pca | 易学教程

PCA局部与整体的关系

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哈喽，今天周六啦。不知道有多少妹子想我呢。哈哈。言归正传。这个问题源于菜鸟思维。数据集X shape （1000,64）的整体进行PCA与分成两部分或多部分是否结果相同？？为何不同？差别大不大？为何？依旧以MNIST数据集为例进行探索： 1-整体PCA与结果展示，64->20 奇异值： [567.0065665 542.25185421 504.63059421 426.11767608 353.33503278 325.82036568 305.26157987 281.16033046 269.06977886 257.8239478 226.3187942 221.51478853 198.33066914 195.70009822 177.97288431 174.46075724 168.72640164 164.15235888 148.22422881 139.8223383 ] 占比：0.8942989517025197 2-分成两部分各自PCA，PCA后都是20维 [494.16894798 449.86043083 361.65617118 248.75442367 238.56963133 219.44600126 190.14159973 182.20945787 174.00574178 156.07163314 148.54921821 138

ggbiplot - change the group color and marker

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问题 In the example ggbiplot script plot there are 3 groups, how can I change the marker colors and shapes? library(ggbiplot) data(wine) wine.pca <- prcomp(wine, scale. = TRUE) ggbiplot(wine.pca, obs.scale = 1, var.scale = 1, group=wine.class, varname.size = 3, labels.size=3, ellipse = TRUE, circle = TRUE) + scale_color_discrete(name = '') + geom_point(aes(colour=wine.class), size = 3) + theme(legend.direction ='horizontal', legend.position = 'top') 回答1: The following works for me. ggbiplot(wine

【Matlab】PCA降维实现人脸识别（附学习资料、代码程序及注解、运行结果）

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Matlab实现PCA人脸识别寒假来了，阿汪先生总结了这一学期里学到的一些东西，并来和大家分享一下。一、理论知识基础 1、一些前辈的经验分享（不局限于这些）（1） PCA人脸识别详解——初学者必看 . （2）理解主成分分析 (PCA) . （3） LLE算法 . （4）拉格朗日乘子法 . 2、阿汪先生做的一些笔记和用到的资料原理资料上讲的很好，阿汪做了一些批注。水平不够，大家见谅呀！^-^ （1） 05-人脸图像超分辨率重建 . （2） 6.5-基于K-L变换的特征提取 . （3） Matlab_PCA_图像降维和人脸匹配_笔记 . 主要用到的资料：人脸识别与人体动作识别技术及应用 [专著] / 曹林著.——北京：电子工业出版社，2015.8，ISBN:978-7-121-26660-7. 模式识别及MATLAB实现 [专著] / 杨杰主编.——北京：电子工业出版社，2017.8，ISBN:978-7-121-32127-6. 二、注解代码程序 1、重塑训练数据-T（） function T = CreateDatabase(TrainDatabasePath) %此函数重塑训练数据库的所有2D图像放入一维列向量中。 %然后，将这些一维列向量放在一行中构造2D矩阵“ T”。 %一个2D矩阵，包含所有1D图像矢量。 %假设训练数据库中的所有P图像的MxN大小相同。

数据降维（PCA、KPCA、PPCA）及C++实现

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1、何为数据降维 1.1维数灾难：往往满足采样条件所需的样本数目巨大、样本稀疏、距离计算困难。 1.2降维：利用数学变换将原始高维属性空间转变为低维“子空间”，即在高维采样数据中提取能够表达原始数据的特征。 1.3 降维优点：数据集更易懂、使用和显示；降低算法计算开销；去除噪声。 2、一些降维算法 Principal Component Analysis （PCA） Linear Discriminant Analysis（LDA） Locally linear embedding（LLE） Laplacian Eigenmaps 本文主要针对以下三种算法： 2.1 PCA：PCA算法是一种线性投影技术，利用降维后使数据的方差最大原则保留尽可能多的信息； 2.2 KPCA：PCA仅考虑了数据的二阶统计信息，而没有利用高阶统计信息，忽略了数据的非线性相关性，而KPCA，通过非线性变换将数据映射到了高维，在高维空间中进行特征提取，获得了更好的特征提取性能； 2.3 PPCA：PCA没有将数据的概率分布考虑，PPCA对PCA做了概率上的解释，延伸了PCA算法。总之：PPCA和KPCA都是针对PCA算法的缺陷，做出了不同方向上的改进。 3 PCA、KPCA、PPCA算法步骤 3.1 PCA：数据在低维线性空间上的正交投影，这个线性空间被称为主子空间，使得投影数据的方差被最大化。

Principal component analysis in R with prcomp and by myself: different results

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问题 Where do I am wrong? I am trying to perform PCA through prcomp and by myself, and I get different results, can you please help me? DOING IT BY MYSELF: >database <- read.csv("E:/R/database.csv", sep=";", dec=",") #it's a 105 rows x 8 columns, each column is a variable >matrix.cor<-cor(database) >standardize<-function(x) {(x-mean(x))/sd(x)} >values.standard<-apply(database, MARGIN=2, FUN=standardize) >my.eigen<-eigen(matrix.cor) >loadings<-my.eigen$vectors >scores<-values.standard %*% loadings

Plot PCA loadings and loading in biplot in sklearn (like R's autoplot)

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问题 I saw this tutorial in R w/ autoplot . They plotted the loadings and loading labels: autoplot(prcomp(df), data = iris, colour = 'Species', loadings = TRUE, loadings.colour = 'blue', loadings.label = TRUE, loadings.label.size = 3) https://cran.r-project.org/web/packages/ggfortify/vignettes/plot_pca.html I prefer Python 3 w/ matplotlib, scikit-learn, and pandas for my data analysis. However, I don't know how to add these on? How can you plot these vectors w/ matplotlib ? I've been reading

Plot PCA loadings and loading in biplot in sklearn (like R's autoplot)

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Extracting Principal Components in FactoMiner R

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问题 I am trying to extract the principal components for a covariance matrix using PCA in FactoMiner. However, for some reason , I only see n-1 components in the var-->coord variable library(FactoMineR) x = matrix(rnorm(10000),nrow = 100,ncol = 100) y = PCA(x,ncp = 100,graph = FALSE) dim(y$var$coord) This leads to an output of 100 99. I am new to this package and hope to get more insights 回答1: The maximum number of dimensions in a principal component analysis performed on p variables and n

How to extract Principal Components using FactoMineR package

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问题 I have a dataset with a mixture of categorical and numeric features. I have used the FAMD function from the FactoMineR package to perform Principal Component Analysis. However, I am unable to figure out a way to extract them into another dataframe, so that I can perform Principal Component Regression. I have attached an image of a subset my data. #Performing Principal Component Analysis on Mixed Data library(FactoMineR) pca = FAMD(train[3:378],ncp=10) #Displaying the eigen value matrix pca

Normalize PCA with scikit-learn when data is split

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问题 I have a followup question on: How to normalize with PCA and scikit-learn. I'm creating an emotion detection system and what I do now is: Split data over all emotion (distributing data over multiple subsets). Add all data together (the multiple subsets into 1 set) Get PCA parameters of combined data (self.pca = RandomizedPCA(n_components=self.n_components, whiten=True).fit(self.data)) Per emotion (per subset), apply PCA to data of that emotion (subset). I should do the normalization at: step

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