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(Data Science Learning Codex 20) Derivation of principal component Analysis principle &python self-programmed function realization

Principal component Analysis (principal component, or PCA) is a classic and simple machine learning algorithm whose main purpose is to use fewer variables to explain most of the variation in the original data. It is expected that many variables with high correlation can be converted into independent variables, and some new variables which are less than the number of original variables and which can explain most of the data variation are selected to ac

Principal Component Analysis

Question: In the document-term matrix created in IR, two word items are "Learn" and "study". In the traditional vector space model, the two are considered independent. However, from the semantic point of view, the two are similar, and their appearance frequency is similar. Can they be combined into a feature? The feature selection problem mentioned in Model Selection and normalization is that the features to be removed are mainly those irrelevant to class tags. For example, the "Student name" ha

Full introduction to dynamic route configuration statements

Currently, dynamic routing and Static Routing are widely used. Here we mainly analyze the statements and steps of dynamic routing configuration for dynamic routing. Dynamic Routing means that the dynamic routing protocol (such as RIP) automatically creates a route table. When you remove a line, it automatically removes its route. Each interface in the dynamic routing configuration corresponds to a different network, and the IP addresses of the two endpoints connecting the two routers should belo

Matrix decomposition (rank decomposition) Article code summary

includethe following most excellent sites:stephen Becker ' s Page,raghunanda N H. Keshavan ' Spage,nuclear Norm and Matrix recoverythrough SDP bychristoph helmberg, Arvind Ganesh ' Slow-rank Matrix Recovery and completion via convex optimizationwho provide more in-depth additi Onal information.additional codes were featured also Onnuit Blanche. The following people provided additional Inputs:olivier Grisel,matthieu puigt. Most of the algorithms listed below generally rely on using the nuclear

Principal components analysis-maximum variance Interpretation

The previous content of this article is "Factor Analysis". Due to its extraordinary theories, I plan to finish the entire course and then write it again. Before writing this article, I have read PCA, SVD, and lda. These models are similar, but they all have their own characteristics. This article will first introduce PCA. The relationship between them can only be learned and understood.

Stanford UFLDL Tutorial Data preprocessing _stanford

pca-albinism) assume that the data has been scaled to a reasonable interval. Example: When dealing with natural images, the pixel values we get are in [0,255] intervals, and the usual processing is to divide the pixel values by 255 to make them scale to [0,1]. Reduction of the mean value on a per-sample basis If your data is stationary (that is, the statistics for each dimension of the data are subject to the same distribution), you can consider subt

"Deeplearning" EXERCISE:PCA and Whitening

EXERCISE:PCA and WhiteningExercise Links:EXERCISE:PCA and WhiteningPca_gen.m%%================================================================%%Step 0a:load Data%Here we provide the code to load natural image data into X.% x would be a144*10000Matrixwherethe kth column x (:, k) corresponds to% The RAW image data fromThe kth 12x12 image patch sampled.% You DoNot need to change the code below.x=Sampleimagesraw (); figure ('name','Raw Images'); Randsel= Randi (Size (x,2), $,1); % A random selection

Scikit-learn Machine learning Module (next)

GRIDSEARCHCV function to automatically find the optimal alpha value: From Sklearn.grid_search import GRIDSEARCHCV GSCV = GRIDSEARCHCV (Model (), Dict (Alpha=alphas), cv=3). Fit (X, y) Scikit-learn also provides an inline CV model, such as From Sklearn.linear_model import Ridgecv, LASSOCV Model = RIDGECV (Alphas=alphas, cv=3). Fit (X, y)This method can get the same result as GRIDSEARCHCV, but if it is to do the verification of the model, it also needs to use the Cross_val_score function

[Machine learning Article] handwriting recognition based on KNN,SVM algorithm in Scikit learn Library

Preface In this paper, how to use the KNN,SVM algorithm in Scikit learn library for handwriting recognition. Data Description: The data has 785 columns, the first column is label, and the remaining 784 columns of data store the pixel values of the grayscale image (0~255) 28*28=784 installation Scikit Learn library See a lot of installation tutorials, have not been installed successfully. Finally refer to the official Website installation documentation, only need to follow the steps to successfu

Example of using Python to read external data files

Whether it's data analysis, data visualization, or data mining, everything is based on data as the most basic element. Using Python for data analysis, the same most important step is how to import data into Python before you can implement data analysis, data visualization, data mining, and so on. In this period of Python learning, we will take a detailed description of how Python obtains external data, from which we will learn about the following 4 areas of data acquisition:

