## 计算机代写|神经网络代写neural networks代考|CS224W

statistics-lab™ 为您的留学生涯保驾护航 在代写神经网络neural networks方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写神经网络neural networks代写方面经验极为丰富，各种代写神经网络neural networks相关的作业也就用不着说。

## 计算机代写|神经网络代写neural networks代考|Introduction and Role of Artificial Neural Networks

Artificial neural networks are, as their name indicates, computational networks which attempt to simulate, in a gross manner, the networks of nerve cell (neurons) of the biological (human or animal) central nervous system. This simulation is a gross cell-by-cell (neuron-by-neuron, element-by-element) simulation. It borrows from the neurophysiological knowledge of biological neurons and of networks of such biological neurons. It thus differs from conventional (digital or analog) computing machines that serve to replace, enhance or speed-up human brain computation without regard to organization of the computing elements and of their networking. Still, we emphasize that the simulation afforded by neural networks is very gross.
Why then should we view artificial neural networks (denoted below as neural networks or ANNs) as more than an exercise in simulation? We must ask this question especially since, computationally (at least), a conventional digital computer can do everything that an artificial neural network can do.

The answer lies in two aspects of major importance. The neural network, by its simulating a biological neural network, is in fact a novel computer architecture and a novel algorithmization architecture relative to conventional computers. It allows using very simple computational operations (additions, multiplication and fundamental logic elements) to solve complex, mathematically ill-defined problems, nonlinear problems or stochastic problems. A conventional algorithm will employ complex sets of equations, and will apply to only a given problem and exactly to it. The ANN will be (a) computationally and algorithmically very simple and (b) it will have a self-organizing feature to allow it to hold for a wide range of problems.
For example, if a house fly avoids an obstacle or if a mouse avoids a cat, it certainly solves no differential equations on trajectories, nor does it employ complex pattern recognition algorithms. Its brain is very simple, yet it employs a few basic neuronal cells that fundamentally obey the structure of such cells in advanced animals and in man. The artificial neural network’s solution will also aim at such (most likely not the same) simplicity. Albert Einstein stated that a solution or a model must be as simple as possible to fit the problem at hand. Biological systems, in order to be as efficient and as versatile as they certainly are despite their inherent slowness (their basic computational step takes about a millisecond versus less than a nanosecond in today’s electronic computers), can only do so by converging to the simplest algorithmic architecture that is possible. Whereas high level mathematics and logic can yield a broad general frame for solutions and can be reduced to specific but complicated algorithmization, the neural network’s design aims at utmost simplicity and utmost self-organization. A very simple base algorithmic structure lies behind a neural network, but it is one which is highly adaptable to a broad range of problems. We note that at the present state of neural networks their range of adaptability is limited. However, their design is guided to achieve this simplicity and self-organization by its gross simulation of the biological network that is (must be) guided by the same principles.

## 计算机代写|神经网络代写neural networks代考|Fundamentals of Biological Neural Networks

The biological neural network consists of nerve cells (neurons) as in Fig. 2.1, which are interconnected as in Fig. 2.2. The cell body of the neuron, which includes the neuron’s nucleus is where most of the neural “computation” takes place. Neural activity passes from one neuron to another in terms of electrical triggers which travel from one cell to the other down the neuron’s axon, by means of an electrochemical process of voltage-gated ion exchange along the axon and of diffusion of neurotransmitter molecules through the membrane over the synaptic gap (Fig. 2.3). The axon can be viewed as a connection wire. However, the mechanism of signal flow is not via electrical conduction but via charge exchange that is transported by diffusion of ions. This transportation process moves along the neuron’s cell, down the axon and then through synaptic junctions at the end of the axon via a very narrow synaptic space to the dendrites and/or soma of the next neuron at an average rate of $3 \mathrm{~m} / \mathrm{sec}$., as in Fig. 2.3 .

Figures 2.1 and 2.2 indicate that since a given neuron may have several (hundreds of) synapses, a neuron can connect (pass its message/signal) to many (hundreds of) other neurons. Similarly, since there are many dendrites per each neuron, a single

neuron can receive messages (neural signals) from many other neurons. In this manner, the biological neural network interconnects [Ganong, 1973].

