The existence of a strongly polynomial time simplex method

It is well known how to clarify whether there is a polynomial time simplex algorithm for linear programming (LP) is the most challenging open problem in optimization and discrete geometry. This paper gives a affirmative answer to this open question by the use of the parametric analysis technique that we recently proposed. We show that there is a simplex algorithm whose number of pivoting steps does not exceed the number of variables of a LP problem.Comment: 17 pages, 1 figur

Part-Based Visual Tracking via Online Weighted P-N Learning

We propose a novel part-based tracking algorithm using online weighted P-N learning. An online weighted P-N learning method is implemented via considering the weight of samples during classification, which improves the performance of classifier. We apply weighted P-N learning to track a part-based target model instead of whole target. In doing so, object is segmented into fragments and parts of them are selected as local feature blocks (LFBs). Then, the weighted P-N learning is employed to train classifier for each local feature block (LFB). Each LFB is tracked through the corresponding classifier, respectively. According to the tracking results of LFBs, object can be then located. During tracking process, to solve the issues of occlusion or pose change, we use a substitute strategy to dynamically update the set of LFB, which makes our tracker robust. Experimental results demonstrate that the proposed method outperforms the state-of-the-art trackers

Adaptive Initialization Method Based on Spatial Local Information for k

k-means algorithm is a widely used clustering algorithm in data mining and machine learning community. However, the initial guess of cluster centers affects the clustering result seriously, which means that improper initialization cannot lead to a desirous clustering result. How to choose suitable initial centers is an important research issue for k-means algorithm. In this paper, we propose an adaptive initialization framework based on spatial local information (AIF-SLI), which takes advantage of local density of data distribution. As it is difficult to estimate density correctly, we develop two approximate estimations: density by t-nearest neighborhoods (t-NN) and density by ϵ-neighborhoods (ϵ-Ball), leading to two implements of the proposed framework. Our empirical study on more than 20 datasets shows promising performance of the proposed framework and denotes that it has several advantages: (1) can find the reasonable candidates of initial centers effectively; (2) it can reduce the iterations of k-means’ methods significantly; (3) it is robust to outliers; and (4) it is easy to implement

Robust Visual Tracking via Local-Global Correlation Filter

Correlation filter has drawn increasing interest in visual tracking due to its high efficiency, however, it is sensitive to partial occlusion, which may result in tracking failure. To address this problem, we propose a novel local-global correlation filter (LGCF) for object tracking. Our LGCF model utilizes both local-based and global-based strategies, and effectively combines these two strategies by exploiting the relationship of circular shifts among local object parts and global target for their motion models to preserve the structure of object. In specific, our proposed model has two advantages: (1) Owing to the benefits of local-based mechanism, our method is robust to partial occlusion by leveraging visible parts. (2) Taking into account the relationship of motion models among local parts and global target, our LGCF model is able to capture the inner structure of object, which further improves its robustness to occlusion. In addition, to alleviate the issue of drift away from object, we incorporate temporal consistencies of both local parts and global target in our LGCF model. Besides, we adopt an adaptive method to accurately estimate the scale of object. Extensive experiments on OTB15 with 100 videos demonstrate that our tracking algorithm performs favorably against state-of-the-art methods

Adaptive Aggregating Multiresolution Feature Coding for Image Classification

The Bag of Visual Words (BoW) model is one of the most popular and effective image classification frameworks in the recent literature. The optimal formation of a visual vocabulary remains unclear, and the size of the vocabulary also affects the performance of image classification. Empirically, larger vocabulary leads to higher classification accuracy. However, larger vocabulary needs more memory and intensive computational resources. In this paper, we propose a multiresolution feature coding (MFC) framework via aggregating feature codings obtained from a set of small visual vocabularies with different sizes, where each vocabulary is obtained by a clustering algorithm, and different clustering algorithm discovers different aspect of image features. In MFC, feature codings from different visual vocabularies are aggregated adaptively by a modified Online Passive-Aggressive Algorithm under the histogram intersection kernel, which lead to a closed-form solution. Experiments demonstrate that the proposed method (1) obtains the same if not higher classification accuracy than the BoW model with a large visual vocabulary; and (2) needs much less memory and computational resources

Strong Heterogeneity in Shallow Lunar Subsurface Detected by Apollo Seismic Data

International audienceExperiencing heavy impacting, the Moon preserves a megaregolith in its shallow subsurface with physical properties that carry implications for lunar history. A strong scattering of seismic waves associated with the heterogeneous lunar megaregolith appears to be systematic, but deriving a statistical law of the random heterogeneities has remained elusive. Apollo seismic data are characterized by ultra-long coda waves with weak amplitude decay that provide an opportunity to explore the extent of heterogeneity in the lunar crust. We obtain by numerical simulation the appropriate parameters for seismic velocity and density perturbation of the shallow lunar crust that match Apollo seismic data. The perturbations of the shallow lunar crust identified here, which are at least 50%, are much larger than previously thought. This physical behavior thus both confirms a strongly heterogeneous surface layer as well as provides a new constraint on the structural characteristics of the megaregolith