### 计算机代写|机器学习代写machine learning代考|COMP30027

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 计算机代写|机器学习代写machine learning代考|Contrast Enhancement

The contrasting of the resized input image $\operatorname{Im}^{\mathrm{g}}$ is enhanced here. The particular procedure controls the image intensity $[16,22,23]$ and thus the image resolution is developed via the brightness and darkness of $\mathrm{Im}^{\mathrm{g}}$, as given by Equation (1.1), in which $V$ refers to the contrast improvement of the image. Therefore, the current $\operatorname{Im}^{\mathrm{g}}$ transforms into a grey image $\operatorname{Im}_{n e w}^{\mathrm{g}}$.
$$V=\left(\begin{array}{l} \left.((\text { Im -low_in }) /(\text { high_in-low_in }))^{\wedge} \text { gamma }\right) \ *(\text { high_out-low_out }) \end{array}\right)+\text { low_out }$$
Grey thresholding: The Otsu’s oriented grey thresholding [20] method portrays the threshold of the image, which is exploited for converting the grey pixel to either black or white. This is performed depending on the grey intensity (refer Figure 1.3).

Active contour [19]: Here, 2 types of driven forces namely, external and internal energy are exploited. This framework gets smoothed via internal forces and it is reallocated in the direction through the external energy. Therefore, the contour $G(n)$ is formed by the coordinate sets such as $l(n)$ and $k(n)$ as given in Equation (1.2), where $(k, l)$ indicates the contour coordinates and denotes the normalized index of the control point.
$$G(n)=(k(n) l(n)) ; G(n) \in \operatorname{Im}{n e w}^{C}(k, l)$$ Equation (1.3) shows the total energy of deformed design, where $\operatorname{Im}^{\mathrm{g}^{\text {int }} \text { indi- }}$ cates the internal energy of the curve, $\operatorname{Im}^{\mathrm{g}^{\text {con }}}$ denotes the exterior restriction, denotes the energy of the image. $$F O^{*}=\int{0}^{1}\left(F O^{\text {int } l} G(n)+F O^{i m} G(n)+F O^{c o n} G(n)\right) d n$$
In addition, the bending energy and elastic energy are summed up to form the internal energy as specified in Equation (1.4), where $\alpha(n), \beta(n)$ indicates the varying parameter that denotes continuity and contour curving respectively.
\begin{aligned} F O^{\text {int } l} &=F O^{\text {elastic }}+F O^{\text {bend }}=\alpha(n)\left|\frac{d u}{d n}\right|^{2}+\beta(n)\left|\frac{d^{2} u}{d n^{2}}\right|^{2} \ F O^{\text {elastic }} &=\alpha(G(n)-G(n-1))^{2} d n \ F O^{\text {bend }} &=\beta\left(G(n-1)-G(n)+(G(n+1))^{2} d n\right. \end{aligned}
Finally, the pre-processed image $\operatorname{Im}_{\text {pre }}$ is determined from the initial stage.

## 计算机代写|机器学习代写machine learning代考|Classification

This work exploits $\mathrm{NN}[18,24]$ for recognizing caries. The input feature set is given by Equation (1.7), in which $N_{D}$ denotes the count of elected features.
$$F E^{\text {weight }}=\left[F_{1}, F_{2}, F_{3}, F_{4} \ldots F_{N_{D}}\right]$$
The weight $W E$ of the network model is portrayed by the LM framework. Equation (1.8) portrays the NN framework, in which the resultant output from $i^{\text {th }}$ node of $j^{\text {th }}$ layer is given by $o u_{l}^{(j)}$. The input is signified by $F E^{\text {weight }}{ }{i}^{j}$, $a f(\bullet)$ indicates the activation function, the entire count of input to $j^{\text {th }}$ layer is given by $n u^{(j)}, b i{i}$ symbolizes the input bias to $j^{\text {th }}$ layer, $c$ and $d$ denotes the weight coefficient of $W E$ as specified in Equation (1.9). The predicted network output $\hat{P}$ is given by Equation (1.10), in which $w^{0}$ signifies the bias weight and $w^{(h)}$ defines the hidden neuron weight.
$$\begin{gathered} o u_{l}^{(j)}=a f\left[c_{l}^{(j)} b i_{j}+\sum_{i=1}^{n u^{(j)}} F E_{i}^{\text {weight }(j)} d_{i l}^{(j)}\right] \ W E=[c ; d] \ \hat{P}=w^{0}+\sum_{i=1}^{n u^{(j)}} o u_{l}^{(j)} w_{i}^{(h)} W E \end{gathered}$$
So as to train the network, the network weight $W E^{*}$ is optimally chosen with the determination of objective function as in Equation (1.11), where $P$ indicates the actual output.
$$W E^{*}=\arg \min [W E]|P-\hat{P}|$$
Thus the classifier classifies the input image (non-caries or caries image).

