## 统计代写|化学计量学作业代写chemometrics代考|Self-Organizing Maps

statistics-lab™ 为您的留学生涯保驾护航 在代写化学计量学chemometrics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。我们的专家在代写化学计量学chemometrics代写方面经验极为丰富，各种代写化学计量学chemometrics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

## 统计代写|化学计量学作业代写chemometrics代考|Training SOMs

A SOM is trained by repeatedly presenting the individual samples to the map. At each iteration, the current sample is compared to the codebook vectors. The most similar codebook vector (the “winning unit”) is then shifted slightly in the direction of the mapped object. This is achieved by replacing it with a weighted average of the old values of the codebook vector, $c v_{i}$, and the values of the new object obj:
$$c v_{i+1}=(1-\alpha) c v_{i}+\alpha o b j$$
The weight, also called the learning rate $\alpha$, is a small value, typically in the order of $0.05$, and decreases during training so that the final adjustments are very small.
As we shall see in Sect. $6.2 .1$, the algorithm is very similar in spirit to the one used in $k$-means clustering, where cluster centers and memberships are alternatingly estimated in an iterative fashion. The crucial difference is that not only the winning unit is updated, but also the other units in the “neighborhood” of the winning unit. Initially, the neighborhood is fairly large, but during training it decreases so that finally only the winning unit is updated. The effect is that neighboring units in general are more similar than units far away. Or, to put it differently, moving through the map by jumping from one unit to its neighbor would see gradual and more or less smooth transitions in the values of the codebook vectors. This is clearly visible in the mapping of the autoscaled wine data to a 5-by-4 SOM, using the kohonen package:

The result is shown in Fig. 5.2. Units in this example are arranged in a hexagonal fashion and are numbered row-wise from left to right, starting from the bottom left. The first unit at the bottom left for instance, is characterized by relatively large values of alcohol, flavonoids and proanth; the second unit, to the right of the first, has lower values for these variables, but still is quite similar to unit number one.
The codebook vectors are usually initialized by a random set of objects from the data, but also random values in the range of the data can be employed. Sometimes a grid is used, based on the plane formed by the first two PCs. In practice, the initialization method will hardly ever matter, however, starting from other random initial values will lead to different maps. The conclusions drawn from the different maps, however, tend to be very similar.

## 统计代写|化学计量学作业代写chemometrics代考|Visualization

Several different visualization methods are provided in the kohonen package: one can look at the codebook vectors, the mapping of the samples, and one can also use SOMs for prediction. Here, only a few examples are shown. For more information, consult the manual pages of the plot. kohonen function, or the software description (Wehrens and Buydens 2007; Wehrens and Kruisselbrink 2018).

For multivariate data, the locations of the codebook vectors can not be visualized as was done for the two-dimensional data in Fig. 5.1. In the kohonen package, the default is to show segment plots, such as in Fig. $5.2$ if the number of variables is smaller than 15, and a line plot otherwise. One can also zoom in and concentrate on the values of just one of the variables:
$>\operatorname{for}(1 \ln c(1,8,11,13))$

• plotiwines.som. “property”.

for $(1 \ln c(1,8,11,13))$
$+\quad$ plot $($ wines.som, “property”
$+\quad$ property = getcodes(wines.som, 1) $[, 1] .$
$+\quad$ main = colnames $($ wines $)[1])$
property = getcodes (wines.som, 1) $[, 1]$.
main = colnames (Wines $[1]}$

Clearly, in these plots, shown in Fig. 5.3, there are regions in the map where specific variables have high values, and other regions where they are low. Areas of high values and low values are much more easily recognized than in Fig.5.2. Note the use of the accessor function getcodes here.

