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# 计算机代写|计算机视觉代写Computer Vision代考|AMME4710 Stochastic Steepest Descent and Simulated Annealing

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## 计算机代写|计算机视觉代写Computer Vision代考|General Proceeding

A special case of objective functions which can be found quite often in practice is characterized by the fact that the objective function can be written as a sum of $N$ elements:

$$f(\mathbf{x})=\sum_{n=1}^N f_n(\mathbf{x})$$
This splitting of $f(\mathbf{x})$ into $N$ summands can be observed, e.g., for MRF-based energy functions. This structure is similar to $(2.21)$, but in contrast to $(2.21)$, the summands are not restricted to be square terms.

If we want to apply gradient-based optimization, even simple methods like steepest descent would involve a calculation of $\partial f_n(\mathbf{x}) / \partial \mathbf{x}$ for all $N$ components in every iteration, which could be infeasible as far as time demand is concerned.

An alternative approach is to perform an iterative optimization which considers only one of the summands of (2.44) at each iteration. Clearly, now more iterations are necessary, but at the same time, each iteration can be performed much faster, which should overcompensate for the increase in the number of iterations. The proceeding suggested here comprises the following steps:

1. Pick one $f_n(\mathbf{x})$ at random.
2. Try to reduce $f(\mathbf{x})$ by optimizing $f_n(\mathbf{x})$ with steepest descent, i.e., calculate $\partial f_n(\mathbf{x}) / \partial \mathbf{x}$ and perform a one-dimensional optimization in this direction.

## 计算机代写|计算机视觉代写Computer Vision代考|Example: Classiﬁﬁed Training for Object Class Recognition

Vijnhoven et al. [15] showed how stochastic gradient descent optimization can be successfully applied to the task of training a decision function for object detection. They considered the application of detecting instances of a certain object category, e.g., “cars” or “pedestrians,” in an image, which can be solved by the approach suggested in [4].

Dalal et al. derive a feature vector d (a so-called descriptor) which they call “Histograms of Oriented Gradients” (HOG) from a subregion of the image and, based on d, run a classifier which decides whether an instance of the object category to be searched is present at this particular position or not. The classifier has a binary output: $-1$ for “object not present” and 1 for “object present.” In order to scan the image, they propose a so-called sliding window approach, where the region for calculating the descriptor is shifted pixel by pixel over the entire image, with a subsequent classification at every position. Finally, they obtain a position vector where each element reveals the position of a detected instance of the searched object category.

The classifier has to be trained prior to recognition in an off-line teaching phase with the help of example images. A Support Vector Machine (SVM) for classification is used in [4], whereas the authors of [15] suggest to employ SGD in the classifier training step. Through the usage of SGD, they showed to reduce training times by a factor of $100-1,000$ with similar recognition performance.

Before we describe in detail how SGD is utilized in training, let’s first take a closer look at some different aspects of the proceeding of [4] (HOG descriptor, sliding window, and classifier design) in order to get a better understanding of the method.

## 计算机代写|计算机视觉代写Computer Vision代考|General Proceeding

$$f(\mathbf{x})=\sum_{n=1}^N f_n(\mathbf{x})$$

## 计算机代写|计算机视觉代写Computer Vision代考|Example: Classifified Training for Object Class Recognition

Vijnhoven 等人。 [15] 展示了如何将随机梯度下降优化成功应用于训绩目标检则夫策函数的任务。他们考虑了在图像中检则特定 对象类别的实例的应用，例吅“汽车“或”行人”，这可以通过 [4] 中建仪的方法来解快。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。