Foundation of Image Processing-geometric significance of feature vectors

"Features" of the Space represented by a matrix ", their feature values represent the energy of each angle (as you can imagine, the longer the axis, the more it represents the space, its "feature" is stronger or more explicit, and the short axis is naturally a hidden feature). Therefore, the feature vector/value can fully describe the characteristics of a geometric space, feature vectors and feature values can be used in ry (especially space ry) and their applications.There are too many applica

Physical significance of High-number feature vectors

vector can be written as VN = (E1 * v1n, e2 * v2n... Em * vmn), and the matrix becomes a square matrix. If the rank of the matrix is smaller, the storage of the matrix can be compressed. Furthermore, because the projection size represents the projection of each component of a in the feature space, we can use the least 2 multiplication to find the components with the largest projection energy, remove the remaining components to save the information represented by the matrix to the maximum extent

Partial Least Square regression (partial least squares regression)

Problem 1. This section shows the final plsr related to component analysis and regression. Plsr feels that it has brought component analysis and regression to the extreme. The following describes the idea rather than the complete tutorial. Let's review the disadvantages of the earliest linear regression: if the number of samples m is less than the number of features N (M To solve this problem, we will use PCA to reduce the dimensionality of sample

Rules for machine learning norms (two) preferences for nuclear power codes and rules

given m*n matrix A, and if some of the elements are lost for some reason, can we restore the elements according to the elements of other rows and columns? Of course, assuming there are no other criteria for the test, it is very difficult to determine the data. But assuming we know rank rank (a) As a result, low-rank refactoring allows you to predict how much your users will like their non-rated videos.The matrix is then populated.2) Robust PCA: princ

"Python" uses Python for principal component analysis

Principal component analysis is performed using PCA classes in the Sklearn library.Import the library you want to use, and the direct PIP installation is OK.from sklearn.decomposition import PCAimport numpy as np # 如果使用numpy的array作为参数的数据结构就需要,其他type没试过是否可以import pandas as pd # 非必要The main input parameters of the PCA class are as follows: n_components: This parameter can help us specify the number of fea

Configuration instance for single-arm Routing

Ethernet0.3 172.16.3.1/32 Direct 0 0 127.0.0.1 LoopBack0Edit single-arm route settings for one vlan in this sectionIn a vlan, you can set the computer's secondary ip addressPhysical NetworkLast twoChina Unicom with different IP address segments.1. Set the IP address of the computer's PCA[Root # PCA root] # ipconfig eth0 10.65.1.1 netmask 255.255.0.0 [root # PCB root] # ipconfig eth0 10.66.1.1 netmask 255.2

Feature value and feature vector: Application in signal processing

on each feature vector. For example, if A is a matrix of M * n and N> m, then the feature vector is m (because the maximum rank is m), and N row vectors are projected on each feature vector E, its feature value V is the weight. Now, each row vector can be written as VN = (E1 * v1n, e2 * v2n... Em * vmn), and the matrix becomes a square matrix. If the rank of the matrix is smaller, the storage of the matrix can be compressed. Furthermore, because the projection size represents the projection of

Pcanet:a Simple deep learning Baseline for Image classification?----Chinese Translation

A summaryIn this paper, we present a very simple image classification deep learning framework, which relies on several basic data processing methods: 1) Cascade principal component Analysis (PCA), 2) Two value hash coding, 3) chunking histogram. In the proposed framework, the multi-layer filter kernel is first studied by PCA method, and then sampled and encoded using two-valued hash coding and block histogr

Spss_ statistical analysis of normality test

The importance of data distribution patterns In the process of data analysis, the different distribution patterns of data will directly affect the choice of data analysis strategy. Therefore, it is very important to judge the distribution pattern of the data series. The common distribution pattern of data is normal distribution, random distribution (evenly distributed), Poisson distribution, exponential distribution, etc., but in data analysis, the most important distribution pattern is normal,

A concise introductory course for linear discriminant analysis

classification degree. Ronald Fisher presented a linear discriminant (Problems Linear) method in 1936 (the "Use of multiple measurements in taxonomic discriminant"), which is sometimes used to solve classification questions Problem. The initial linear discriminant applied to two classification problems, later in 1948, by C. R. Rao (The utilization of multiple measurements in problems of biological classification) is extended to "multiple linear discriminant analysis" or "Multiple discriminant a

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