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

Labeling the Features Not the Samples: Efficient Video Classification with Minimal Supervision

Feature selection is essential for effective visual recognition. We propose an efficient joint classifier learning and feature selection method that discovers sparse, compact representations of input features from a vast sea of candidates, with an almost unsupervised formulation. Our method requires only the following knowledge, which we call the \emph{feature sign}---whether or not a particular feature has on average stronger values over positive samples than over negatives. We show how this can be estimated using as few as a single labeled training sample per class. Then, using these feature signs, we extend an initial supervised learning problem into an (almost) unsupervised clustering formulation that can incorporate new data without requiring ground truth labels. Our method works both as a feature selection mechanism and as a fully competitive classifier. It has important properties, low computational cost and excellent accuracy, especially in difficult cases of very limited training data. We experiment on large-scale recognition in video and show superior speed and performance to established feature selection approaches such as AdaBoost, Lasso, greedy forward-backward selection, and powerful classifiers such as SVM.Comment: arXiv admin note: text overlap with arXiv:1411.771

Distributed Low-rank Subspace Segmentation

Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and corrupted input data. Low-Rank Representation (LRR), a convex formulation of the subspace segmentation problem, is provably and empirically accurate on small problems but does not scale to the massive sizes of modern vision datasets. Moreover, past work aimed at scaling up low-rank matrix factorization is not applicable to LRR given its non-decomposable constraints. In this work, we propose a novel divide-and-conquer algorithm for large-scale subspace segmentation that can cope with LRR's non-decomposable constraints and maintains LRR's strong recovery guarantees. This has immediate implications for the scalability of subspace segmentation, which we demonstrate on a benchmark face recognition dataset and in simulations. We then introduce novel applications of LRR-based subspace segmentation to large-scale semi-supervised learning for multimedia event detection, concept detection, and image tagging. In each case, we obtain state-of-the-art results and order-of-magnitude speed ups

Weakly-Supervised Alignment of Video With Text

Suppose that we are given a set of videos, along with natural language descriptions in the form of multiple sentences (e.g., manual annotations, movie scripts, sport summaries etc.), and that these sentences appear in the same temporal order as their visual counterparts. We propose in this paper a method for aligning the two modalities, i.e., automatically providing a time stamp for every sentence. Given vectorial features for both video and text, we propose to cast this task as a temporal assignment problem, with an implicit linear mapping between the two feature modalities. We formulate this problem as an integer quadratic program, and solve its continuous convex relaxation using an efficient conditional gradient algorithm. Several rounding procedures are proposed to construct the final integer solution. After demonstrating significant improvements over the state of the art on the related task of aligning video with symbolic labels [7], we evaluate our method on a challenging dataset of videos with associated textual descriptions [36], using both bag-of-words and continuous representations for text.Comment: ICCV 2015 - IEEE International Conference on Computer Vision, Dec 2015, Santiago, Chil