It is important to note that not all interconnections, are equally weighted. Some have a higher priority (a higher weight) than others. Also some are excitory and some are inhibitory (serving to block transmission of a message). These differences are effected by differences in chemistry and by the existence of chemical transmitter and modulating substances inside and near the neurons, the axons and in the synaptic junction. This nature of interconnection between neurons and weighting of messages is also fundamental to artificial neural networks (ANNs).

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 计算机代写|神经网络代写neural networks代考|CS182

statistics-lab™ 为您的留学生涯保驾护航 在代写神经网络neural networks方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写神经网络neural networks代写方面经验极为丰富，各种代写神经网络neural networks相关的作业也就用不着说。

## 计算机代写|神经网络代写neural networks代考|Training a SOM

In the previous chapters, we learned several methods for training a feedforward neural network. We learned about such techniques as backpropagation, RPROP and LMA. These are all supervised training methods. Supervised training methods work by adjusting the weights of a neural network to produce the correct output for a given input.

A supervised training method will not work for a SOM. SOM networks require unsupervised training. In this section, we will learn to train a SOM with an unsupervised method. The training technique generally used for SOM networks is shown in Equation 8.2.
Equation 8.2: Training a SOM
$$W_v(t+1)=W_v(t)+\theta(v, t) c(t)\left(D(t)-W_v(t)\right)$$
The above equation shows how the weights of a SOM neural network are updated as training progresses. The current training iteration is noted by the letter $\mathbf{t}$, and the next training iteration is noted by $\mathbf{t}+\mathbf{1}$. Equation 8.2 allows us to see how weight $\mathbf{v}$ is adjusted for the next training iteration.

The variable $\mathbf{v}$ denotes that we are performing the same operation on every weight. The variable $\mathbf{W}$ represents the weights. The symbol theta is a special function, called a neighborhood function. The variable $\mathbf{D}$ represents the current training input to the SOM.

The symbol alpha denotes a learning rate. The learning rate changes for each iteration. This is why Equation 8.2 shows the learning rate with the symbol $\mathbf{t}$, as the learning rate is attached to the iteration. The learning rate for a SOM is said to be monotonically decreasing. Monotonically decreasing means that the learning rate only falls, and never increases.

## 计算机代写|神经网络代写neural networks代考|SOM Training Example

We will now find out how to train a SOM. We will apply the equation presented in the previous section. However, we will approach it more from an algorithm perspective so we can see the actual learning strategy behind the equation. To see the SOM in action, we need a very simple example. We will use a SOM very similar to the one that we saw in Figure 8.1. This SOM will attempt to match colors. However, instead of the $4 \times 4$ lattice we saw in Figure 8.1 , we will have a lattice of $50 \times 50$. This results in a total of 2,500 output neurons.

The SOM will use its three input neurons to match colors to the 2,500 output neurons. The three input neurons will contain the red, blue and green components of the color that is currently being submitted to the SOM. For training, we will generate 15 random colors. The SOM will learn to cluster these colors.

This sort of training is demonstrated in one of the Encog examples. You can see the output from this example program in Figure 8.2.

As you can see from the above figure, similar colors are clustered together. Additionally, there are 2,500 output neurons, and only 15 colors that were trained with. This network could potentially recognize up to 2,500 colors. The fact that we trained with only 15 colors means we have quite a few unutilized output neurons. These output neurons will learn to recognize colors that are close to the 15 colors that we trained with.

What you are actually seeing in Figure 8.2 are the weights of SOM network that has been trained. As you can see, even though the SOM was only trained to recognize 15 colors, it is able to recognize quite a few more colors. Any new color provided to the SOM will be mapped to one of the 2,500 colors seen in the above image. The SOM can be trained to recognize more classes than are in its provided training data. This is definitely the case in Figure 8.2. The unused output neurons will end up learning to recognize data that falls between elements of the smaller training set.