Perhaps the most important visualization is to show which objects map in which units. In the kohonen package, this is achieved by supplying the the type = “mapping ” argument to the plotting function. It allows for using different plotting characters and colors (see Fig. 5.4):

plot (wines.som, type = “mapping” ,

$c o 1=a s .$ integer (vintages), pch $=$ as. integer (vintages) )

Again, one can see that the wines are well separated. Some class overlap remains, especially for the Grignolinos (pluses in the figure). These plots can be used to make predictions for new data points: when the majority of the objects in a unit are, e.g., of the Barbera class, one can hypothesize that this is also the most probably class for future wines that end up in that unit. Such predictions can play a role in determining authenticity, an economically very important application.

Since SOMs are often used to detect grouping in the data, it makes sense to look at the codebook vectors more closely, and investigate if there are obvious class boundaries in the map-areas where the differences between neighboring units are relatively large. Using a color code based on the average distance to neighbors one can get a quick and simple idea of where the class boundaries can be found. This

## 统计代写|化学计量学作业代写chemometrics代考|Application

The main attraction of SOMs lies in the applicability to large data sets; even if the data are too large to be loaded in memory in one go, one can train the map sequentially on (random) subsets of the data. It is also possible to update the map when new data points become available. In this way, SOMs provide a intuitive and simple visualization of large data sets in a way that is complementary to PCA. An especially interesting feature is that these maps can show grouping of the data without explicitly performing a clustering. In large maps, sudden transitions between units, as visualized by, e.g., a U-matrix plot, enable one to view the major structure at a glance. In smaller maps, this often does not show clear differences between groups-see Fig. $5.5$ for an example. One way to find groups is to perform a clustering of the individual codebook vectors. The advantage of clustering the codebook vectors rather than the original data is that the number of units is usually orders of magnitude smaller than the number of objects.

The kohonen package used in this chapter, originally based on the class package (Venables and Ripley 2002), has several noteworthy features not discussed yet (Wehrens and Kruisselbrink 2018). It can use distance functions other than the usual Euclidean distance, which might be extremely useful for some data sets, often avoiding the need for prior data transformations. One example is the WCC function mentioned earlier: this can be used to group sets of X-ray powder diffractograms where the position rather than the position of peaks contains the primary information (Wehrens and Willighagen 2006; Wehrens and Kruisselbrink 2018). For numerical variables, the sum-of-squares distance is the default (slightly faster than the Euclidean distance); for factors, the Tanimoto distance. In the kohonen package it is possible to supply several different data layers, where the rows in each layer correspond to different bits of information on the same objects. Separate distance functions can be defined for each single layer, which are then combined into one overall distance measure using weights that can be defined by the user. Apart from the usual “online” training algorithm described in this chapter, a “batch” algorithm is implemented as well, where codebook vectors are not updated until all records have been presented to the map. One advantage of the batch algorithm is that it dispenses with one of the parameters of the SOM: the learning rate $\alpha$ is no longer needed. The main disadvantage is that it is sometimes less stable and more likely to end up in a local optimum. The batch algorithm also allows for parallel execution by distributing the comparisons of objects to all codebook vectors over several cores (Lawrence et al. 1999) which may lead to considerable savings with larger data sets (Wehrens and Kruisselbrink 2018).

## 统计代写|化学计量学作业代写chemometrics代考|Training SOMs

C在一世+1=(1−一种)C在一世+一种这bj

## 统计代写|化学计量学作业代写chemometrics代考|Visualization

kohonen 包中提供了几种不同的可视化方法：一种可以查看码本向量、样本的映射，还可以使用 SOM 进行预测。这里只展示了几个例子。有关更多信息，请参阅该图的手册页。kohonen 函数或软件描述（Wehrens 和 Buydens 2007；Wehrens 和 Kruisselbrink 2018）。

>为了⁡(1ln⁡C(1,8,11,13))

