A Graph-Based Semi-Supervised k Nearest-Neighbor Method for Nonlinear Manifold Distributed Data Classification

$k$ Nearest Neighbors ($k$NN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially when a very limited amount of labeled samples are available. In this paper, we propose a new graph-based $k$NN algorithm which can effectively handle both Gaussian distributed data and nonlinear manifold distributed data. To achieve this goal, we first propose a constrained Tired Random Walk (TRW) by constructing an $R$-level nearest-neighbor strengthened tree over the graph, and then compute a TRW matrix for similarity measurement purposes. After this, the nearest neighbors are identified according to the TRW matrix and the class label of a query point is determined by the sum of all the TRW weights of its nearest neighbors. To deal with online situations, we also propose a new algorithm to handle sequential samples based a local neighborhood reconstruction. Comparison experiments are conducted on both synthetic data sets and real-world data sets to demonstrate the validity of the proposed new $k$NN algorithm and its improvements to other version of $k$NN algorithms. Given the widespread appearance of manifold structures in real-world problems and the popularity of the traditional $k$NN algorithm, the proposed manifold version $k$NN shows promising potential for classifying manifold-distributed data.Comment: 32 pages, 12 figures, 7 table

Socializing the Semantic Gap: A Comparative Survey on Image Tag Assignment, Refinement and Retrieval

Where previous reviews on content-based image retrieval emphasize on what can be seen in an image to bridge the semantic gap, this survey considers what people tag about an image. A comprehensive treatise of three closely linked problems, i.e., image tag assignment, refinement, and tag-based image retrieval is presented. While existing works vary in terms of their targeted tasks and methodology, they rely on the key functionality of tag relevance, i.e. estimating the relevance of a specific tag with respect to the visual content of a given image and its social context. By analyzing what information a specific method exploits to construct its tag relevance function and how such information is exploited, this paper introduces a taxonomy to structure the growing literature, understand the ingredients of the main works, clarify their connections and difference, and recognize their merits and limitations. For a head-to-head comparison between the state-of-the-art, a new experimental protocol is presented, with training sets containing 10k, 100k and 1m images and an evaluation on three test sets, contributed by various research groups. Eleven representative works are implemented and evaluated. Putting all this together, the survey aims to provide an overview of the past and foster progress for the near future.Comment: to appear in ACM Computing Survey