## 计算机代写|神经网络代写neural networks代考|Training a SOM

$$W_v(t+1)=W_v(t)+\theta(v, t) c(t)\left(D(t)-W_v(t)\right)$$

## 计算机代写|神经网络代写neural networks代考|SOM Training Example

SOM将使用它的三个输入神经元来匹配2500个输出神经元的颜色。三个输入神经元将包含当前提交给SOM的颜色的红色，蓝色和绿色成分。对于训练，我们将随机生成15种颜色。SOM将学习对这些颜色进行聚类。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 计算机代写|神经网络代写neural networks代考|DAT111

statistics-lab™ 为您的留学生涯保驾护航 在代写神经网络neural networks方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写神经网络neural networks代写方面经验极为丰富，各种代写神经网络neural networks相关的作业也就用不着说。

## 计算机代写|神经网络代写neural networks代考|LMA with Multiple Outputs

Some implementations of the LMA algorithm only support a single output neuron. This is primarily because the LMA algorithm has its roots in mathematical function approximation. In mathematics, functions typically only return a single value. As a result, there is not a great deal of information on support for multiple neurons.

Support for multiple output neurons involves simply summing each cell of the Hessian as the additional output neurons are calculated. It is as if you calculated a separate Hessian matrix for each output neuron, and then summed the Hessian matrices together. This is the approach that Encog uses, and it leads to very fast convergence times.

One important aspect to consider with multiple outputs is that not every connection will be used. Depending on which output neuron you are currently calculating for, there will be unused connections for the other output neurons. It is very important that the partial derivative for each of these unused connections be set to zero when the other output neuron is being calculated for.

For example, consider a neural network that has two output neurons and three hidden neurons. Each of these two output neurons would have a total of four connections from the hidden layer. There would be three from the three hidden neurons, and a fourth for the bias neuron. This segment of the neural network would look like Figure 7.2.

Here we are calculating output neuron one. Notice that there are also four connections for output neuron two? It is critical that the derivatives of the four connections to output neuron two calculate to zero when output neuron one is calculated. If this process is not followed, the Hessian will not work for multiple outputs.

## 计算机代写|神经网络代写neural networks代考|Overview of the LMA Process

So far, we have only seen the math behind LMA. LMA must be part of an algorithm for it to be effective. The LMA process can be summarized in the following steps:

Calculate the first derivative of output of the neural networ

Calculate the Hessian

Calculate the gradients of the error (ESS) with respect to er

Either set lambda to a low value (first iteration) or the lat

Save the weights of the neural network

Calculate delta weight based on the lambda, gradients and He:

Apply the deltas to the weights and evaluate error

If error has improved, end the iteration

If error has not improved increase lambda (up to a max lambdi
As you can see, the process for LMA revolves around setting the lambda value low and then slowly increasing it if the error rate does not improve. It is important to save the weights at each change in lambda so that they can be restored if the error does not improve.

## 计算机代写|神经网络代写neural networks代考|LMA with Multiple Outputs

LMA算法的一些实现只支持单个输出神经元。这主要是因为LMA算法植根于数学函数近似。在数学中，函数通常只返回一个值。因此，关于支持多神经元的信息并不多。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 计算机代写|神经网络代写neural networks代考|Looking at the Weights

statistics-lab™ 为您的留学生涯保驾护航 在代写神经网络neural networks方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写神经网络neural networks代写方面经验极为丰富，各种代写神经网络neural networks相关的作业也就用不着说。

## 计算机代写|神经网络代写neural networks代考|Looking at the Weights

In previous chapters, we looked at the weights of a neural network as an array of numbers. You can’t typically glance at a weight array and see any sort of meaningful pattern. However, if the weights are represented graphically, patterns begin to emerge.

One common way to view the weights of a neural network is using a special type of chart called a histogram. You’ve probably seen histograms many times before – a histogram is a chart made up of vertical bars that count the number of occurrences in a population. Figure 6.1 is a histogram showing the popularity of operating systems. The $y$-axis shows the number of occurrences of each of the groups in the x-axis.

We can use a histogram to look at the weights of a neural network. You can typically tell a trained from an untrained neural network by looking at this histogram. Figure 6.2 shows a trained neural network.

A neural network histogram uses the same concept as the operating system histogram shown earlier. The y-axis specifies how many weights fell into the ranges specified by the numbers on the x-axis. This allows you to see the distribution of the weights.

Most trained neural networks will look something like the above chart. Their weights will be very tightly clustered around zero. A trained neural network will typically look like a very narrow Gaussian curve.

## 计算机代写|神经网络代写neural networks代考|Range Randomization

In the last section, we saw what a trained neural network looks like in a weight histogram. Untrained neural networks can have a variety of appearances. The appearance of the weight histogram will be determined by the weight initialization method used.

