System and method of pattern recognition in very high-dimensional space

2006 ◽  
Vol 120 (2) ◽  
pp. 582
Author(s):  
Bishnu Saroop Atal
Keyword(s):  
Pattern Recognition ◽  
Dimensional Space ◽  
High Dimensional ◽  
High Dimensional Space ◽  
Very High

A Text Classification Algorithm Based on Improved Multidimensional–Multiresolution Topological Pattern Recognition

2019 ◽  
Vol 33 (10) ◽  
pp. 1950016 ◽  
Author(s):  
Zhichao Li ◽  
Jilin Huang
Keyword(s):  
Pattern Recognition ◽  
Text Classification ◽  
Dimensional Space ◽  
Set Cover ◽  
High Dimensional ◽  
High Dimensional Space ◽  
Sample Number ◽  
Training Time ◽  
Topological Pattern ◽  
Traditional Pattern

Traditional pattern recognition is based on “optimal partition” and the goal is to find an optimal classification interface based on the distribution of each category in high-dimensional space, thus has its inherent shortcomings and deficiencies. While topology pattern recognition can effectively compensate for the shortcomings of traditional pattern recognition, topological pattern recognition is based on “cognition” and the goal is to find the appropriate cover according to the “complex set cover” in high-dimensional space to achieve cognitive effect. Topological pattern recognition can effectively consummate the characteristics of high error rate, low recognition rate and repetitive training in the existing recognition system with low training sample number. At present, topology pattern recognition has been applied in many areas of social life. However, one problem that can’t be ignored is that topological pattern recognition requires a long training time and low fault tolerance rate. Therefore, this paper proposes an improved multidimensional–multiresolution topological pattern recognition, and applies it to text classification and recognition. The results show that the improved multidimensional–multiresolution topological pattern recognition method can effectively reduce the training time of text classification and improve the classification efficiency.

scholarly journals New Lattice Packings of Spheres

1983 ◽  
Vol 35 (1) ◽  
pp. 117-130 ◽  
Author(s):  
E. S. Barnes ◽  
N. J. A. Sloane
Keyword(s):  
Complex Space ◽  
Dimensional Space ◽  
Infinite Family ◽  
High Dimensional ◽  
High Dimensional Space ◽  
Image Position ◽  
Very High ◽  
Lattice Packings

1. Introduction. In this paper we give several general constructions for lattice packings of spheres in real n-dimensional space Rn and complex space Cn. These lead to denser lattice packings than any previously known in R36, R64, R80, …, R128, …. A sequence of lattices is constructed in Rn for n = 24m ≦ 98328 (where m is an integer) for which the density Δ satisfies log2 Δ ≈ – (1.25 …)n, and another sequence in Rn for n = 2m (m any integer) withThe latter appear to be the densest lattices known in very high dimensional space. (See, however, the Remark at the end of this paper.) In dimensions around 216 the best lattices found are about 2131000 times as dense as any previously known.Minkowski proved in 1905 (see [20] and Eq. (23) below) that lattices exist with log2 Δ > –n as n → ∞, but no infinite family of lattices with this density has yet been constructed.

Neural networks trained with high-dimensional functions approximation data in high-dimensional space

2021 ◽  
pp. 1-12
Author(s):  
Jian Zheng ◽  
Jianfeng Wang ◽  
Yanping Chen ◽  
Shuping Chen ◽  
Jingjin Chen ◽  
...  
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
Data Distribution ◽  
High Dimensional ◽  
Sufficient Information ◽  
Sufficient Data ◽  
High Dimensional Space ◽  
Positive Effects ◽  
The Neural Networks ◽  
Using Data

Neural networks can approximate data because of owning many compact non-linear layers. In high-dimensional space, due to the curse of dimensionality, data distribution becomes sparse, causing that it is difficulty to provide sufficient information. Hence, the task becomes even harder if neural networks approximate data in high-dimensional space. To address this issue, according to the Lipschitz condition, the two deviations, i.e., the deviation of the neural networks trained using high-dimensional functions, and the deviation of high-dimensional functions approximation data, are derived. This purpose of doing this is to improve the ability of approximation high-dimensional space using neural networks. Experimental results show that the neural networks trained using high-dimensional functions outperforms that of using data in the capability of approximation data in high-dimensional space. We find that the neural networks trained using high-dimensional functions more suitable for high-dimensional space than that of using data, so that there is no need to retain sufficient data for neural networks training. Our findings suggests that in high-dimensional space, by tuning hidden layers of neural networks, this is hard to have substantial positive effects on improving precision of approximation data.

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