• plotiwines.som。“财产”。

+阴谋(wines.som，“财产”
+属性 = getcodes(wines.som, 1)[,1].
+主要 = 列名(葡萄酒)[1])

main = colnames（葡萄酒[1]}[1]}

C这1=一种s.整数（年份），pch=作为。整数（年份））

## 统计代写|化学计量学作业代写chemometrics代考|Application

SOM 的主要吸引力在于对大数据集的适用性；即使数据太大而无法一次性加载到内存中，也可以在数据的（随机）子集上按顺序训练地图。当新的数据点可用时，也可以更新地图。通过这种方式，SOM 以与 PCA 互补的方式提供了大型数据集的直观和简单的可视化。一个特别有趣的功能是这些地图可以显示数据的分组，而无需明确执行聚类。在大型地图中，单元之间的突然转换，例如通过 U 矩阵图可视化，使人们能够一目了然地查看主要结构。在较小的地图中，这通常不会显示组之间的明显差异——见图。5.5例如。找到组的一种方法是对各个码本向量进行聚类。对码本向量而不是原始数据进行聚类的优点是单元的数量通常比对象的数量小几个数量级。

## 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。

## 统计代写|化学计量学作业代写chemometrics代考|Statistical Tests

statistics-lab™ 为您的留学生涯保驾护航 在代写化学计量学chemometrics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。我们的专家在代写化学计量学chemometrics代写方面经验极为丰富，各种代写化学计量学chemometrics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

## 统计代写|化学计量学作业代写chemometrics代考|Related Methods

PCA is not alone in its aim to find low-dimensional representations of highdimensional data sets. Several other methods try to do the same thing, but rather than finding the projection that maximizes the explained variance, they choose other criteria. In Principal Coordinate Analysis (PCoA) and the related Multidimensional Scaling (MDS) methods, the aim is to find a low-dimensional projection that reproduces the experimentally found distances between the data points. When these distances are Euclidean, the results are the same or very similar to PCA results; however, other distances can be used as well. Independent Component Analysis maximizes deviations from normality rather than variance, and Factor Analysis concentrates on reproducing covariances. We will briefly review these methods in the next paragraphs.

## 统计代写|化学计量学作业代写chemometrics代考|Multidimensional Scaling

In some cases, applying PCA to the raw data matrix is not appropriate, for example in situations where regular Euclidean distances do not apply-similarities between chemical structures, e.g., can be expressed easily in several different ways, but it is not at all clear how to represent molecules into fixed-length structure descriptors (Baumann 1999), something that is required by distance measures such as the Euclidean distance. Even when comparing spectra or chromatograms, the Euclidean distance can be inappropriate, for instance in the presence of peak shifts (Bloemberg et al. 2010 ; de Gelder et al. 2001). In other cases, raw data are simply not available and the only information one has consists of similarities. Based on the sample similarities, the goal of methods like Multidimensional Scaling (MDS, (Borg and Groenen 2005; Cox and Cox 2001)) is to reconstruct a low-dimensional map of samples that leads to the same similarity matrix as the original data (or a very close approximation).

Since visualization usually is one of the main aims, the number of dimensions usually is set to two, but in principle one could find an optimal configuration with other dimensionalities as well.

The problem is something like making a topographical map, given only the distances between the cities in the country. In this case, an exact solution is possible in two dimensions since the original distance matrix was calculated from twodimensional coordinates. Note that although distances can be reproduced exactly, the map still has rotational and translational freedom-in practice this does not pose any problems, however. An amusing example is given by maps not based on kilometers but rather on travel time-the main cities will be moved to the center of the plot since they usually are connected by high-speed trains, whereas smaller villages will appear to be further away. In such a case, and in virtually all practical applications, a two-dimensional plot will not be able to reproduce all similarities exactly.

In MDS, there are several ways to indicate the agreement between the two distance matrices, and these lead to different methods. The simplest approach is to perform $\mathrm{PCA}$ on the double-centered distance matrix, ${ }^{4}$ an approach that is known as Principal Coordinate Analysis, or Classical MDS (Gower 1966). The criterion to be minimized is called the stress, and is given by
$$S=\sum_{j<i}\left(\left|x_{i}-x_{j}\right|-e_{i j}\right)^{2}=\sum_{j<i}\left(d_{i j}-e_{i j}\right)^{2}$$
where $e_{i j}$ corresponds with the true, given, distances, and $d_{i j}$ are the distances between objects $x_{i}$ and $x_{j}$ in the low-dimensional space.