Range randomization produces a very simple looking chart. The more weights there are, the flatter the top will be. This is because the random number generator should give you an even distribution of numbers. If you are randomizing to the range of -1 to 1 , you would expect to have approximately the same number of weights above zero as below.

Using Nguyen-Widrow
We will now look at the Nguyen-Widrow weight initialization method. The Nguyen-Widrow method starts out just like the range randomized method. Random values are chosen between -0.5 and +0.5 . However, a special algorithm is employed to modify the weights. The histogram of a NguyenWidrow weight initialization looks like Figure 6.4.

As you can see, the Nguyen-Widrow initialization has a very distinctive pattern. There is a large distribution of weights between -0.5 and 0.5 . It gradually rises and then rapidly falls off to around -3.0 and +3.0 .
Performance of Nguyen-Widrow
You may be wondering how much advantage there is to using NguyenWidrow. Take a look at the average number of training iterations needed to train a neural network initialized by range randomization and Nguyen-Widrow.
Average iterations needed (lower is better)
Range random: 502.86
Nguyen-Widrow: 454,88
As you can see from the above information, the Nguyen-Widrow outperforms the range randomizer.

## 计算机代写|神经网络代写neural networks代考|C alculating th e N o d e D eltas


\delta_i= \begin{cases}-E f_i^{\prime}， &， \text{输出节点}\ f_i^{\prime} \sum_k \omega_{h i} \delta_k &， \text{中间节点}\end{cases}



E =(ⅰ)



E = 0.75 – -1.00 = -0.25



-(-0.25) * d A(1.1254)=0.185 * 0.25=0.05


## 计算机代写|神经网络代写neural networks代考|C alculating the Individual Gradients


\压裂{\部分E}{\部分w_ {(k)}} = \ delta_k \ cdot o_j




& \text {output}(\ mathm {h} 1) * \text {nodeDe1ta (o1)} \
& (0.37 * 0.05)=0.01677



## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 计算机代写|神经网络代写neural networks代考|Other Error Calculation Methods

statistics-lab™ 为您的留学生涯保驾护航 在代写神经网络neural networks方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写神经网络neural networks代写方面经验极为丰富，各种代写神经网络neural networks相关的作业也就用不着说。

## 计算机代写|神经网络代写neural networks代考|Other Error Calculation Methods

Though MSE is the most common method of calculating global error, it is not the only method. In this section, we will look at two other global error calculation methods.
Sum of Squares Error
The sum of squares method (ESS) uses a similar formula to the MSE error method. However, ESS does not divide by the number of elements. As a result, the ESS is not a percent. It is simply a number that is larger depending on how severe the error is. Equation 2.3 shows the MSE error formula.
Equation 2.3: Sum of Squares Error
$$\mathrm{ESS}=\frac{1}{2} \sum_v E^2$$
As you can see above, the sum is not divided by the number of elements. Rather, the sum is simply divided in half. This results in an error that is not a percent, but instead a total of the errors. Squaring the errors eliminates the effect of positive and negative errors.

Some training methods require that you use ESS. The Levenberg Marquardt Algorithm (LMA) requires that the error calculation method be ESS. LMA will be covered in Chapter 7, “LMA Training”.

## 计算机代写|神经网络代写neural networks代考|Calculating the Slope of a Line

The slope of a line is a numerical quality of a line that tells you the direction and steepness of a line. In this section, we will see how to calculate the slope of a straight line. In the next section, we will find out how to calculate the slope of a curved line at a single point.

The slope of a line is defined as the “rise” over the “run”, or the change in $\mathbf{y}$ over the change in $\mathbf{x}$. The slope of a line can be written in the form of Equation 3.1.
Equation 3.1: The Slope of a Straight Line
$$m=\frac{\Delta y}{\Delta r}=\frac{v_2-v_1}{x_2-x_1}$$
This can be visualized graphically as in Figure 3.1.

We could easily calculate the slope of the above line using Equation 3.1. Filling in the numbers for the two points we have on the line produces the following:
$$(8-3) /(6-1)=1$$
The slope of this line is one. This is a positive slope. When a line has a positive slope, it goes up left to right. When a line has a negative slope, it goes down left to right. When a line is horizontal, the slope is 0 , and when the line is vertical, the slope is undefined. Figure 3.2 shows several slopes for comparison.

