### cs代写|机器学习代写machine learning代考|Classification with support vector machines

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• 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

## cs代写|机器学习代写machine learning代考|multilayer perceptrons

We will show here how to apply three different types of machine learning classifiers using sklearn implementations, that of a support vector classifier (SVC), a random forest classifier (RFC), and a multilayer perceptron (MLP). We therefore concentrate on the mechanisms and will discuss what is behind these classifiers using the classical example of the iris flowers dataset that we discussed in the previous chapter to demonstrate how to read data into NumPy arrays. We will start with the $\mathrm{SVC}$, which is support vector machine (SVM $)^{1}$. The sklearn implementation is actually a wrapper for the SVMLIB implementation by Chih-Chung Chang and Chih-Jen Lin that has been very popular for classification applications. Later in this chapter describe more of the math and tricks behind this method, but for now we use it to demonstrate the mechanics of applying this method.

To apply this machine learning technique of a classifier to the iris data-set in the program IrisClassificationSklearn. ipynb. The program starts as usual by importing the necessary libraries. We then import the data similar to the program discussed in the previous chapter. We choose here to split the data into a training set and a test set by using every second data point as training point and every other as a test point. This is accomplished with the index specifications $0:-1: 2$ which is a list that starts at index ” 0 “, iterates until the end specified by index ” $-1^{\prime \prime}$ and uses a step of ” $2 . “$ ” Since the data are ordered and well balanced in the original data file, this will leave us also with a balanced dataset. Balance here means here that we have the same, or nearly the same, number data in the training set for each class. It turns out that this is often important for the good performance of the models. Also, instead of using the names features and target, we decided to shorten the notation by denoting the input features as $\mathrm{x}$ and the targets as $\mathrm{y}$ values.

## cs代写|机器学习代写machine learning代考|Performance measures and evaluations

We used the percentage of misclassification as an objective function to evaluate the performance of the model. This is a common choice and often a good start in our examples, but there are other commonly used evaluation measures that we should understand. Let us consider first a binary classification case where it is common to call one class “positive” and the other the “negative” class. This nomenclature comes from diagnostics such as trying to decide if a person has a disease based on some clinical tests. We can then define the following four performance indicators,

• True Positive (TP): Number of correctly predicted positive samples
• True Negative (TN): Number of correctly predicted negative samples
• False Positive (FP): Number of incorrectly predicted positive samples
• False Negative (FN): Number of incorrectly predicted negative samples
These numbers are often summarized in a confusion matrix, and such a matrix layout is shown in Fig. 3.2A.If we have more than two classes we could generalize this to measures of True Class 1, True Class 2, True Class 3, False Class 1, etc. It is convenient to summarize these numbers in a matrix which lists the true class down the columns and the predicted label along the rows. An example of a confusion matrix for the iris dataset that has three classes is shown in Fig. 3.2B. The plot is produced with the following code.

## cs代写|机器学习代写machine learning代考|Cross-validation

The performance of a model on the training data can always be improved and even made perfect on the training data when making the model more complex. This is the essence of overfitting. Basically, we can always write a model that can memorize a finite dataset. However, machine learning is about generalization that can only be measured with data points that have not been used during training. This is why in the examples earlier we split our data into a training set and into a test set.

Just splitting the data into these two sets is sufficient if we have enough. In practice, having enough labeled data for supervised training is often a problem. We therefore now introduce a method that is much better in using the data to their full potential. The method is called k-fold cross-validation for evaluating a model’s performance. This

method is based on the premise that all the data are used at some time for training and testing (validation) at some point throughout the evaluation procedure. For this, we partition our data into $k$ partitions as shown in Fig. $3.4$ for $k=4$. In this example we assumed to have a dataset with twenty samples, so that each partition would have five samples. In every step of the cross-validation procedure we are leaving one partition out for validating (testing) the trained model and use the other $k-1$ partitions for training. Hence, we get $k$ values for our evaluation measure, such as accuracy. We could then simply use the average as a final measure for the accuracy of the model’s fit. However, since we have several measures, we now have the opportunity to look at the distribution itself for more insights. For example, we could also report the variance if we assume a Gaussian distribution of the performance of the different models that result from training with different training sets.

Of course, the next question is then what should the value of $k$ be? As always in machine learning, the answer is not as simple as merely stating a number. If we have only a small number of data, then it would be wise to use as many data as possible for training. Hence, an $N$-fold cross-validation, where $N$ is the number of samples, would likely be useful. This is also called leave-one-out cross-validation (LOOCV). However, this procedure also requires $N$ training sessions and evaluations which might be computationally too expensive with larger datasets. The choice of $k$ is hence important to balance computational realities. We of course assume here that all samples are ‘nicely’ distributed in the sense that their order in the dataset is not biased. For example, cross-validation would be biased if we have data points from one class in the first part of the dataset and the other in the second part. A random resampling of the dataset is a quick way of avoiding most of these errors. Sklearn has of course a good way of implementing this. A corresponding code is given below.

## cs代写|机器学习代写machine learning代考|Performance measures and evaluations

• 真阳性（TP）：正确预测的阳性样本数
• True Negative (TN)：正确预测的负样本数
• 假阳性 (FP)：错误预测的阳性样本数
• 假阴性（FN）：错误预测的负样本的
数量这些数字通常被总结在一个混淆矩阵中，这种矩阵布局如图 3.2A 所示。如果我们有两个以上的类，我们可以将其推广到 True 的度量1 类、真类 2、真类 3、假类 1 等。将这些数字总结在一个矩阵中很方便，该矩阵在列中列出了真实类，沿行列出了预测标签。具有三个类别的 iris 数据集的混淆矩阵示例如图 3.2B 所示。该图是使用以下代码生成的。

## 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。