## 统计代写|化学计量学作业代写chemometrics代考|Independent Component Analysis and Projection Pursuit

Variation in many cases equals information, one of the reasons behind the widespread application of PCA. Or, to put it the other way around, a variable that has a constant value does not provide much information. However, there are many examples where the relevant information is hidden in small differences, and is easily overwhelmed by other sources of variation that are of no interest. The technique of Projection Pursuit (Friedman 1987; Friedman and Tukey 1974; Huber 1985) is a generalization of PCA where a number of different criteria can be optimized. One can for instance choose a viewpoint that maximizes some grouping in the data. In general, however, there is no analytical solution for any of these criteria, except for the variance criterion used in PCA. A special case of Projection Pursuit is Independent Component Analysis (ICA, Hyvärinen et al. 2001), where the view is taken to maximize deviation from multivariate normality, given by the negentropy $J$. This is the difference of the entropy of a normally distributed random variable $H\left(x_{\mathrm{G}}\right)$ and the entropy of the variable under consideration $H(x)$
$$J(x)=H\left(x_{\mathrm{G}}\right)-H(x)$$
where the entropy itself is given by
$$H(x)=-\int f(x) \log f(x) d x$$
Since the entropy of a normally distributed variable is maximal, the negentropy is always positive (Cover and Thomas 1991). Unfortunately, this quantity is hard to calculate, and in practice approximations, such as kurtosis and the fourth moment are used.

## 统计代写|化学计量学作业代写chemometrics代考|Related Methods

PCA 并不是唯一一个致力于寻找高维数据集的低维表示的人。其他几种方法尝试做同样的事情，但不是找到最大化解释方差的投影，而是选择其他标准。在主坐标分析 (PCoA) 和相关的多维缩放 (MDS) 方法中，目标是找到一个低维投影，该投影再现实验发现的数据点之间的距离。当这些距离为欧式时，结果与 PCA 结果相同或非常相似；然而，也可以使用其他距离。独立成分分析最大限度地偏离正态性而不是方差，因子分析专注于再现协方差。我们将在接下来的段落中简要回顾这些方法。

## 统计代写|化学计量学作业代写chemometrics代考|Independent Component Analysis and Projection Pursuit

Ĵ(X)=H(XG)−H(X)

H(X)=−∫F(X)日志⁡F(X)dX

## 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。

## 统计代写|化学计量学作业代写chemometrics代考|The Machinery

statistics-lab™ 为您的留学生涯保驾护航 在代写化学计量学chemometrics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。我们的专家在代写化学计量学chemometrics代写方面经验极为丰富，各种代写化学计量学chemometrics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

## 统计代写|化学计量学作业代写chemometrics代考|The Machinery

Currently, PCA is implemented even in low-level numerical software such as spreadsheets. Nevertheless, it is good to know the basics behind the computations. In almost all cases, the algorithm used to calculate the PCs is Singular Value Decomposition (SVD). ${ }^{2}$ It decomposes an $n \times p$ mean-centered data matrix $\boldsymbol{X}$ into three parts:
$$\boldsymbol{X}=\boldsymbol{U} \boldsymbol{D} \boldsymbol{V}^{T}$$
where $\boldsymbol{U}$ is a $n \times a$ orthonormal matrix containing the left singular vectors, $\boldsymbol{D}$ is a diagonal matrix $(a \times a$ ) containing the singular values, and $V$ is a $p \times a$ orthonormal matrix containing the right singular vectors. The latter are what in PCA terminology is called the loadings-the product of the first two matrices forms the scores:
$$\boldsymbol{X}=(\boldsymbol{U} \boldsymbol{D}) \boldsymbol{V}^{T}=\boldsymbol{T} \boldsymbol{P}^{T}$$
The interpretation of matrices $T, P, U, D$ and $V$ is straightforward. The loadings, columns in matrix $\boldsymbol{P}$ (or equivalently, the right singular vectors, columns in matrix $V$ ) give the weights of the original variables in the PCs. Variables that have very low values in a specific column of $\boldsymbol{V}$ contribute only very little to that particular latent variable. The scores, columns in $T$, constitute the coordinates in the space of the latent variables. Put differently: these are the coordinates of the samples as we see them from our new PCA viewpoint. The columns in $\boldsymbol{U}$ give the same coordinates in a normalized form – they have unit variances, whereas the columns in $T$ have variances corresponding to the variances of each particular PC. These variances $\lambda_{i}$ are proportional to the squares of the diagonal elements in matrix $\boldsymbol{D}$ :
$$\lambda_{i}=d_{i}^{2} /(n-1)$$
The fraction of variance explained by PC $i$ can therefore be expressed as
$$F V(i)=\lambda_{i} / \sum_{j=1}^{a} \lambda_{j}$$
One main problem in the application of PCA is the decision on how many PCs to retain; we will come back to this in Section 4.3.

