Combining gradient ascent search and support vector machines for effective autofocus of a field emission–scanning electron microscope

Autofocus is an important issue in electron microscopy, particularly at high magnification. It consists in searching for sharp image of a specimen, that is corresponding to the peak of focus. The paper presents a machine learning solution to this issue. From seven focus measures, support vector machines fitting is used to compute the peak with an initial guess obtained from a gradient ascent search, that is search in the direction of higher gradient of focus. The solution is implemented on a Carl Zeiss Auriga FE-SEM with a three benchmark specimen and magnification ranging from x300 to x160 000. Based on regularized nonlinear least squares optimization, the solution overtakes the literature non-regularized search and Fibonacci search methods: accuracy improvement ranges from 1.25 to 8 times, fidelity improvement ranges from 1.6 to 28 times, and speed improvement ranges from 1.5 to 4 times. Moreover, the solution is practical by requiring only an off-line easy automatic train with cross-validation of the support vector machines

Differentiation of Linear Optical Circuits

Experimental setups based on linear optical circuits and single photon sources offer a promising platform for near-term quantum machine learning. However, current applications are all based on support vector machines and gradient-free optimization methods. Differentiating an optical circuit over a phase parameter poses difficulty because it results in an operator on the Fock space which is not unitary. In this paper, we show that the derivative of the expectation values of a linear optical circuit can be computed by sampling from a larger circuit, using one additional photon. In order to express the derivative in terms of expectation values, we develop a circuit extraction procedure based on unitary dilation. We end by showing that the full gradient of a universal programmable interferometer can be estimated using polynomially many queries to a boson sampling device. This is in contrast to the qubit setting, where exponentially many parameters are needed to cover the space of unitaries. Our algorithm enables applications of photonic technologies to machine learning, quantum chemistry and optimization, powered by gradient descent

Separable Convex Optimization with Nested Lower and Upper Constraints

We study a convex resource allocation problem in which lower and upper bounds are imposed on partial sums of allocations. This model is linked to a large range of applications, including production planning, speed optimization, stratified sampling, support vector machines, portfolio management, and telecommunications. We propose an efficient gradient-free divide-and-conquer algorithm, which uses monotonicity arguments to generate valid bounds from the recursive calls, and eliminate linking constraints based on the information from sub-problems. This algorithm does not need strict convexity or differentiability. It produces an $\epsilon$-approximate solution for the continuous problem in $\mathcal{O}(n \log m \log \frac{n B}{\epsilon})$ time and an integer solution in $\mathcal{O}(n \log m \log B)$ time, where $n$ is the number of decision variables, $m$ is the number of constraints, and $B$ is the resource bound. A complexity of $\mathcal{O}(n \log m)$ is also achieved for the linear and quadratic cases. These are the best complexities known to date for this important problem class. Our experimental analyses confirm the good performance of the method, which produces optimal solutions for problems with up to 1,000,000 variables in a few seconds. Promising applications to the support vector ordinal regression problem are also investigated

A Novel Approach for Image Localization Using SVM Classifier and PSO Algorithm for Vehicle Tracking

In this paper, we propose a novel methodology for vehicular image localization, by incorporating the surveillance image object identification, using a local gradient model, and vehicle localization using the time of action. The aerial images of different traffic densities are obtained using the Histograms of Oriented Gradients (HOG) Descriptor. These features are acquired simply based on locations, angles, positions, and height of cameras set on the junction board. The localization of vehicular image is obtained based on the different times of action of the vehicles under consideration. Support Vector Machines (SVM) classifier, as well as Particle Swarm Optimization (PSO), is also proposed in this work. Different experimental analyses are also performed to calculate the efficiency of optimization methods in the new proposed system. Outcomes from experimentations reveal the effectiveness of the classification precision, recall, and F measure