# Graph Learning-Based Ontology Sparse Vector Computing

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## Abstract

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## 1. Introduction of Ontology and Ontology Learning

- Individuals: also called examples;
- Category: abstract representation of concept sets;
- Attribute: the characteristics of the class;
- Constraint: also called restriction;
- Functional terminology: an abstract representation of specific terms in mathematical expressions;
- Rules: statements in the form of antecedent and consequence statements;
- Axiom: a statement that is asserted as a priori knowledge.

- Top ontology: describing concepts and relationships among concepts that are common in all domains;
- Domain ontology: expressing the terminology of a specific domain, and comprehensively describing the characteristics of the domain;
- Task ontology: the set of concepts needed to solve a specific task;
- Application ontology: describing concepts and relationships between concepts that depend on specific fields and tasks.

## 2. Ontology Learning Algorithm

#### 2.1. Ontology Sparse Vector Learning

- The simplest expression,$$\Omega \left(\beta \right)={\parallel \beta \parallel}_{1}.$$
- Mixed norm representation with parameter $c\in [0,1]$,$$\Omega \left(\beta \right)={c\parallel \beta \parallel}_{1}+(1-c){\parallel \beta \parallel}_{2}^{2}.$$
- Fused expression with parameter $c\in [0,1]$,$$\Omega \left(\beta \right)={c\parallel \beta \parallel}_{1}+(1-c){\parallel \mathbf{D}\beta \parallel}_{1},$$$${({\beta}_{1},\cdots ,{\beta}_{p})}^{\mathrm{T}}\to {({\beta}_{2}-{\beta}_{1},\cdots ,{\beta}_{p}-{\beta}_{p-1})}^{\mathrm{T}}$$
- Structure version with parameter $c\in [0,1]$,$$\Omega \left(\beta \right)={c\parallel \beta \parallel}_{1}+(1-c){\beta}^{\mathrm{T}}\Xi \beta ,$$

#### 2.2. Graph Learning-Based Ontology Sparse Vector Learning

## 3. Experiment

#### 3.1. Experiment on Mathematics-Physics Disciplines

- The Langlands program in number theory and algebraic geometry. Main research directions in this branch include: fontaine-Mazur conjecture expressed by geometric p-adic Galois; stable trace formula of sub-symplectic group; cohomology of Shimura cluster; irreducible index problem of the algebraic group on characteristic p; representation of reduced groups and their twisting the relationship of Jacquet modules; BSD conjecture and related problems.
- Analysis, geometry and algebraic methods in differential equations. Main research directions in this branch include: geometric equation singularity problem and manifold classification; Morse theory and index theory and application; high-definition Lagrangian Floer coherence theory; dynamic instability of Hamilton system; ergodic theory of dynamic system; Navier–Stokes equation global well-posedness; the universal supervised conjecture of Einstein equation in general relativity, and related inverse problem mathematical theories and methods.
- Random analysis method and its application. Main research directions in this branch include: stochastic differential equations under nonlinear expectations; stochastic partial differential equations and regular structures; stochastic differential geometry, Dirichlet types and applications; Markov Ergodic theory; fine characterization of discrete Markov processes; random matrix, limit theory deviations, and applications in finance, networking, monitoring, biology, medicine, and image processing.
- Non-linear dynamic theory, methods and experimental techniques of high-dimensional/non-smooth systems. Main research directions in this branch include: dynamic modeling, analysis and control of high-dimensional constrained systems with factors such as nonlinearity, non-smoothness, time delay and uncertainty, and new concepts and theories in interdisciplinary; related large-scale calculation and experimental methods and technical research.
- Deformation and strength theory of solid under abnormal conditions. Main research directions in this branch include: the theory of deformation and strength of solids under abnormal conditions, the constitutive relationship and function of multi-field large deformation of flexible structures-the principle of integrated design of material-structure, the dynamic response of uncertainties of new complex structures and the propagation of elastic waves in solids mechanism; related new experimental methods and instruments, multi-scale algorithms and software.
- The mechanism and method of high-speed flow and control. Main research directions in this branch include: turbulence mechanism and control methods related to high-speed spacecraft and ocean vehicle flow and multiphase complex flow; theory, simulation methods and experimental techniques of rare gas flow and high-speed flow.
- The integrated history of the Milky Way and its evolutionary connection with the large-scale structure of the universe. Main research directions in this branch include: integrated history of the Milky Way; the material distribution of the Milky Way; the detection of dark matter particle properties; the formation of the universe’s large-scale structure; the observation of the accelerated expansion of the universe; the nature of dark energy and the universe’s gravity theory; the relationship between large-scale structures; the formation of massive black holes and their influence on the formation of galaxies.
- The formation and evolution of stars and the source of solar activity. Main research directions in this branch include: interstellar material circulation, molecular cloud formation, properties and evolution; star formation, internal structure and evolution; dense celestial bodies and their high-energy processes; the magnetic field structure of the solar atmosphere; solar generator theory and the law of solar activity cycle evolution.
- Multi-body interactions of spin, orbit, charge, phonon and their macroscopic quantum properties. Main research directions in this branch include: new quantum multibody theory and calculation methods; new high-temperature superconductivity and topological superconducting systems, physical mechanism problems of copper-based, iron-based and heavy fermion superconductors, preparation and mechanism of interface superconducting systems; control mechanism of topological quantum states such as topological insulators, topological magnetic structures in different material systems; principle devices for high-density, low-energy information topological magnetic storage; control of energy valleys and spin states in new low-dimensional semiconductor materials, high mobility Impurity band and multi-band effects.
- Light field regulation and its interaction with matter. Main research directions in this branch include: time-domain, frequency-domain, spatial control of the light field, dynamic behavior of atoms and molecules in ultra-fast, strong fields and hot dense environments; strong laser-driven particle acceleration, radiation source generation and laser fusion physics; nanoscale extremes light focusing, characterization and manipulation; precise description of mesoscopic structured light processes and new mechanisms of interactions between photons, electrons, and phonons in micro-nano structures, photon-optoelectronic device coupling and manipulation, and generation and transmission of plasmons.
- New states of cold atoms and their quantum optics. Main research directions in this branch include: advanced technology of photon–matter interaction and quantum manipulation, construction, control and measurement of novel light quantum states, photodynamics of solid-state system interaction; new principles and methods of precision measurement based on quantum optics; cold atoms high-precision imaging technology and quantum simulation of molecular gas, new principles and methods of molecular gas cooling; new mechanisms for precise manipulation of atomic and molecular internal states, external environment and interactions.
- The physical basis of quantum information technology and new quantum devices. The main research directions in this branch include: scalable solid-state physical system quantum computing and simulation; practical application-oriented quantum communication, quantum network and quantum metrology, and other cutting-edge new technologies of quantum technology; logical interpretation of physics theory, and its related research fields in quantum information.
- Subatomic physics and detection in the post-Higgs era. Main research directions in this branch include: superstring/M-theory, the study of the interaction of the very early universe to explore the unity of interaction; TeV physics, higgs characteristics, supersymmetric particles and other new particles, hadron physics and taste physics, symmetry research and lattice QCD calculation; the phase structure of quantum chromodynamics and the new material properties of quark–gluon plasma; the precise measurement of the reaction of unstable nuclei and key celestial nuclei, the strange structure of nuclei in the drip line region and the isospin correlation decay spectroscopy, and the new mechanism for the synthesis of superheavy nuclei and new technologies.
- Neutrino characteristics, dark matter search and cosmic ray detection. Main research directions in this branch include: neutrino oscillation, neutrino mass, neutrino-free double $\beta $ decay, direct and indirect search for the composition and acceleration mechanism of dark matter, cosmic ray sources; radiation resistance, large area, space, time and high-energy sensitive, high-resolution nuclear and particle detection principles, methods and techniques; ultra-weak signal, ultra-low background detection mechanism and technology.
- Plasma multi-scale effect and high stability operation dynamics control.