## 计算机代写|神经网络代写neural networks代考|Other Error Calculation Methods

$$\mathrm{ESS}=\frac{1}{2} \sum_v E^2$$

## 计算机代写|神经网络代写neural networks代考|Calculating the Slope of a Line

$$m=\frac{\Delta y}{\Delta r}=\frac{v_2-v_1}{x_2-x_1}$$

$$(8-3) /(6-1)=1$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 计算机代写|神经网络代写neural networks代考|NIT6004

statistics-lab™ 为您的留学生涯保驾护航 在代写神经网络neural networks方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写神经网络neural networks代写方面经验极为丰富，各种代写神经网络neural networks相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

Traditional graph embedding methods are originally studied as dimension reduction techniques. A graph is usually constructed from a feature represented data set, like image data set. As mentioned before, graph embedding usually has two goals, i.e. reconstructing original graph structures and support graph inference. The objective functions of traditional graph embedding methods mainly target the goal of graph reconstruction.

Specifically, Tenenbaum et al (2000) first constructs a neighborhood graph $G$ using connectivity algorithms such as $K$ nearest neighbors (KNN). Then based on $G$, the shortest path between different data can be computed. Consequently, for all the $N$ data entries in the data set, we have the matrix of graph distances. Finally, the classical multidimensional scaling (MDS) method is applied to the matrix to obtain the coordinate vectors. The representations learned by Isomap approximately preserve the geodesic distances of the entry pairs in the low-dimensional space. The key problem of Isomap is its high complexity due to the computing of pair-wise shortest pathes. Locally linear embedding (LLE) (Roweis and Saul, 2000) is proposed to eliminate the need to estimate the pairwise distances between widely separated entries. LLE assumes that each entry and its neighbors lie on or close to a locally linear patch of a mainfold. To characterize the local geometry, each entry can be reconstructed from its neighbors. Finally, in the low-dimensional space, LLE constructs a neighborhood-preserving mapping based on locally linear reconstruction. Laplacian eigenmaps (LE) (Belkin and Niyogi, 2002) also begins with constructing a graph using $\varepsilon$-neighborhoods or $\mathrm{K}$ nearest neighbors. Then the heat kernel (Berline et al, 2003) is utilized to choose the weight of two nodes in the graph. F1nally, the node representations can be obtained by based on the Laplacian matrix regularization. Furthermore, the locality preserving projection (LPP) (Berline et al, 2003), a linear approximation of the nonlinear LE, is proposed.

## 计算机代写|神经网络代写neural networks代考|Structure Preserving Graph Representation Learning

Graph structures can be categorized into different groups that present at different granularities. The commonly exploited graph structures in graph representation learning include neighborhood structure, high-order node proximity and graph communities.

How to define the neighborhood structure in a graph is the first challenge. Based on the discovery that the distribution of nodes appearing in short random walks is similar to the distribution of words in natural language, DeepWalk (Perozzi et al, 2014) employs the random walks to capture the neighborhood structure. Then for each walk sequence generated by random walks, following Skip-Gram, DeepWalk aims to maximize the probability of the neighbors of a node in a walk sequence. Node2vec defines a flexible notion of a node’s graph neighborhood and designs a second order random walks strategy to sample the neighborhood nodes, which can smoothly interpolate between breadth-first sampling (BFS) and depth-first sampling (DFS). Besides the neighborhood structure, LINE (Tang et al, 2015b) is proposed for large scale network embedding. which can preserve the first and second order proximities. The first order proximity is the observed pairwise proximity between two nodes. The second order proximity is determined by the similarity of the “contexts” (neighbors) of two nodes. Both are important in measuring the relationships beetween two nodess. Essentially, LINE is based on the shallow model, consequently, the representation ability is limited. SDNE (Wang et al, 2016) proposes a deep model for network embedding, which also aims at capturing the first and second order proximites. SDNE uses the deep auto-encoder architecture with multiple non-linear layers to preserve the second order proximity. To preserve the first-order proximity, the idea of Laplacian eigenmaps (Belkin and Niyogi, 2002) is adopted. Wang et al (2017g) propose a modularized nonnegative matrix factorization (M-NMF) model for graph representation learning, which aims to preserve both the microscopic structure, i.e., the first-order and second-order proximities of nodes, and the mesoscopic community structure (Girvan and Newman, 2002).

