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# 计算机代写|机器学习代写Machine Learning代考|MKTG6010

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## 计算机代写|机器学习代写Machine Learning代考|ECOC Weighted Decoding

The ECOC method consists of repeatedly partitioning the full set of $N$ classes $\Omega=\left{\omega_i \mid i=1 \ldots N\right}$ into $L$ super-class pairs. The choice of partitions is represented by an $N \times L$ binary code matrix $\mathbf{Z}$. The rows $\mathbf{Z}i$ are unique codewords that are associated with the individual target classes $\omega_i$ and the columns $\mathbf{Z}^j$ represent the different super-class partitions. Denoting the $j$ th super-class pair by $\mathrm{S}^j$ and $\overline{\mathrm{S}^j}$, element $Z{i j}$ of the code matrix is set to 1 or $0^1$ depending on whether class $\omega_i$ has been put into $\mathrm{S}^j$ or its complement. A separate base classifier is trained to solve each of these 2-class problems.

Given an input pattern vector $\mathbf{x}$ whose true class $c(\mathbf{x}) \in \Omega$ is unknown, let the soft output from the $j$ th base classifier be $s_j(\mathbf{x}) \in[0,1]$. The set of outputs from all the classifiers can be assembled into a vector $\mathbf{s}(\mathbf{x})=\left[s_1(\mathbf{x}), \ldots, s_L(\mathbf{x})\right]^{\mathrm{T}} \in[0,1]^L$ called the output code for $\mathbf{x}$. Instead of working with the soft base classifier outputs, we may also first harden them, by rounding to 0 or 1 , to obtain the binary vector $\mathbf{h}(\mathbf{x})=\left[h_1(\mathbf{x}), \ldots, h_L(\mathbf{x})\right]^{\mathrm{T}} \in{0,1}^L$. The principle of the ECOC technique is to obtain an estimate $\hat{c}(\mathbf{x}) \in \Omega$ of the class label for $\mathbf{x}$ from a knowledge of the output code $\mathbf{s}(\mathbf{x})$ or $\mathbf{h}(\mathbf{x})$.

In its general form, a weighted decoding procedure makes use of an $N \times L$ weights matrix $\mathbf{W}$ that assigns a different weight to each target class and base classifier combination. For each class $\omega_i$ we may use the $\mathrm{L}1$ metric to compute a class score $F_i(\mathbf{x}) \in[0,1]$ as follows: $$F_i(\mathbf{x})=1-\sum{\mathrm{j}=1}^{\mathrm{L}} \mathbf{W}{\mathrm{ij}}\left|\mathrm{s}{\mathrm{j}}(\mathbf{x})-\mathbf{Z}{\mathrm{ij}}\right|,$$ where it is assumed that the rows of $\mathbf{W}$ are normalized so that $\sum{j=1}^L \mathbf{W}{i j}=1$ for $i=$ $1 \ldots N$. Patterns may then be assigned to the target class $\hat{c}(\mathbf{x})=\arg \max {\omega_i} F_i(\mathbf{x})$. If the base classifier outputs $s_j(\mathbf{x})$ in Eq. 1.1 are replaced by hardened values $h_j(\mathbf{x})$ then this describes the weighted Hamming decoding procedure.

In the context of this chapter $\Omega$ is the set of known AU groups and we are also interested in combining the class scores to obtain values that measure the likelihood that AUs are present; this is done by summing the $F_i(\mathbf{x})$ over all $\omega_i$ that contain the given $\mathrm{AU}$ and dividing by $N$. That is, the score $G_k \in[0,1]$ for $\mathrm{AU}{\mathrm{k}}$ is given by: $$G_k(\mathbf{x})=\frac{1}{N} \sum{A U_k \in \omega_i} F_i(\mathbf{x})$$

## 计算机代写|机器学习代写Machine Learning代考|Platt Scaling

It often arises in pattern recognition applications that we would like to obtain a probability estimate for membership of a class but that the soft values output by our chosen classification algorithm are only loosely related to probability. Here, this applies to the scores $G_k(\mathbf{x})$ obtained by applying Eq. 1.2 to detect individual AUs in an image. Ideally, the value of the scores would be balanced, so that a value $>0.5$ could be taken to indicate that $\mathrm{AU}{\mathrm{k}}$ is present. In practice, however, this is often not the case, particularly when $\mathrm{AU}{\mathrm{k}}$ belongs to more than or less than half the number of AU groups.

To correct for this problem Platt scaling [15] is used to remap the training-set output scores $G_k(\mathbf{x})$ to values which satisfy this requirement. The same calibration curve is then used to remap the test-set scores. An alternative approach would have been to find a separate threshold for each AU but the chosen method has the added advantage that the probability information represented by the remapped scores could

be useful in some applications. Another consideration is that a wide range of thresholds can be found that give low training error so some means of regularisation must be applied in the decision process.Platt scaling, which can be applied to any 2-class problem, is based on the regularisation assumption that the correct form of calibration curve that maps classifier scores $G_k(\mathbf{x})$ to probabilities $p_k(\mathbf{x})$, for an input pattern $\mathbf{x}$, is a sigmoid curve described by the equation:
$$p_k(\mathbf{x})=\frac{1}{1+\exp \left(A G_k(\mathbf{x})+B\right)},$$
where the parameters $A$ and $B$ together determine the slope of the curve and its lateral displacement. The values of $A$ and $B$ that best fit a given training set are obtained using an expectation maximisation algorithm on the positive and negative examples. A separate calibration curve is computed for each value of $k$.

## 计算机代写|机器学习代写Machine Learning代考|ECOC Weighted Decoding

ECOC方法包括将完整的$N$类集$\Omega=\left{\omega_i \mid i=1 \ldots N\right}$重复划分为$L$超类对。分区的选择由一个$N \times L$二进制代码矩阵$\mathbf{Z}$表示。行$\mathbf{Z}i$是与各个目标类$\omega_i$相关联的唯一码字，列$\mathbf{Z}^j$表示不同的超类分区。通过$\mathrm{S}^j$和$\overline{\mathrm{S}^j}$表示$j$超类对，代码矩阵的元素$Z{i j}$被设置为1或$0^1$，这取决于类$\omega_i$是否被放入$\mathrm{S}^j$或它的补充中。一个单独的基分类器被训练来解决这两类问题。

## 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。