Total variation and euler elastic rod-based supervised mode identification method

A technology of pattern recognition and total variation, applied in the field of pattern recognition, which can solve the problems of inconsistent actual distribution, difficulty in effectively estimating the probability density function of data, and penalizing the gap width of the interface.

Inactive Publication Date: 2012-09-12
PEKING UNIV
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  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0006] Some existing methods, such as SVM, use the hinge loss function, and the regular term punishes the gap width of the interface, but it is still based on statistical learning theory
Although commonly used statistical methods such as Bayesian inference have achieved fruitful results, they have gradu

Method used

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  • Total variation and euler elastic rod-based supervised mode identification method
  • Total variation and euler elastic rod-based supervised mode identification method
  • Total variation and euler elastic rod-based supervised mode identification method

Examples

Experimental program
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Effect test

Embodiment 1

[0030] Example 1: USPS handwritten digit recognition

[0031] The USPS (U.S.Postal Service) dataset uses handwritten digital pictures scanned on US postal envelopes. Each picture is a 16*16 grayscale picture, containing a number, such as figure 2 (a) shows part of its data display, from 0 to 9, a total of 10 categories. In this embodiment, 1000 samples were randomly selected for experiments. Since the original data had a high dimension, principal component analysis (PCA) was used to reduce it to 30 dimensions and normalize it to the [0, 1] interval.

[0032] Step 1: Construct the energy functional under the regularization framework

[0033] (a) Total variation energy functional

[0034] Mathematically, the Total Variation of the function f(x) has the form in the one-dimensional case and when the function is continuous: Represents the total variation of f(x), a and b are the endpoints of the interval, and f'(x) is the derivative of the function. It can be seen that tota...

Embodiment 2

[0089] Embodiment 2: Applied to some other common classification data

[0090] This embodiment is based on the data sets of 8 classifications in the libsvm website and the UCI machine learning library, including two types and multiple types of data. For all data sets are normalized to the interval [0, 1], the operation steps are the same as those in the first embodiment. For all methods, five-fold cross-validation is still used to select the optimal parameters. The comparison of the optimal accuracy of each method is shown in Table 3:

[0091] Table 3 Comparison of classification accuracy of each method (%)

[0092]

[0093] As can be seen from Table 3, the IagLE solution of the TV and EE pattern recognition methods proposed by the present invention is generally better than that of GD, and the effect of EE is slightly better than that of TV, and they are all more accurate than BPNN on all data sets to be tall. The EE method surpassed the SVM on six data sets under the Ia...

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Abstract

Disclosed in the invention is a total variation and euler elastic rod-based supervised mode identification method, comprising: constructing a total variation and Euler elastic rod-based energy function under the framework of least square regularization; utilizing a variational method to convert solution of energy function minimization into solution of a corresponding Euler-Lagrange differential equation; solving the differential equation to further obtain a final classifier; and carrying out mode identification on data by utilizing the classifier. According to the invention, a novel method is provided for solution of a supervised mode identification problem and in general, can be applied to solution of a classification problem like handwriting digit identification; and the provided method enables an effect that is comparable with one caused by an existing popular method to be realized for most of data sets.

Description

technical field [0001] The invention belongs to the technical field of pattern recognition, and in particular relates to applying a model based on total variation and Euler elastic bars in image processing to an energy-minimized least squares regularization (RLS) framework for supervised pattern recognition. Background technique [0002] Supervised learning technology is a hot issue in the field of pattern recognition, and has a wide range of applications in many fields such as computer vision. The essence of pattern recognition research is classification technology. In the absence of ambiguity, the term classification is used to refer to pattern recognition in this specification. Supervised classification refers to using a labeled training sample set to train a rule (classifier) ​​to predict new samples, and its general form is described as: [0003] Given a training set {(x 1 ,y 1 ),...(x n ,y n )}, where x i ∈R d , R d is a d-dimensional real vector space, for the...

Claims

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Application Information

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IPC IPC(8): G06K9/62
Inventor 林通薛涵凛查红彬
Owner PEKING UNIV
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