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Principal component analysis method of two-dimensional probability

A principal component analysis, probabilistic technology, applied in instruments, character and pattern recognition, computer parts, etc., can solve problems such as noise irregularity, deviation from the principal component of data, etc.

Inactive Publication Date: 2015-06-10
BEIJING UNIV OF TECH
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Problems solved by technology

However, the noise that exists in reality is often irregular, especially when there are outliers in the data set, the main direction found by PCA based on Gaussian error will be biased towards the outliers, thus deviating from the real principal components of the data

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  • Principal component analysis method of two-dimensional probability
  • Principal component analysis method of two-dimensional probability
  • Principal component analysis method of two-dimensional probability

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[0012] This two-dimensional probabilistic principal component analysis method uses the error measurement method of L1-norm and reduces the dimension on two-dimensional data based on the probability PCA model. In this model, the error obeys the Laplace distribution. During the solution process, by introducing The new hidden variable replaces the Laplace distribution with the sum of infinite Gaussian distributions. The hidden variable is used as a tool to detect outliers, and then the dimensionality reduction matrix in the row and column directions is obtained.

[0013] The present invention is based on the L1-norm probabilistic PCA model for dimensionality reduction of two-dimensional data, and the error obeys the Laplace distribution, so it can not only utilize the spatial structure of the two-dimensional data, but also be robust to outliers.

[0014] Preferably, the method comprises the steps of:

[0015] (1) Establish the second-order PCA of probability according to formula ...

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Abstract

The invention discloses a principal component analysis method of two-dimensional probability; not only the space structure of two-dimensional data can be utilized, but off-group points are robust. In the principal component analysis method of the two-dimensional probability, an L1-norm error measurement mode is utilized to reduce the dimensions of the two-dimensional data based on a probability PCA (Principal Component Analysis) model; in the model, errors comply with Laplace distribution; in the solving process, the Laplace distribution is replaced to be a form of infinite Gauss distributions by adding new hidden variables; the hidden variables are used as a tool for detecting off-group points, and further, dimension-reducing matrixes in the line and row directions are obtained.

Description

technical field [0001] The invention belongs to the technical field of feature extraction and data dimensionality reduction, and in particular relates to a two-dimensional probability principal component analysis method. Background technique [0002] High-dimensional and multimodal data are ubiquitous in modern computer vision research. The high dimensionality of the data not only increases the complexity of the algorithm and storage overhead, but also reduces the generality of the algorithm in practical applications. However, high-dimensional data are often uniformly distributed over a low-dimensional or popular space. Therefore, finding a mapping relationship between high-dimensional observation data and low-dimensional space has become a challenging problem in machine learning research. In the past few decades, algorithms for data dimensionality reduction have made great progress. [0003] Principal Component Analysis (PCA) is a dimensionality reduction method widely u...

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Application Information

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IPC IPC(8): G06K9/62
Inventor 孙艳丰句福娇胡永利尹宝才
Owner BEIJING UNIV OF TECH
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