Clustering method based on manifold learning and rank constraint
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A clustering method and manifold learning technology, applied in the field of pattern recognition, which can solve the problems of weak robustness and low clustering accuracy.
Pending Publication Date: 2021-03-09
GUANGDONG UNIV OF TECH
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[0004] The present invention provides a clustering method based on manifold learning and rank constraints in order to overcome the disadvantages of low clustering accuracy and weak robustness in clustering segmentation using the least squares regression method described in the prior art
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Embodiment 1
[0086] This embodiment proposes a clustering method based on manifold learning and rank constraints, such as figure 1 Shown is a flow chart of the clustering method based on manifold learning and rank constraints in this embodiment.
[0087] In the clustering method based on manifold learning and rank constraints proposed in this embodiment, it specifically includes the following steps:
[0088] S1: Obtain the original data and preprocess it, and construct the feature matrix X of the original data.
[0089] In this step, the step of preprocessing the original data includes performing noise removal and data cleaning on the original data.
[0090] Further, the steps of constructing the characteristic matrix X of the original data are as follows:
[0091] S1.1: Preprocess the original data, extract features to obtain n feature points and form the initial feature matrix S=[s 1 ,s 2 ,...,s n ]∈R m×n , m represents the dimension;
[0092] S1.2: Normalize the feature points in...
Embodiment 2
[0163] In this embodiment, the clustering method based on manifold learning and rank constraints proposed in Embodiment 1 is used to conduct simulation experiments.
[0164] The HW data set used in this example is used as the original data, where the HW data set is a large sample data set, which contains features of 10 handwritten digits from '0' to '9' extracted from the collection of Dutch utility diagrams , each number has 200 samples. Such as figure 2 Shown is an example diagram of the HW database. In this embodiment, 240 pixel average values (mfeat-PIX) in a 240-dimensional 2×3 window are selected and extracted from the HW data set as data samples to obtain sampling samples of the original image.
[0165] For the sampling samples of the above original images, SPC (spectral clustering, spectral clustering algorithm), LSR (Least Squares Regression, least squares method of linear regression), LRR (Low-Rank Representation, low-rank representation), CLR (Constrained Lapla...
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Abstract
In order to overcome the defects of low clustering precision and weak robustness in clustering segmentation by adopting a least square regression method, the invention provides a manifold learning andrank constraint-based clustering method, which comprises the following steps of: obtaining original data, preprocessing the original data, and constructing a feature matrix X of the original data; based on a k-nearest neighbor method, calculating similarity among elements in the feature matrix X by adopting a similarity measurement function to obtain a weight matrix W corresponding to the featurematrix X; taking the weight matrix W as an initial matrix of a low-rank representation matrix Z, solving the low-rank representation matrix Z through a least square regression method, and applying manifold constraint and rank constraint to the low-rank representation matrix Z to obtain a final target function; and converting the final objective function from a constrained problem to an unconstrained problem by adopting a Lagrange multiplier method, alternately iteratively optimizing variables in the final objective function until convergence to obtain an optimal low-rank representation matrixZ ', and then obtaining a clustering result by adopting a spectral clustering graph cutting method for the optimal low-rank representation matrix Z'.
Description
technical field [0001] The present invention relates to the technical field of pattern recognition, more specifically, to a clustering method based on manifold learning and rank constraints. Background technique [0002] The purpose of clustering is to segment data without any label information into its corresponding natural groups. There are many current clustering algorithms, such as hierarchical clustering, density clustering, K-means clustering, etc. Among them, the spectral clustering algorithm is a clustering method based on graph theory. The eigenvectors of the Adams matrix are analyzed to complete the clustering. Compared with the traditional clustering algorithm, it has the characteristics of being able to cluster on the sample space of any shape and converge to the global optimum, so it is widely used. The clustering-based spectral clustering method is usually divided into two steps: first, calculate an affinity matrix W for the input feature points to measure th...
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