Recently, convolutional neural network (CNN) visual features have demonstrated their powerful ability as a universal representation for various recognition tasks. In this paper, cross-modal retrieval with CNN visual features is implemented with several classic methods. Specifically, off-the-shelf CNN visual features are extracted from the CNN model, which is pretrained on ImageNet with more than one million images from 1000 object categories, as a generic image representation to tackle cross-modal retrieval. To further enhance the representational ability of CNN visual features, based on the pretrained CNN model on ImageNet, a fine-tuning step is performed by using the open source Caffe CNN library for each target data set. Besides, we propose a deep semantic matching method to address the cross-modal retrieval problem with respect to samples which are annotated with one or multiple labels. Extensive experiments on five popular publicly available data sets well demonstrate the superiority of CNN visual features for cross-modal retrieval.
The total rAFS score, but not rAFS stage, is a risk factor for recurrence of both endometrioma and dysmenorrhea, indicating that the rAFS stage has little prognostic value. The existence of a completely random recurrence period may be a universal phenomenon, with its duration and the magnitude of recurrence risk determined by patient characteristics and quality of care. The second phase of much higher recurrence risk may reflect successful reseeding, reimplantation, and regrowth of ectopic endometrium. Therefore, the identification of risk factors as well as patterns of recurrence should shed better light on possible causes for recurrence, which is now poorly understood.
This paper considers general rank-constrained optimization problems that minimize a general objective function f (X) over the set of rectangular n × m matrices that have rank at most r. To tackle the rank constraint and also to reduce the computational burden, we factorize X into U V T where U and V are n × r and m × r matrices, respectively, and then optimize over the small matrices U and V . We characterize the global optimization geometry of the nonconvex factored problem and show that the corresponding objective function satisfies the robust strict saddle property as long as the original objective function f satisfies restricted strong convexity and smoothness properties, ensuring global convergence of many local search algorithms (such as noisy gradient descent) in polynomial time for solving the factored problem. We also provide a comprehensive analysis for the optimization geometry of a matrix factorization problem where we aim to find n × r and m × r matrices U and V such that U V T approximates a given matrix X . Aside from the robust strict saddle property, we show that the objective function of the matrix factorization problem has no spurious local minima and obeys the strict saddle property not only for the exact-parameterization case where rank(X ) = r, but also for the over-parameterization case where rank(X ) < r and the under-parameterization case where rank(X ) > r. These geometric properties imply that a number of iterative optimization algorithms (such as gradient descent) converge to a global solution with random initialization.
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