Application and prospect of manifold learning

typical applications for first-class learning 1 Visualization

People cannot intuitively perceive the internal structure of a high-dimensional data set, but have a strong sense of the inherent law of the data set below three-dimensional. Manifold learning can show the intrinsic relationship of high-dimensional data in less than three-dimensional space, so that people can intuitively understand the inherent law of high-dimensional data, and understand the changes of the main factors affecting the internal structure of the data set.

2 reasoning and semi-supervised learning

Since the manifold expresses the common state of a thing in different states, while the motion of the manifold expresses the change of the state of things, then we can use the Flow shape learning algorithm to learn the state parameter of the data which is unknown in the state parameter by using some data known state parameters of the manifold (essentially its coordinates in the hidden space). This inference mechanism of manifold learning is necessary for semi-supervised learning, and the application of manifold learning in reasoning and semi-supervised learning is estimated by the rotation degree of the hand rotor [1], the location of the target in the video image [2], the semi-supervised text classification [3], and so on.

3 Feature Extraction

The characteristics of the manifold learning method are often advantageous to the subsequent clustering or classification tasks, because the same thing but different kinds of samples may be located in different regions of the manifold that characterize the thing. Manifold learning method can effectively approximate the flow shape of the object, so that the difference of different regions in the manifold is embodied in the characteristic space.

4 Classification

Manifold learning is also applied in the problem of classification and Supervision feature extraction. In the classification problem, if each class of samples can be well described by a manifold, then we only need to learn a manifold for each type of sample, in the classification, the sample to the distance of each manifold, classify it into the class with its nearest manifold.

5 Data Description

For the data Description task, an important application of manifold learning is in the field of image processing. The contour and skeleton of the object in the image can be regarded as one-dimensional manifold embedded in the two-dimensional plane or composed of a set of one-dimensional manifolds. Manifold Learning has a powerful manifold approximation capability, which has been successfully applied in the contour description and skeleton extraction of image processing.

Two research prospects

(1) parameter selection problem of manifold learning method

At present, most of the manifold learning algorithms are related to the selection of parameters such as the nearest neighbor number and Eigen dimension. Manifold learning to detect the success of a low-dimensional manifold structure depends largely on the selection of the nearest neighbor number, however, the selection of the nearest neighbor number is influenced by the distribution density and spatial structure of the data, so far it lacks a good theoretical guidance, which is often only chosen through experience. The Eigen dimension estimation is a basic problem of manifold learning, which reflects the topological properties of latent low-dimensional manifolds hidden in high-dimensional observational data, and the accuracy of intrinsic dimension estimation has an important influence on the embedding results of low-dimensional space. (2) performance evaluation of manifold learning algorithms

For a given high-dimensional data set, embedding it into low-dimensional space after using the manifold learning algorithm, the low-dimensional embedding quality of high-dimensional nonlinear data, that is, the degree of low-dimensional embedding reveals the inherent law and topological structure of the high-dimensional nonlinear data sets. This actually involves the performance evaluation of the results of a manifold learning algorithm mapping. At present, it is commonly used to map data sets to two-dimensional or three-dimensional visualization space, and to evaluate the embedding performance of different manifold learning algorithms by visual inspection.

(3) robustness and convergence of manifold learning algorithms

At present, the manifold learning method based on spectral graph theory is sensitive to noise and outliers, and is also the cause of the significant deviation of manifold learning methods, so it is a meaningful task to study the influence mode and influence degree of the convective shape learning method of various noise models.

The current manifold learning method relies on the data itself to be studied, and its effectiveness is related to the algorithm itself, however, to make a learning algorithm complete, it is necessary to consider whether the geometric structure described by the algorithm can approximate the real internal geometric structure. Therefore, it is a very important step to perfect the study of manifold learning to construct a data-independent manifold learning and derive the convergence of manifold learning to the real embedded manifold approximation. (4) Multi-sub-manifold learning problems

At present, most manifold learning algorithms assume that high-dimensional input data is in a connected manifold, but many high-dimensional nonlinear datasets in reality contain multiple sub-manifolds, such as different face data and protein interaction data, etc. The existing manifold learning methods cannot map all the sub-manifolds contained in a dataset to the same low-dimensional space and maintain their own manifold structure, which is a problem to be solved when applying manifold learning to the tasks of pattern recognition and image processing, so it is necessary to study the dimensionality reduction of high dimensional data on the non-connected manifold. (5) research on the application of manifold learning

At present, the application object of manifold learning is mainly limited moment static image data, such as human face, handwritten data, palmprint data and so on. Usually data flow is a series of real-time, continuous, ordered data composition, it is widely used in real-world and engineering experiments, such as network monitoring and communication engineering, Web services generated by logging, sensor monitoring, video streaming monitoring, stock exchange volatility analysis in financial markets, weather or environmental monitoring can generate a lot of data flow. How to apply manifold learning methods to various data streams is still worth further research.

Reference Documents:

[1] Zhang Junping, Wang Jue. Manifold Learning and application [D][d]. , 2003.

[2] Yang X, Fu H, Zha H, et al. semi-supervised nonlinear dimensionality reduction[c]//proceedings of the 23rd Internation Al Conference on machine learning. ACM, 2006:1065-1072.

[3] Belkin M, Niyogi p. Using manifold stucture for partially labeled classification[c]//advances in neural information p Rocessing systems. 2002:929-936.

[4] Huang Qihong. Theoretical study of manifold learning methods and its application in images [J]. Degree thesis. Chengdu: Shanghai, 2007.

[5] Huanghong. A study on the theory and application of the image embedding framework in the form of indecent learning [D]. Chongqing: Chongqing University, 2008.

[6] Reico. A study on manifold learning algorithm and its application [D]. China University of Science and Technology, 2011.

[7] Zhang XINGFO. Research on local dimensionality reduction algorithm based on manifold learning [D]. Harbin Engineering University, 2012