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 计算机代写|神经网络代写neural networks代考|STAT3007

statistics-lab™ 为您的留学生涯保驾护航 在代写神经网络neural networks方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写神经网络neural networks代写方面经验极为丰富，各种代写神经网络neural networks相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|神经网络代写neural networks代考|Representation Learning for Networks

Beyond popular data like images, texts, and sounds, network data is another important data type that is becoming ubiquitous across a large scale of real-world applications ranging from cyber-networks (e.g., social networks, citation networks, telecommunication networks, etc.) to physical networks (e.g., transportation networks, biological networks, etc). Networks data can be formulated as graphs mathematically, where vertices and their relationships jointly characterize the network information. Networks and graphs are very powerful and flexible data formulation such that sometimes we could even consider other data types like images, and texts as special cases of it. For example, images can be considered as grids of nodes with RGB attributes which are special types of graphs, while texts can also be organized into sequential-, tree-, or graph-structured information. So in general, representation learning for networks is widely considered as a promising yet more challenging tasks that require the advancement and generalization of many techniques we developed for images, texts, and so forth. In addition to the intrinsic high complexity of network data, the efficiency of representation learning on networks is also an important issues considering the large-scale of many real-world networks, ranging from hundreds to millions or even billions of vertices. Analyzing information networks plays a crucial role in a variety of emerging applications across many disciplines. For example, in social networks, classifying users into meaningful social groups is useful for many important tasks, such as user search, targeted advertising and recommendations; in communication networks, detecting community structures can help better understand the rumor spreading process; in biological networks, inferring interactions between proteins can facilitate new treatments for diseases. Nevertheless, efficient and effective analysis of these networks heavily relies on good representations of the networks.

## 计算机代写|神经网络代写neural networks代考|Graph Representation Learning: An Introduction

Many complex systems take the form of graphs, such as social networks, biological networks, and information networks. It is well recognized that graph data is often sophisticated and thus is challenging to deal with. To process graph data effectively, the first critical challenge is to find effective graph data representation, that is, how to represent graphs concisely so that advanced analytic tasks, such as pattern discovery, analysis, and prediction, can be conducted efficiently in both time and space.

Traditionally, we usually represent a graph as $\mathscr{G}=(\mathscr{V}, \mathscr{E})$, where $\mathscr{V}$ is a node set and $\mathscr{E}$ is an edge set. For large graphs, such as those with billions of nodes, the traditional graph representation poses several challenges to graph processing and analysis.
(1) High computational complexity. These relationships encoded by the edge set $E$ take most of the graph processing or analysis algorithms either iterative or combinatorial computation steps. For example, a popular way is to use the shortest or average path length between two nodes to represent their distance. To compute such a distance using the traditional graph representation, we have to enumerate many possible paths between two nodes, which is in nature a combinatorial problem. Such methods result in high computational complexity that prevents them from being applicable to large-scale real-world graphs.
(2) Low parallelizability. Parallel and distributed computing is de facto to process and analyze large-scale data. Graph data represented in the traditional way, however, casts severe difficulties to design and implementat of parallel and distributed algorithms. The bottleneck is that nodes in a graph are coupled to each other explicitly reflected by $E$. Thus, distributing different nodes in different shards or servers often causes demandingly high communication cost among servers, and holds back speed-up ratio.

## 计算机代写|神经网络代写neural networks代考|Graph Representation Learning: An Introduction

(1) 计算复杂度高。这些由边集编码的关系和采用大多数图形处理或分析算法迭代或组合计算步骤。例如，一种流行的方法是使用两个节点之间的最短或平均路径长度来表示它们的距离。为了使用传统的图形表示来计算这样的距离，我们必须枚举两个节点之间的许多可能路径，这本质上是一个组合问题。这样的方法导致高计算复杂性，从而阻止它们适用于大规模的真实世界图。
(2) 并行性低。并行和分布式计算实际上是处理和分析大规模数据。然而，以传统方式表示的图形数据给并行和分布式算法的设计和实现带来了严重的困难。瓶颈是图中的节点相互耦合，显式反映为和. 因此，将不同的节点分布在不同的分片或服务器中往往会导致服务器之间的通信成本很高，并且会阻碍加速比。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 计算机代写|神经网络代写neural networks代考|COMP5329

statistics-lab™ 为您的留学生涯保驾护航 在代写神经网络neural networks方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写神经网络neural networks代写方面经验极为丰富，各种代写神经网络neural networks相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|神经网络代写neural networks代考|Representation Learning for Speech Recognition

