assignmentutor-lab™ 为您的留学生涯保驾护航 在代写数据可视化Data visualization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。我们的专家在代写数据可视化Data visualization代写方面经验极为丰富，各种代写数据可视化Data visualization相关的作业也就用不着说。

• 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

统计代写|数据可视化代写Data visualization代考|EXAMPLES AND TUTORIAL

While most of the real-world datasets like images and text data are very high dimensional, we will use the MNIST handwritten digits dataset for simplicity. The MNIST dataset is a collection of grayscale images of handwritten single digits between 0 and 9 that contains 60,000 images of size $28 \times 28$ pixels. Thus, this dataset has 60,000 data samples with a dimensionality of 784 . To demonstrate dimensionality reduction on this dataset, we use Isomap to reduce the data’s dimensionality and project the data onto a low dimensional feature space. This example will map the data with 784 features to two-dimensional feature space and visualize the results.

Let us import the MNIST handwritten digits dataset from the tensorflow library. Next, we will use the sklearn.manifold module from the scikit-learn library for dimensionality reduction. Finally, after applying Isomap on the dataset, we will plot the results to visualize the low dimensional representation of the data using the matplotlib library.Each image is of size $28 \times 28$ pixels which is flattened into a vector of size 784 . Hence, mnist.train.images is an n-dimensional array (tensor) whose shape is $[55000$, $784]$, whereas, the shape of mnist.train.labels is $[55000,10]$ since there are 10 class labels from 0 to $9 .$

统计代写|数据可视化代写Data visualization代考|EXPLANATION AND WORKING

In application areas such as computer vision and pattern recognition where the dataset not only has a large number of data points but also has data of very high dimensionality, PCA might not be a feasible technique as it becomes computationally expensive to handle the entire data matrix [1]. In such cases, random projection proves to be a powerful method for dimensionality reduction that creates compact representations of high dimensional data, preserving well the distances between data points. This method involves choosing a random subspace for projection that is independent of the input data by using a projection matrix with its entries being randomly sampled and at the same time exhibits substantial computational efficiency and accuracy in projecting data from a very high dimension to a lower dimensional space when compared to other dimensionality reduction methods like PCA. Random projections deal with high dimensional data by mapping them into a lower dimensional space while they guarantee approximate preservation of distances between data points in the lower dimensional space.

Let $\mathrm{X} \in \mathbb{R}^{d}$ be an $n \times d$ matrix of $\mathrm{n}$ data points in high dimensional space $d$. We choose a randomly sampled $d \times k$ projection matrix, $W$, and define the projection of $X$ in lower dimensional space $k$ to be
$$Y=X W$$
where $\mathrm{Y} \in \mathbb{R}^{k}$ is an $n \times k$ matrix that gives the $k$-dimensional approximations of the $n$ data points.

Here $W$ is a $d \times k$ matrix with entries $w_{i j}$ sampled independently at random using distributions such as the Gaussian distribution. The projection matrix $W$ can also be sampled from various other distributions as follows:
$$w_{i j}=\left{\begin{array}{l} +1, p=1 / 2 \ -1, p=1 / 2 \end{array}\right.$$
and
$$w_{i j}=\sqrt{3}\left{\begin{array}{c} +1, p=1 / 6 \ 0, p=2 / 3 \ -1, p=1 / 6 \end{array}\right.$$

数据可视化代考

统计代写|数据可视化代写Data visualization代考|EXPLANATION AND WORKING

$$Y=X W$$

$\$ \$$w_{-}{i j}=\backslash \operatorname{left}{$$
+1, p=1 / 2-1, p=1 / 2
$$正确的。 and w_{-}{i j}=\backslash sqrt {3} \backslash left {$$
+1, p=1 / 60, p=2 / 3-1, p=1 / 6
$$正确的。 \ \$$

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。

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