## 统计代写|化学计量学作业代写chemometrics代考|Doing It Yourself

Calculating scores and loadings is easy: consider the wine data first. We perform PCA on the autoscaled data to remove the effects of the different scales of the variables using the svd function provided by $R$ :

• wines.svd <- svd (wines. sc)
• wines. scores <- wines . svdș q t

wines. loadings <- wines.svd\$v The first two PCs represent the plane that contains most of the variance; how much exactly is given by the squares of the values on the diagonal of$\boldsymbol{D}$. The importance of individual PCs is usually given by the percentage of the overall variance that is explained:$>$wines. vars <-wines . svd\$ $\mathrm{d}^{n} 2 /$ (nrow (wines) – 1)
wines.totalvar <- sum (wines.vars)
wines.relvars <- wines. vars / wines.totalvar
variances <- 100 * round (wines . relvars, digits = 3)
variances [1:5]
[1] $36.0 \quad 19.2 \quad 11.2 \quad 7.1 \quad 6.6$
The first PC covers more than one third of the total variance; for the fifth PC this amount is down to one fifteenth.

## 统计代写|化学计量学作业代写chemometrics代考|Scree Plots

The amount of variance per PC is usually depicted in a scree plot: either the variances themselves or the logarithms of the variances are shown as bars. Often, one also considers the fraction of the total variance explained by every single PC. The last few PCs usually contain no information and, especially on a log scale, tend to make the scree plot less interpretable, so they are usually not taken into account in the plot.
$>$ barplot (wines, $\operatorname{vars}[1: 10]$, main = “Variances”,
names.arg = paste (“PC”, 1:10))
barplot(log (wines. vars $[1: 10])$, main = “log (Variances) “,
names.arg = paste (“PC”, 1:10))

barplot(wines. relvars $[1: 10]$, main = “Relative variances”,
names.arg = paste $(” \mathrm{PC} “, 1: 10))$
b barplot (cumsum $(100$ * wines. relvars $[1: 10])$ ).
main = “Cumulative variances (8)”,
names $\cdot a r g=$ paste( “PC”, 1:10), ylim $=c(0,100))$
This leads to the plots in Fig. 4.2. Clearly, PCs 1 and 2 explain much more variance than the others: together they cover $55 \%$ of the variance. The scree plots show no clear cut-off, which in real life is the rule rather than the exception. Depending on the goal of the investigation, for these data one could consider three or five PCs. Choosing four PCs would not make much sense in this case, since the fifth PC would explain almost the same amount of variance: if the fourth is included, the fifth should be, too.

