New Variants of Frank-Wolfe Algorithm for Video Co-localization Problem

The co-localization problem is a model that simultaneously localizes objects of the same class within a series of images or videos. In \cite{joulin2014efficient}, authors present new variants of the Frank-Wolfe algorithm (aka conditional gradient) that increase the efficiency in solving the image and video co-localization problems. The authors show the efficiency of their methods with the rate of decrease in a value called the Wolfe gap in each iteration of the algorithm. In this project, inspired by the conditional gradient sliding algorithm (CGS) \cite{CGS:Lan}, We propose algorithms for solving such problems and demonstrate the efficiency of the proposed algorithms through numerical experiments. The efficiency of these methods with respect to the Wolfe gap is compared with implementing them on the YouTube-Objects dataset for videos.Comment: 20 pages, 7 figures, Future Technologies Conference (FTC) 202

On Variants of Sliding and Frank-Wolfe Type Methods and Their Applications in Video Co-localization

In this dissertation, our main focus is to design and analyze first-order methods for computing approximate solutions to convex, smooth optimization problems over certain feasible sets. Specifically, our goal in this dissertation is to explore some variants of sliding and Frank-Wolfe (FW) type algorithms, analyze their convergence complexity, and examine their performance in numerical experiments. We achieve three accomplishments in our research results throughout this dissertation. First, we incorporate a linesearch technique to a well-known projection-free sliding algorithm, namely the conditional gradient sliding (CGS) method. Our proposed algorithm, called the conditional gradient sliding with linesearch (CGSls), does not require the knowledge of Lipschitz constant of the gradient of objective function, which is critical in the numerical implementation of the CGS method. Second, we explore the possibility of designing a bundle level type version of the CGS method, which to the best of our knowledge has not yet appeared in the literature. Our proposed sliding APL (SAPL) method achieves the same complexity to the CGS method. Third, we study numerical algorithms for solving the image co-localization problem. For this problem, we propose new variants of the Frank-Wolfe (FW) method and compare their empirical performance with other existing methods. The dissertation is organized as follows. In the first chapter, we review some projection-based and projection-free algorithms, their variants, and their respective advantages and disadvantages. Several useful definitions, theorems, and lemmas are also introduced in this chapter that will be utilized throughout the dissertation. For completeness, we prove most of the known results listed in this chapter (proof deferred to the appendix). In the second chapter, we incorporate a linesearch technique to the well-known CGS method and propose the CGSls method. We show that the proposed CGSls method converges with similar complexity to the CGS method. We also examine the performance of the proposed algorithm by comparing it to the CGS method and other projection-free algorithms. In the third chapter, we explore the possibility of designing a bundle level type variant of the CGS method. The proposed SAPL method is inspired by previous literature on bundle level type method. Such bundle level type method has not yet appeared in any literature on sliding algorithms. We show that the proposed SAPL method converge with the same order of complexity as the CGS and CGSls methods. In the fourth chapter, we apply the algorithms studied in previous chapters to the well-known video co-localization problem. We also propose new variants of the FW method and compare their empirical performance with other numerical methods

A Projection-Free Algorithm for Solving Support Vector Machine Models

In this thesis our goal is to solve the dual problem of the support vector machine (SVM) problem, which is an example of convex smooth optimization problem over a polytope. To this goal, we apply the conditional gradient (CG) method by providing explicit solution to the linear programming (LP) subproblem. We also describe the conditional gradient sliding (CGS) method that can be considered as an improvement of CG in terms of number of gradient evaluations. Even though CGS performs better than CG in terms of optimal complexity bounds, it is not a practical method because it requires the knowledge of the Lipschitz constant and also the number of iterations. As an improvement of CGS, we designed a new method, conditional gradient sliding with line search (CGS-ls) that resolves the issues in CGS method. CGS-ls requires $O(1/\sqrt{1/\epsilon})$ gradient evaluations and $O(1/\epsilon)$ linear optimization calls that achieves the optimal complexity bounds in CGS method. We also compare the performance of our method with CG and CGS methods as numerical results by experimenting them in dual problem of SVM for binary classification of two subsets of the MNIST hand-written digits dataset