Nowadays, speech interfaces or systems have become widely developed and integrated into various real-life applications and devices. Services like Siri ${ }^{1}$, Cortana ${ }^{2}$, and Google Voice Search ${ }^{3}$ have become a part of our daily life and are used by millions of users. The exploration in speech recognition and analysis has always been motivated by a desire to enable machines to participate in verbal human-machine interactions. The research goals of enabling machines to understand human speech, identify speakers, and detect human emotion have attracted researchers’ attention for more than sixty years across several distinct research areas, including but not limited to Automatic Speech Recognition (ASR), Speaker Recognition (SR), and Speaker Emotion Recognition (SER).

Analyzing and processing speech has been a key application of machine learning (ML) algorithms. Research on speech recognition has traditionally considered the task of designing hand-crafted acoustic features as a separate distinct problem from the task of designing efficient models to accomplish prediction and classification decisions. There are two main drawbacks of this approach: First, the feature engineering is cumbersome and requires human knowledge as introduced above; and second, the designed features might not be the best for the specific speech recognition tasks at hand. This has motivated the adoption of recent trends in the speech community towards the utilization of representation learning techniques, which can learn an intermediate representation of the input signal automatically that better fits into the task at hand and hence lead to improved performance. Among all these successes, deep learning-based speech representations play an important role. One of the major reasons for the utilization of representation learning techniques in speech technology is that speech data is fundamentally different from two-dimensional image data. Images can be analyzed as a whole or in patches, but speech has to be formatted sequentially to capture temporal dependency and patterns.

## 计算机代写|神经网络代写neural networks代考|Representation Learning for Natural Language Processing

Besides speech recognition, there are many other Natural Language Processing (NLP) applications of representation learning, such as the text representation learning. For example, Google’s image search exploits huge quantities of data to map images and queries in the same space (Weston et al, 2010) based on NLP techniques. In general, there are two types of applications of representation learning in $\mathrm{NLP}$. In one type, the semantic representation, such as the word embedding, is trained in a pre-training task (or directly designed by human experts) and is transferred to the model for the target task. It is trained by using language modeling objective and is taken as inputs for other down-stream NLP models. In the other type, the semantic representation lies within the hidden states of the deep learning model and directly aims for better performance of the target tasks in an end-to-end fashion. For example, many NLP tasks want to semantically compose sentence or document representation, such as tasks like sentiment classification, natural language inference, and relation extraction, which require sentence representation.

Conventional NLP tasks heavily rely on feature engineering, which requires careful design and considerable expertise. Recently, representation learning, especially deep learning-based representation learning is emerging as the most important technique for NLP. First, NLP is typically concerned with multiple levels of language entries, including but not limited to characters, words, phrases, sentences, paragraphs, and documents. Representation learning is able to represent the semantics of these multi-level language entries in a unified semantic space, and model complex semantic dependence among these language entries. Second, there are various NLP tasks that can be conducted on the same input. For example, given a sentence, we can perform multiple tasks such as word segmentation, named entity recognition, relation extraction, co-reference linking, and machine translation. In this case, it will be more efficient and robust to build a unified representation space of inputs for multiple tasks. Last, natural language texts may be collected from multiple domains, including but not limited to news articles, scientific articles, literary works, advertisement and online user-generated content such as product reviews and social media. Moreover, texts can also be collected from different languages, such as English, Chinese, Spanish, Japanese, etc. Compared to conventional NLP systems which have to design specific feature extraction algorithms for each domain according to its characteristics, representation learning enables us to build representations automatically from large-scale domain data and even add bridges among these languages from different domains. Given these advantages of representation learning for NLP in the feature engineering reduction and performance improvement, many researchers have developed efficient algorithms on representation learning, especially deep learning-based approaches, for NLP.

## 有限元方法代写

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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。