## 统计代写|化学计量学作业代写chemometrics代考|The Machinery

X=在D在吨

X=(在D)在吨=吨磷吨

λ一世=d一世2/(n−1)
PC 解释的方差分数一世因此可以表示为
F在(一世)=λ一世/∑j=1一种λj
PCA 应用的一个主要问题是决定保留多少 PC；我们将在第 4.3 节中回到这一点。

## 统计代写|化学计量学作业代写chemometrics代考|Doing It Yourself

• wines.svd <- svd (wines.sc)
• 葡萄酒。分数 <- 葡萄酒。svd qt

• matplot (wavelengths $[-1]+1$, t(nir.diff),
$\mathrm{xlab}=$ “Wavelength $(\mathrm{nm}\rangle^{*}, y 1 a b=” 1 / \mathrm{R}$ (1st deriv.)”,
type $=” n$ “)
$>a b l i n e(h=0$, col = “gray” $)$

matines (wavelengths $[-1]+1, t$ (nir.diff), lty = 1)
Note that the number of variables decreases by one. The result is shown in Fig. 3.5. Comparison with the original data (Fig. 2.1) shows more detailed structure; the price is an increase in noise. A better way to obtain first-derivative spectra is given by the Savitsky-Golay filter (here using the sgolayfilt function from the signal package), which is not only a smoother but can also be used to calculate derivatives:
nir.deriv <- apply(gasoline\$NIR, 1, sgolayfilt, m = 1) In this particular case, the differences between the two methods are very small. Also second derivatives are used in practice-the need to control noise levels is even bigger in that case. Another way to remove scatter effects in infrared spectroscopy is Multiplicative Scatter Correction (MSC, Geladi et al. 1985; Nis et al. 1990). One effectively models the signal of a query spectrum as a linear function of the reference spectrum: $$y_{q}=a+b y_{r}$$ ## 统计代写|化学计量学作业代写chemometrics代考|Aligning Peaks—Warping Many analytical data suffer from small shifts in peak positions. In NMR spectroscopy, for example, the position of peaks may be influenced by the$\mathrm{pH}$. What complicates matters is that in NMR, these shifts are by no means uniform over the data; rather, only very few peaks shift whereas the majority will remain at their original locations. The peaks may even move in different directions. In mass spectrometry, the shift is more uniform over the$m / z$axis and is more easy to account for-if one aims to analyse the data in matrix form, binning is required, and in many cases a suitable choice of bins will already remove most if not all of the effects of shifts. Moreover, peak shifts are usually small, and may be easily corrected for by the use of standards. The biggest shifts, however, are encountered in chromatographic applications, especially in liquid chromatography. Two different chromatographic columns almost never give identical elution profiles, up to the extent that peaks may even swap posi-tions. The situation is worse than in gas chromatography, since retention mechanisms are more complex in the liquid phase than in the gas phase. In all forms of column chromatography, column age is an important factor: a column that has been used for some time almost certainly will show different chromatograms than when freshly installed. ## 化学计量学代写 ## 统计代写|化学计量学作业代写chemometrics代考|Dealing with Noise 物理化学数据总是包含噪声，其中术语“噪声”通常用于响应的小、快速、随机波动。任何科学实验的首要目标是产生最高质量的数据 通常会降低噪音水平。最简单的实验方法是执行n重复测量，并对单个光谱进行平均，从而降低噪声n. 例如，在核磁共振光谱中，一种相对不敏感的分析方法，信号平均是常规做法，人们必须在测量时间和数据质量之间取得平衡。 作为一个例子，我们考虑前列腺数据，其中每个样本都进行了两次测量。前列腺数据的重复测量覆盖数据矩阵中的连续行。可以使用以下步骤进行平均。 同样在平均数据中，噪声是可观的；在注意不破坏数据结构的同时降低噪声水平将使后续分析更加容易。 最简单的方法是应用运行平均值，即将每个值替换为ķ它周围的点。的价值ķ，即所谓的窗口大小，需要优化；较大的值会导致高度平滑，但也会导致峰值失真，而较低的值ķ只能对信号做小的改动。常常ķ是在视觉检查的基础上选择的，无论是平滑信号本身还是残差。使用函数 embed 可以很容易地计算运行均值，提供包含原始数据向量的连续块作为行的矩阵；使用函数 rowMeans 即可获得所需的运行方式。 ## 统计代写|化学计量学作业代写chemometrics代考|Baseline Removal 在某些形式的光谱学中，人们可能会遇到远离零电平的基线或“背景信号”。由于这会影响峰高和峰面积等测量值，因此纠正此类现象至关重要。 例如，红外光谱会导致散射效应——样品表面会影响测量。结果，人们经常观察到光谱偏移：同一材料的两个光谱可能在整个波长范围内显示出恒定的差异。这可以通过采用一阶导数轻松消除（即，查看连续波长的强度之间的差异，而不是强度本身）。看一下汽油数据： >nir.diff$<-t(apply{gasoline $NIR, 1,d一世FF))$

