates both basis matrix and coefficients of unlabeled examples. Since LWNMF learns comprehensive class centroids, labels iteratively walk to unlabeled examples through these significant centroids.