## 计算机代写|机器学习代写machine learning代考|Nonlinear Programming Optimization

The issue regarding the nonlinear program is given in Equation (1.15), in which $\hat{h}(\hat{x}), \hat{i}(\hat{x})$ and $\hat{j}(\hat{x})$ are portrayed as ‘deferential functions’.
$$\min {\hat{y}} \hat{h}(\hat{x})=0$$ So that \begin{aligned} &\hat{i}(\hat{x})=0 \ &\hat{j}(\hat{x})=0 \end{aligned} The substitution of Equation (1.15) is done by a sequence of barrier sub issues as specified in Equation (1.17), in which $\hat{l}>0$ points out the vector of slack parameters, $\hat{k}=(\hat{x}, \hat{l})$ and $\mu>0$ denotes the barrier constraint. $$\min {\hat{k}} \varphi_{\mu}(\hat{k}) \equiv \hat{h}(\hat{x})-\mu \sum_{\hat{o}}^{\hat{n}} \operatorname{In} \hat{l}_{\hat{o}}$$ $$\hat{i}(\hat{y})=0$$
So that $\hat{j}(\hat{x})+\hat{l}=0$
The Lagrangian function associated with Equation (1.17) is specified in Equation (1.19), in which $\zeta_{\hat{i}}, \zeta_{\hat{a}}$ indicates the ‘Lagrange multipliers’ and $\zeta=\left(\zeta_{\hat{i}}, \zeta_{\hat{a}}\right)$
$$\aleph(\hat{k}, \zeta ; \mu)=\varphi_{\mu}(\hat{k})+\zeta_{\hat{i}}^{\hat{v}} \hat{i}(\hat{x})+\zeta_{\hat{a}}^{\hat{v}}(\hat{a}(\hat{x})+\hat{l})$$
The optimality states in Equation (1.17) could be specified as per Equation (1.20), in which $\hat{l}$ and $\zeta_{\hat{a}}$ are non-negative, $\hat{Y}{\hat{i}}$ and $\hat{Y}{\hat{a}}$ refers to Jacobian matrices, $\hat{D}$ and $\Gamma_{\hat{a}}$ points out the diagonal matrices.
$$\left[\begin{array}{c} \nabla \hat{h}(\hat{x})+\hat{Y}{\hat{i}}(\hat{x})^{\hat{v}} \zeta{\hat{i}}+\hat{Y}{\hat{a}}(\hat{x})^{\hat{v}} \zeta{\hat{a}} \ \hat{D} \Gamma_{\hat{a}} \hat{e}-\mu \hat{e} \end{array}\right]=\left[\begin{array}{l} 0 \ 0 \end{array}\right]$$
Further, the current iterate $(\hat{k}, \zeta)$ outcomes in the primal-dual system as given by Equation (1.21), in which $\hat{z}{\hat{k}}=\left[\begin{array}{c}\dot{z}{\hat{x}} \ \hat{z}{\hat{l}}\end{array}\right], \quad \hat{z}{\zeta}=\left[\begin{array}{c}\dot{z}{\hat{i}} \ \hat{z}{\hat{a}}\end{array}\right]$,
$\hat{c}(\hat{k})=\left[\begin{array}{l}\hat{i}(\hat{x}) \ \hat{j}(\hat{x})+\hat{l}\end{array}\right], \hat{Y}(\hat{x})=\left[\begin{array}{cc}\hat{Y}{\hat{i}}(\hat{x}) & o \ \hat{Y}{\hat{a}}(\hat{x}) & 1\end{array}\right]$ and $\hat{R}(\hat{k}, \zeta ; \mu)=$
$\left[\begin{array}{cc}\nabla_{\hat{x} \hat{x}}^{2} \aleph(\hat{k}, \zeta ; \mu) & 0 \ 0 & \hat{D}^{-1} \Gamma_{\hat{a}}\end{array}\right]$
$\left[\begin{array}{cc}\hat{R}(\hat{\hat{k}}, \zeta ; \mu) & \hat{Y}(\hat{x})^{\hat{v}} \ \hat{Y}(\hat{x}) & 0\end{array}\right]\left[\begin{array}{c}\hat{z}{\hat{k}} \ \hat{z}{\zeta}\end{array}\right]=-\left[\begin{array}{c}\nabla_{\dot{k}} \aleph(\hat{k}, \zeta ; \mu) \ \hat{c}(\hat{k})\end{array}\right]$

