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# CS代写|机器学习代写Machine Learning代考|COMP5318 Neuron Model

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## CS代写|机器学习代写Machine Learning代考|Neuron Model

Research on neural networks started quite a long time ago, and it has become a broad and interdisciplinary research field today. Though neural networks have various definitions across disciplines, this book uses a widely adopted one: “Artificial neural networks are massively parallel interconnected networks of simple (usually adaptive) elements and their hierarchical organizations which are intended to interact with the objects of the real world in the same way as biological nervous systems do” (Kohonen 1988). In the context of machine learning, neural networks refer to “neural networks learning”, or in other words, the intersection of machine learning research and neural networks research.

The basic element of neural networks is neuron, which is the “simple element” in the above definition. In biological neural networks, the neurons, when “excited”, send neurotransmitters to interconnected neurons to change their electric potentials. When the electric potential exceeds a threshold, the neuron is activated (i.e., “excited”), and it will send neurotransmitters to other neurons.

In 1943, (McCulloch and Pitts 1943) abstracted the above process into a simple model called the McCulloch-Pitts model (M-P neuron model), which is still in use today. As illustrated in – Figure 5.1, each neuron in the M-P neuron model receives input signals from $n$ neurons via weighted connections. The weighted sum of received signals is compared against the threshold, and the output signal is produced by the activation function.

The ideal activation function is the step function illustrated in – Figure 5.2a, which maps the input value to the output value ” 0 ” (non-excited) or ” 1 ” (excited). Since the step function has some undesired properties such as being discontinuous and non-smooth, we often use the sigmoid function instead. – Figure 5.2b illustrates a typical sigmoid function that squashes the input values from a large interval into the open unit interval $(0,1)$, and hence also is known as the squashing function.

## CS代写|机器学习代写Machine Learning代考|Perceptron and Multi-layer Network

Perceptron is a binary classifier consisting of two layers of neurons, as illustrated in $-$ Figure 5.3. The input layer receives external signals and transmits them to the output layer, which is an M-P neuron, also known as threshold logic unit.

Perceptron can easily implement the logic operations “AND”, “OR”, and “NOT”. Suppose the function $f$ in $y=$ $f\left(\sum_i w_i x_i-\theta\right)$ is the step function shown in $\bullet$ Figure $5.2$, the logic operations can be implemented as follows:

• “AND” $\left(x_1 \wedge x_2\right)$ : letting $w_1=w_2=1, \theta=2$, then $y=$ $f\left(1 \cdot x_1+1 \cdot x_2-2\right)$, and $y=1$ if and only if $x_1=x_2=1$;
• “OR” $\left(x_1 \vee x_2\right)$ : letting $w_1=w_2=1, \theta=0.5$, then $y=$ $f\left(1 \cdot x_1+1 \cdot x_2-0.5\right)$, and $y=1$ when $x_1=1$ or $x_2=1$;
• “NOT” $\left(\neg x_1\right)$ : letting $w_1=-0.6, w_2=0, \theta=-0.5$, then $y=f\left(-0.6 \cdot x_1+0 \cdot x_2+0.5\right)$, and $y=0$ when $x_1=1$ and $y=1$ when $x_1=0$.

More generally, the weight $w_i(i=1,2, \ldots, n)$ and threshold $\theta$ can be learned from training data. If we consider the threshold $\theta$ as a dummy node with the connection weight $w_{n+1}$ and fixed input $-1.0$, then the weight and threshold are unified as weight learning. The learning of perceptron is simple: for training sample $(\boldsymbol{x}, y)$, if the perceptron outputs $\hat{y}$, then the weight is updated by
$$w_i \leftarrow w_i+\Delta w_i,$$
$$\Delta w_i=\eta(y-\hat{y}) x_i,$$
where $\eta \in(0,1)$ is known as the learning rate. From (5.1) we can see that the perceptron remains unchanged if it correctly predicts the sample $(\boldsymbol{x}, y)$ (i.e., $\hat{y}=y)$. Otherwise, the weight is updated based on the degree of error.

## CS代写|机器学习代写机器学习代考|感知器和多层网络

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Perceptron是一个由两层神经元组成的二元分类器，如$-$图5.3所示。输入层接收外界信号并传输到输出层，输出层为M-P神经元，又称阈值逻辑单元

• “OR” $\left(x_1 \vee x_2\right)$:让$w_1=w_2=1, \theta=0.5$，然后$y=$$f\left(1 \cdot x_1+1 \cdot x_2-0.5\right)，和y=1当x_1=1或x_2=1; • “NOT” \left(\neg x_1\right):让w_1=-0.6, w_2=0, \theta=-0.5，然后y=f\left(-0.6 \cdot x_1+0 \cdot x_2+0.5\right), y=0当x_1=1, y=1当x_1=0。 一般来说，权重w_i(i=1,2, \ldots, n)和阈值\theta可以从训练数据中得到。如果我们将阈值\theta作为一个虚拟节点，连接权值w_{n+1}，固定输入-1.0，则将权值和阈值统一为权值学习。感知机的学习很简单:对于训练样本(\boldsymbol{x}, y)，如果感知机输出\hat{y}，则权值更新为$$ w_i \leftarrow w_i+\Delta w_i,  \Delta w_i=\eta(y-\hat{y}) x_i,$$，其中$\eta \in(0,1)$被称为学习率。从(5.1)我们可以看到，如果感知器正确预测样本$(\boldsymbol{x}, y)$(即$\hat{y}=y)\$)，则感知器保持不变。否则，权重将根据错误程度更新

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## 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。