Algorithm Overview
Principal Component Analysis (PCA) is a common method for processing, compressing, and extracting information based on the variable covariance matrix. It is mainly used for dimensionality reduction of features.
Algorithm hypothesis
The probability distribution of data satisfies the Gaussian distribution or exponential probability distribution. A vector with a high variance is considered as the principal component.
Algorithm in
={x0_te,x1_te,x2_te,x3_te,x4_te,x5_te,x6_te,x7_te,x8_te,x9_te};w={};% array of cells to store the reduced-dimension matrixFor I=1:10Avg = mean (Xte{i}, 2); % for each image pixel strength mean valueD=avg*ones (1,size (xte{i},2));Xte{i} = xte{i}-D;% de-homogenizationSigma = xte{i} * xte{i} '/Size (Xte{i}, 2);% to find Signa value[U,s,v] = SVD (sigma);%xrot = U ' * x; % of rotated dataXtilde = U (:, 1:256) ' * xte{i}; % REDUCED-dimensionality dataW=[w,u (:, 1:256) ']; % Select the first 256 eigenv
components in a lower proportion of PCA dimensionality, it uses a number of random algorithms to accelerate SVD.
Full is the traditional SVD, using the corresponding implementation of the SCIPY library.
Arpack and randomized similar to the applicable scenario, the difference is that randomized uses scikit-learn own SVD implementation, and Arpack directly uses scipy the library sparse SVD implementation.
The default is auto, that is
main component from the largest contribution rate, until the cumulative contribution rate to meet the requirements;Then define the principal component load (loadings, which is called the factor load in the factor analysis):That is, the correlation coefficients of the first principal component and the J Primitive variable, the matrix a= (AIJ) is called the factor load matrix, and in practice the AIJ is used instead of Uij As the principal component coefficient, because it is a standardized coef
EigenTest.cpp:Defines the entry point for the console application.
#include "stdafx.h" void mypca (const Mat &_data, int Dim, Mat &eigenvalues, Mat &eigenvectors);
void Printmat (Mat _data) {Mat data = cv::mat_ (_data); for (int i=0, i (i,j) (
Principle of principal component analysis and its Python implementation preface:This article mainly refers to Andrew Ng's machine learning course handout, I translated, and with a Python demo demo to deepen understanding.This paper mainly introduces a dimensionality reduction algorithm, principal component analysis method, Principal components analyses, referred to as P
InPCAIn other places, when solving extreme values, we always encounterX 'A' axFunction pairXI have always seen the results given by others. Today I have deduced the results carefully. Here I will record this process.
The following is a proof of
A project this semester is really interesting. It seems that it was the first time I felt that everything I learned was useful, and I used git for Version Control for the first time. The lady is easy to use, especially when some feature is needed.
1: There are n faces in total. Each face is calculated from left to right based on pixels, from top to bottom, and the number of pixels in each face is m, which forms the face matrix m * n, then, a new matrix is formed for the values of each row in
lazy Learning Algorithm
Summary
Chapter 4 build a good training set-data preprocessing
Process Missing Values
Remove features or samples with missing values
Rewrite Missing Value
Understanding the estimator API in sklearn
Process classified data
Splits a dataset into a training set and a test set.
Unified feature value range
Select meaningful features
Evaluate feature importance using random Forest
Summary
Chapter 5 compressing data by Dimensionality
that "a dream of Red mansions" in the characters from more to less in turn is Baoyu, Fengjie, Jia Mu, attacked people, Dai Yu, Mrs. Wang and Bao-Chai. However, this ranking is problematic, because "Lin Daiyu" the number of the word has 267 times, need to add to Dai Yu's play, so in fact, Dai Yu's play more than the attack.
Similarly, "old lady" generally refers to the Jia Mu, so the play of the MU is more than the Phoenix sister. The correct ranking should be Baoyu, Jia Mu, Fengjie, Dai Yu, as
In doing data processing, need to use different methods, such as feature standardization, principal component analysis, and so on will be reused some parameters, Sklearn provides a pipeline, can solve the problem at onceFirst show the usual way firstImport Pandas asPD fromsklearn.preprocessing Import Standardscaler fromsklearn.decomposition Import PCA fromSklearn.linear_model Import logisticregressiondf= Pd.read_csv ('Wdbc.csv') X= df.iloc[:,2:].value
first pipelined model clamp, first divide the dataset into a training dataset (data from the original DataSet 80%) and a separate test data set (20% of the original dataset) from sklearn.cross_validation Import train_test_splitx_train,x_test,y_train,y_test=train_test_split (X,y,test _size=0.2, random_state=1)Integrated Data transformation and evaluation operations in the pipelineWe want to compress the initial 30-dimensional data into a two-dimensional subspace through
Python and R for two usage scenarios in data analysis:1. Text Information mining:The application of text information mining is very extensive, for example, according to the Internet purchase evaluation, social networking website tweets or news analysis of emotional polarity. Here we use examples to analyze and compare.Python has a good package to help us with the analysis. such as NLTK, and specifically for the Chinese language snownlp, including Chi
Baptism soul, practice python (2) -- python installation and configuration, python -- python
Install python and basic configurations:
Python Official Website: www.python.org
Open the website and download the corresponding version
Write Python,python, write Python programming, write Python programming, and write in Python for international students.I and write the team members are graduated from the domestic and overseas computer professional well-known institutions , are now employed in the domestic
Machine learning system Design (Building machines learning Systems with Python)-Willi Richert Luis Pedro Coelho General statementThe book is 2014, after reading only found that there is a second version of the update, 2016. Recommended to read the latest version, the ability to read English version of the proposal, Chinese translation in some places more awkward (but the English version of the book is indeed somewhat expensive).The purpose of my readi
Python learning notes-python program running, python-python
I am a beginner in python and write down some of my ideas. Please ignore it.
Install the python editor and configure the environment (see install and configure
information gain
Building a decision Tree
Random Forest
K Nearest neighbor--an algorithm of lazy learning
Summarize
The fourth chapter constructs a good training set---data preprocessing
Handling Missing values
Eliminate features or samples with missing values
Overwrite missing values
Understanding the Estimator API in Sklearn
Working with categorical data
Splitting a dataset into training and test sets
Uniform featu
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