• matplot（波长[−1]+1, t(nir.diff),
Xl一种b=“波长(n米⟩∗,是1一种b=”1/R（一阶导数）”，
输入=”n “)
>一种bl一世n和(H=0, col = “灰色”)

nir.deriv <- apply (gasoline $NIR, 1, sgolayfilt, m = 1) 在这种特殊情况下，两种方法之间的差异非常小。在实践中也使用二阶导数——在这种情况下，控制噪声水平的需要甚至更大。 在红外光谱中消除散射效应的另一种方法是乘法散射校正（MSC，Geladi 等人 1985；Nis 等人 1990）。一个有效的模型 查询频谱的信号作为参考频谱的线性函数： 是q=一种+b是r ## 统计代写|化学计量学作业代写chemometrics代考|Aligning Peaks—Warping 许多分析数据都受到峰位置微小变化的影响。例如，在 NMR 光谱中，峰的位置可能受pH. 使事情复杂化的是，在 NMR 中，这些变化在数据上绝不是一致的。相反，只有极少数峰会移动，而大多数峰将保持在其原始位置。 峰甚至可以向不同的方向移动。在质谱分析中，偏移在整个米/和轴，并且更容易解释——如果要分析矩阵形式的数据，则需要分箱，并且在许多情况下，合适的分箱选择已经消除了大部分（如果不是全部）移位的影响。此外，峰值偏移通常很小，并且可以通过使用标准轻松校正。 然而，最大的转变发生在色谱应用中，尤其是在液相色谱中。两种不同的色谱柱几乎不会给出相同的洗脱曲线，直至峰甚至可能交换位置。这种情况比气相色谱法更糟，因为液相中的保留机制比气相中的更复杂。在所有形式的柱色谱中，柱龄是一个重要因素：使用了一段时间的柱几乎肯定会显示与新安装时不同的色谱图。 统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 ## 金融工程代写 金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。 ## 非参数统计代写 非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。 ## 广义线性模型代考 广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。 术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。 ## 有限元方法代写 有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。 有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。 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。 ## 随机分析代写 随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。 ## 时间序列分析代写 随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。 随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。 ## 回归分析代写 多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。 ## 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。 ## 统计代写|化学计量学作业代写chemometrics代考|Preface to the Second Edition 如果你也在 怎样代写化学计量学chemometrics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。 化学计量学是一门化学学科，它使用数学、统计学和其他采用形式逻辑的方法来设计或选择最佳的测量程序和实验，并通过分析化学数据来提供最大的相关化学信息。 将化学计量学方法与经典方法相比较，也许可以最好地理解它的特点。经典方法旨在理解效应–哪些因素是主要的，哪些因素是可以忽略的–而化学计量学方法则放弃了理解效应的必要性，并指出了其他目标，如预测、模式识别、分类等。 statistics-lab™ 为您的留学生涯保驾护航 在代写化学计量学chemometrics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。我们的专家在代写化学计量学chemometrics代写方面经验极为丰富，各种代写化学计量学chemometrics相关的作业也就用不着说。 我们提供的化学计量学chemometrics及其相关学科的代写，服务范围广, 其中包括但不限于: • 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|化学计量学作业代写chemometrics代考|Preface to the Second Edition Eight years after the appearance of the first edition of this book, the$R$ecosystem has evolved significantly. The number of$R$users has continued to grow, and so has the number of R packages. The latter not only can be found at the two main$R$repositories, CRAN and Bioconductor, where elementary quality control checks are being applied to ascertain that the packages are at least semantically correct and provide a minimum of support, but also at other platforms such as github. Installation of an$\mathrm{R}\$ package is as easy as can be, probably one of the main reasons for the huge success that the language is experiencing. At the same time, this presents the user with a difficult problem: where should I look? What should I use? In keeping with the aims formulated in the first edition, this second edition presents an overview of techniques common in chemometrics, and R packages implementing them. I have tried to remain as close as possible to elementary packages, i.e., packages that have been designed for one particular purpose and do this pretty well. All of them are from CRAN or Bioconductor.