## 计算机代写|机器学习代写machine learning代考|Contrast Enhancement

$$\left.V=\left(((\text { Im-low_in }) /(\text { high_in-low_in }))^{\wedge} \text { gamma }\right) (\text { high_out-low_out })\right)+\text { low_out }$$ 灰度阈值: Otsu 的定向灰度阈值 [20] 方法描绘了图像的阈值，用于将灰度像素转换为黑色或白色。这取决于灰度 强度 (参见图 1.3）。 活动轮廓[19]: 这里利用了两种类型的驱动力，即外部能量和内部能量。这个框架通过内力得到平滑，并通过外部 能量在方向上重新分配。因此，轮廓 $G(n)$ 由坐标集形成，例如 $l(n)$ 和 $k(n)$ 如公式 $(1.2)$ 中给出的，其中 $(k, l)$ 表示 轮廓坐标，表示控制点的归一化索引。 $$G(n)=(k(n) l(n)) ; G(n) \in \operatorname{Im} n e w^{C}(k, l)$$ 等式 (1.3) 显示了变形设计的总能量，其中 $\operatorname{Im}^{\mathrm{g}^{\mathrm{int}}}$ indi- 表示曲线的内能， $\mathrm{Im}^{\mathrm{g}{ }^{\mathrm{con}}}$ 表示外部限制，表示图像的能 量。 $$F O^{}=\int 0^{1}\left(F O^{\text {int } l} G(n)+F O^{i m} G(n)+F O^{c o n} G(n)\right) d n$$

## 计算机代写|机器学习代写machine learning代考|Classification

$$F E^{\text {weight }}=\left[F_{1}, F_{2}, F_{3}, F_{4} \ldots F_{N_{D}}\right]$$ 示为 $F E^{\text {weight }} i^{j}, a f(\bullet)$ 表示激活函数，输入到的整个计数 $j^{\text {th }}$ 层由下式给出 $n u^{(j)}, b i i$ 表示输入偏置为 $j^{\text {th }}$ 层， $c$ 和 $d$ 表示权重系数 $W E$ 如公式 (1.9) 中所述。预测的网络输出 $\hat{P}$ 由公式 (1.10) 给出，其中 $w^{0}$ 表示偏置权重和 $w^{(h)}$ 定 义隐藏的神经元权重。
$$o u_{l}^{(j)}=a f\left[c_{l}^{(j)} b i_{j}+\sum_{i=1}^{n u^{(j)}} F E_{i}^{\text {weight }(j)} d_{i l}^{(j)}\right] W E=[c ; d] \hat{P}=w^{0}+\sum_{i=1}^{n u^{(j)}} o u_{l}^{(j)} w_{i}^{(h)} W E$$

## 计算机代写|机器学习代写machine learning代考|Nonlinear Programming Optimization

$$\min \hat{y} \hat{h}(\hat{x})=0$$

$$\hat{i}(\hat{x})=0 \quad \hat{j}(\hat{x})=0$$

$$\begin{gathered} \min \hat{k} \varphi_{\mu}(\hat{k}) \equiv \hat{h}(\hat{x})-\mu \sum_{\hat{o}}^{\hat{n}} \operatorname{In} \hat{l}{\hat{o}} \ \hat{i}(\hat{y})=0 \end{gathered}$$ 以便 $\hat{j}(\hat{x})+\hat{l}=0$ 与方程 (1.17) 相关的拉格朗日函数在方程 (1.19) 中指定，其中 $\zeta{\hat{i}}, \zeta_{\hat{a}}$ 表示“拉格朗日乘数”和 $\zeta=\left(\zeta_{\hat{i}}, \zeta_{\hat{a}}\right)$
$$\aleph(\hat{k}, \zeta ; \mu)=\varphi_{\mu}(\hat{k})+\zeta_{\hat{i}}^{\hat{i}} \hat{i}(\hat{x})+\zeta_{\hat{a}}^{\hat{v}}(\hat{a}(\hat{x})+\hat{l})$$

$$\left[\nabla \hat{h}(\hat{x})+\hat{Y} \hat{i}(\hat{x})^{\hat{v}} \zeta \hat{i}+\hat{Y} \hat{a}(\hat{x})^{\hat{v}} \zeta \hat{a} \hat{D} \Gamma_{\hat{a}} \hat{e}-\mu \hat{e}\right]=\left[\begin{array}{lll} 0 & 0 \end{array}\right]$$

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