Reliability of functional connectivity in resting-state functional MRI

     Functional MRI is a noninvasive method in brain imaging. Localization, classification, prediction and connectivity are the most common issues. Functional connectivity is a branch of fMRI that focuses on connectivity between voxels and ROIs. There are several methods for investigating functional connectivity such as correlation analysis. In any field, it is very important that results of any research have reliability according to the experiment. Any methods and measurement instruments need to be reliable. Without reliability, results are meaningless and our research is not trustworthy. Brain imaging can be used as a valuable tool for pre-surgical planning, so the results should be highly reproducible. Test-retest reliability can be explored using the intra-class correlation coefficient (ICC). I2C2 is an extent of ICC to verify the reliability in high-dimensional data as imaging studies. 13 subjects of test-retest resting-state fMRI are used to investigate reliability. I2C2 of four ROIs are also computed (Caudate, Cingulate, Cuneus and Precentral regions). Functional connectivity is found to have moderate reliability ranging 0.6244 to 0.6941. 95% confidence interval of I2C2 is calculated by nonparametric bootstrap in which CI of Caudate region I2C2 has the shortest length.

Analysis of the fundamental tourism entrepreneurial factors affecting the sustainable rural development of Koohrang County

The present study tries to investigate to move towards sustainable development what conditions the study population should have in the field of tourism entrepreneurship. The research is descriptive and surveys in terms of nature and method and practical in terms of purpose. data collection is used documentary sources and survey method and based on the distribution of questionnaires among 254 head of households living. The number of samples was selected using Sample power software in a random stratified manner following the principle of proportional division. QCA method was used. The singular analysis showed that the index of "growth and development" and "environmental adaptation" with seven repetitions in different cases have the most support for the result. In the composite analysis, five causal combinations were obtained with acceptable theoretical adequacy. The combination of "socio-cultural adaptation" and "growth and development" conditions with a coverage coefficient of 0.794 and a Consistency coefficient of 0.917, respectively, has the highest impact on sustainable rural development. Then, the combination of "growth and development" and "creativity and innovation" with a coverage coefficient of 0.783 and a Consistency coefficient of 0.895. The combination of "environmental compatibility" and "growth and development" with a coverage coefficient of 0.78 and a Consistency coefficient of 0.888, is the third effective combination. Therefore, to measure the impact of tourism entrepreneurship on sustainable rural development, it is necessary to examine the extent of socio-cultural adaptation, environmental adaptation, innovation, and its growth and development effects in the life of the host community

An exploratory study to identify critical factors of innovation culture in organizations

During the past two decades, there has been a growing trend on knowledge-based organizations. Innovation, on the other hand, plays essential role on building competitive business units. In this paper, we present an exploratory study to identify critical factors of innovation culture in organizations. We detect important factors influencing innovation culture in construction industry based on the implementation of factor analysis. The proposed study designs a questionnaire and distributes it among 400 experts who are involved in construction industry. Cronbach alpha has been calculated as 0.779, which validates the overall questionnaire. The results of factor analysis have indicated that six factors of building cultural infrastructures, education, organizational vision, established culture, strategic culture and flexible culture are the most important items influencing innovation culture

Corporate Life Cycle and the Explanatory Power of Risk Measures versus Performance Measures

The major aim of this paper is to compare the explanatory power of risk measures versus performance measures in different life-cycle stages. To test the hypotheses, first, sample firms were classified into three life-cycle stages (Growth, Mature and Decline). Then, using regression models and Vuong's Z-statistic, the hypotheses were investigated. In this study, financial information of 75 firms which were accepted at Tehran’s Stock Exchange (TSE) from 2003 to 2008 (450 firm-years) was examined. The results of this study show that in growth and decline stages, the explanatory power of risk measures is significantly higher than performance measures and in mature stage, the opposite is true