Maybe somewhat ironically, the R package ChemometricsWithR, accompanying this book, will no longer be hosted on CRAN. Due to package size restrictions, the package accompanying the first edition was forced to be split into two, the data part transferring into a separate package, ChemometricsWithRData. For this new edition, hosting everything on my own github repository has made it possible to reunite the two packages, making life easier for the reader. Installing the ChemometricsWithR package can be done as follows.

## 统计代写|化学计量学作业代写chemometrics代考|Preface to the First Edition

The natural sciences, and the life sciences in particular, have seen a huge increase in the amount and complexity of data being generated with every experiment. It is only some decades ago that scientists were typically measuring single numbers weights, extinctions, absorbances – usually directly related to compound concentrations. Data analysis came down to estimating univariate regression lines, uncertainties and reproducibilities. Later, more sophisticated equipment generated complete spectra, where the response of the system is wavelength-dependent. Scientists were confronted with the question how to turn these spectra into usable results such as concentrations. Things became more complex after that: chromatographic techniques for separating mixtures were coupled to high-resolution (mass) spectrometers, yielding a data matrix for every sample, often with large numbers of variables in both chromatographic and spectroscopic directions. A set of such samples corresponds to a data cube rather than a matrix. In parallel, rapid developments in biology saw a massive increase in the ratio of variables to objects in that area as well.

As a result, scientists today are faced with the increasingly difficult task to make sense of it all. Although most will have had a basic course in statistics, such a course is unlikely to have covered much multivariate material. In addition, many of the classical concepts have a rough time when applied to the types of data encountered nowadays – the multiple-testing problem is a vivid illustration. Nevertheless, even though data analysis has become a field in itself (or rather: a large number of specialized fields), scientists generating experimental data should know at least some of the ways to interpret their data, if only to be able to ascertain the quality of what they have generated. Cookbook approaches, involving blindly pushing a sequence of buttons in a software package, should be avoided. Sometimes the things that deviate from expected behavior are the most interesting in a data set, rather than unfortunate measurement errors. These deviations can show up at any time point during data analysis, during data preprocessing, modelling, interpretation… Every phase in this pipeline should be carefully executed and results, also at an intermediate stage, should be checked using common sense and prior knowledge.

## 统计代写|化学计量学作业代写chemometrics代考|Preprocessing

Textbook examples typically use clean, perfect data, allowing the techniques of interest to be explained and illustrated. However, in real life data are messy, noisy, incomplete, downright faulty, or a combination of these. The first step in any data analysis often consists of preprocessing to assess and possibly improve data quality. This step may actually take more time than the analysis itself, and more often than not the process consists of an iterative procedure where data preprocessing steps are alternated with data analysis steps.

Some problems can immediately be recognized, such as measurement noise, spikes, non-detects, and unrealistic values. In these cases, taking appropriate action is rarely a problem. More difficult are the cases where it is not obvious which characteristics of the data contain information, and which do not. There are many examples where chance correlations lead to statistical models that are perfectly able to describe the training data (the data used to set up the model in the first place) but have no predictive abilities whatsoever.

This chapter will focus on standard preprocessing techniques used in the natural sciences and the life sciences. Data are typically spectra or chromatograms, and topics include noise reduction, baseline removal, peak alignment, peak picking, and scaling. Only the basic general techniques are mentioned here; some more specific ways to improve the quality of the data will be treated in later chapters. Examples include Orthogonal Partial Least Squares for removing uncorrelated variation (Sect. 11.4) and variable selection (Chap. 10).

## 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。