pca python

1, PCA reduced dimensionWhat is the role of dimensionality reduction?Data is easier to handle and easier to use in low-dimensional environments;The relevant characteristics, especially the important features, can be clearly displayed in the data, if only two or three-dimensional, it is more convenient to visualize;Data noise RemovalReduce algorithmic overheadCommon dimensionality reduction algorithms include principal component analysis (principal com

I. K-L transformation If you say PCA, you must first introduce the K-L transformation. The K-L transformation is the abbreviation of Karhunen-loeve transformation and is a special orthogonal transformation. It is based on statistical characteristics of a transformation, and some of the literature is called hotelling (Hotelling) transformation, because he first in 1933 to transform discrete signals into a series of unrelated coefficients of the m

PCA Dimension Reduction-- Minimum Variance interpretation (linear algebra see PCA) Note: According to the online data collation, welcome to discussThe complexity of the machine learning algorithm is closely related to the dimensionality of the data, even with the dimension number of the exponential association. So we have to dimensionality the data.dimensionality, of course, means the loss of information,

Singular Value and principal component analysis (PCA) [Reprint] Original Source: http://blog.sina.com.cn/s/blog_4b16455701016ada.html The PCA problem is actually a base transformation, which makes the transformed data have the largest variance. The variance size describes the amount of information about a variable. When we talk about the stability of a thing, we often say that we need to reduce the v

principal component Analysis ( Principal Component Analysis , PCA is a multivariate statistical analysis method that transforms multiple variables through a linear transformation to select fewer important variables. principle: When we use the statistical analysis method to study the multi-variable problem, the number of variables will increase the complexity of the subject. It is natural to expect a smaller number of variables to get more information.

and C is deduced:Obviously, the covariance matrix D of the transformed Matrix y should be 0 except for the diagonal elements. The p we are looking for is the p that can make the original covariance matrix diagonal.That is, the optimization target becomes: Looking for a matrix p, satisfies is a diagonal matrix, and diagonal elements in order from large to small, then the first k line of P is to find the base, with P's former K-line matrix multiplied by C so that x from n-dimensional to K-dimensi

PCA is an unsupervised learning algorithm, which can effectively reduce the latitude of data in the case of preserving most useful information.It is mainly used in the following three areas:1. Increase the speed of the algorithm2. Compress the data to reduce the consumption of memory and hard disk space3. Visualize data to map high latitude data to 2-D or 3-DAll in all, the PCA thing is to complete a mappin

1 Principal component Analysis(Principal Component ANALYSIS,PCA)2 linear discriminant Analysis(Linear discriminant analysis, LDA)Research backgroundIntroduction to basic knowledgeIntroduction to the Classic methodSummary discussionThe question is raisedGeographic systems are complex systems with multiple elements. In the study of geography, multivariate problems are often encountered. Too many variables will undoubtedly increase the difficulty and com

I. INTRODUCTION of PCA 1. Related background Principal component Analysis (Principal Component ANALYSIS,PCA) is a statistical method. An orthogonal transformation transforms a set of variables that may be related to a set of linearly unrelated variables, and the transformed set of variables is called the principal component. After finishing Chenhonghong teacher's "machine learning and Knowledge discovery" a

Http://blog.json.tw/using-matlab-implementing-pca-dimension-reductionWith M-pen information, each piece of material is n-dimensional, so that they can be regarded as a mxn matrix. If the size of the material is too large, it may be detrimental to analysis, such as this m-pen information used as a machine learning.The idea of PCA is to work out the oblique variance matrices of this MXN matrix, which is NXN,

In fact, previously written in the PCA-related blog post, but because the theoretical knowledge is limited, so the understanding is relatively shallow. This blog post, we understand the PCA in a different way, I assume that we have a preliminary understanding of PCA. First, let's cite an example in a two-dimensional space, such as: The left image represents five

1. PCA Holistic ThinkingPca,principle componet analysis, PCA, mainly used for data dimensionality reduction. By calculating the eigenvalues and eigenvectors of the covariance matrix of a given data set, it obtains the most critical direction of the dataset (the projection variance of the dataset is the largest in this direction, which can keep the most information), and the first k-dimensional space is sele

Welcome reprint, please indicate the source, I have limited ability, mistakes are unavoidable, welcome to guideBased on the first two posts, a sex classifier has been trained. Then this classifier should be used for gender classification.This test process is the same as the training process. However, during training, the sample data is processed in large quantities. The test process is processed for images that need to be identified. First, face recognition, that is, in the image to fin

Netease Open Course: 14th coursesNotes, 10 In the factor analysis mentioned earlier, the EM algorithm is used to find potential factor variables for dimensionality reduction. This article introduces another dimension reduction method, principal components analysis (PCA), which is more direct than factor analysis and easier to calculate. Principal component analysis is based on, In reality, for high-dimensional data, many dimensions are Disturb

principal Component Analysis 1. Description of the problem In many fields of research and application, it is often necessary to make a large amount of observations on multiple variables that reflect things, and collect large amounts of data for analysis to find the law. Large-scale multivariate samples will undoubtedly provide rich information for research and application, but also to some extent increase the workload of data collection, more importantly, in most cases, there may be correlations

This paper realizes PCA principal component analysis based on SVD singular matrix decomposition, uses this algorithm to complete the recognition of human face image, mainly explains the principle of SVD to realize PCA, how to use SVD to realize the dimensionality reduction of image features, and the application of SVD in text clustering, such as weakening synonyms, polysemy, and so on. Solve the problem tha

input_data = rand (1000,3); % randomly generated 1000 samples, each with x, Y, z three properties Figure (1);% control the drawing window to 1Hold off;% so that the current axis and graphics no longer have the nature of being refreshed, close on this basis and then drawPLOT3 (Input_data (:, 1), Input_data (:, 2), Input_data (:, 3), ' Ro '); Percent Function PCA, Input_data, Out_dim % use this to switch methodsuse_svd_method=1;% changed to 0 after u

PCA is a black box type of dimensionality reduction, through mapping, hope that the projected data as far as possible, so to ensure that the map after the variance as large as possible, the direction of the next map and the current mapping direction orthogonalSteps of PCA:The first step: first to the current data (de-mean) to find the covariance matrix, covariance matrix = data * Data of the transpose/(M-1) m for the number of columns, the diagonal is

Reference: Lle principle SummaryPersonal understandingthe defect of PCA dimensionality reduction : There are some linear relationships between samples in high dimensional space, and these relationships are not preserved after dimensionality reduction. For example, in a high-dimensional space, the shortest path is not the shortest line between two points in three-dimensional space, but the distance of the surface, and when we drop the dimension, it bec

PcaMaximize the sensitivity of individual dimensions and reduce the impact between dimensions. Differentiated measures: Variance dimension Effects: Covariance is thus represented by a matrix as the eigenvalues and eigenvectors of the covariance matrix. 1. Construct The matrix. 2. Find the covariance matrix of the Matrix. 3. Find the eigenvalues and eigenvectors of the covariance matrix, which are invariant in these directions. 4. Select a few of these directions to compare the full representatio