1、training images are annotated with a set of keywords describing their contents, but the visual concepts are not explicitly segmented in the images. formulate the weakly-supervised image classification as a low-rank matrix completion problem.三大优势: (1) convex 相较于multiple-instance learning methods . We
2、 propose two alternative algorithms for matrix completionMC-Pos and MC-Simplex, motivated by the multi-label image classification problem and the additive histogram propertyspecifically tailored to visual data, and prove their convergence. (2) is robust to labeling errors, background noise and parti
3、al occlusions. (3) be used for semantic segmentation. Can effectively capturing each class appearance.Methodsimage classification and localizaion problemMIL- consider images as bags with many instances denoting possible regions of interest(BOWS)drawbacks:(1) cast as a NP-hard binary quadratic proble
4、m 、lead to non-convex models 、highly sensible to initialization、heavily rely on an explicit enumeration of instances(2) lack robustness to outliers(3) Unclear to be extended to use partial information , such as incomplete label assignments or missing feature descriptions.For instance, in Fig. 1a one
5、 training image has no label for the category grass.Our methodthe histogram of an entire image is a weighted sum of the histogram information of all of its subparts ( to factorize the histogram of an image as a weighted sum of class histograms (as many as objects are present) plus an error to model
6、the background.) Using this property we bypass the combinatorial nature of finding desired regions in every positive image image classification can be posed as a rank minimization problem, since class histograms are shared across images, and the number of class histograms is small compared to the nu
7、mber of images.a matrix completion framework. 1、Classification as a Matrix Completion Problem the use of matrix completion for general classification tasks use for weakly supervised multi-label image classification and localizationBy directly estimating C:the appearance of individual classes can be
8、recovered from a multi-label data set thus provide the localization for each concept in the images.2、Nuclear Norm as a Convex Surrogate of the Rank Function to minimize (rank is non -convex and non-differentiable function) nuclear norm Z的奇异值的和3、Adding Robustness into Matrix CompletionThe resulting o
9、ptimization problem finds the best label assignment Ytst and error Matrices such that the rank of Z is minimized, as4、Fixed Point Continuation(FPC) for MC-Pos/MC -Simplex enjoy the same convergence properties of fixed point continuation (FPC) methods for rank minimization without constraints.Albeit
10、convex, the nuclear norm makes (24) and (25) not smooth. Since nuclear norm problems are naturally cast as Semidefinite Programs, existing interior point methods are inapplicable due to the large dimension of Z. FPC-总结:1、 key idea histograms of full images contain the information for parts contained
11、 therein, so weakly supervised learning can be formulated as a low-rank problem due to its addive nature, and solved using a transductive matrix completion framework2、 two new convex methods for performing multi-label classification of histogram data, with proven convergence properties3、able to find class histogram representations and provide localization in the images.4、matrix completion allows for handling of missing data, labeling errors, background noise and partial occlusions
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