#### 3.2. Ontology Mapping on Sponge City Rainwater Treatment System Ontologies

- (1)
- The rainfall is very small. The rainwater well collects all the rainwater. The rainwater quickly infiltrates into the permeable sand layer through the permeable gravel well. The infiltration rainfall is the rainwater well.
- (2)
- The rainfall is large. The rainwater collected by the rainwater well is accumulated in the well, but the water level does not reach the height of the overflow area, and the rainwater will also infiltrate into the permeable sand layer through the permeable gravel well, and the infiltration rainfall is the rainfall collected by the rainwater well.
- (3)
- There is a lot of rainfall. The rainwater collected by the rainwater well is accumulated in the well. The water level exceeds the height of the overflow area. Part of the rainwater is drained through the overflow rainwater pipeline. The rainwater below the overflow area infiltrates into the permeable sand layer through the permeable gravel well. The infiltration rainfall is the rainfall infiltration into the sand layer below the height of the overflow area of the rainwater well. The infiltration rainfall, in this case, is the maximum infiltration rainfall of the new infiltration rainwater well.

## 4. Conclusions and Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Table 1.**The experiment data of ontology similarity measuring on mathematics–physics ontology using big smaple data ${S}_{1}$.

P@1 Average | P@3 Average | P@5 Average | P@10 Average | |
---|---|---|---|---|

Precision Ratio | Precision Ratio | Precision Ratio | Precision Ratio | |

Ontology Algorithm in our paper | 0.3163 | 0.4319 | 0.5694 | 0.8592 |

Algorithm in Gao et al. [11] | 0.2755 | 0.4149 | 0.5204 | 0.8204 |

Algorithm in Zhu et al. [16] | 0.2653 | 0.4048 | 0.4878 | 0.7735 |

Algorithm in Zhu et al. [17] | 0.2959 | 0.4117 | 0.5285 | 0.8347 |

**Table 2.**The experiment data of ontology similarity measuring on mathematics–physics ontology using small smaple data ${S}_{2}$.

P@1 Average | P@3 Average | P@5 Average | P@10 Average | |
---|---|---|---|---|

Precision Ratio | Precision Ratio | Precision Ratio | Precision Ratio | |

Ontology Algorithm in our paper | 0.0306 | 0.0697 | 0.2030 | 0.4337 |

Algorithm in Gao et al. [11] | 0.0204 | 0.0510 | 0.1745 | 0.4020 |

Algorithm in Zhu et al. [16] | 0.0153 | 0.0306 | 0.1612 | 0.3872 |

Algorithm in Zhu et al. [17] | 0.0204 | 0.0663 | 0.1826 | 0.4097 |

**Table 3.**The experiment data of ontology mapping on sponge city rainwater treatment system ontologies using big smaple data ${S}_{3}$.

P@1 Average | P@3 Average | P@5 average | |
---|---|---|---|

Precision Ratio | Precision Ratio | Precision Ratio | |

Ontology Algorithm in our paper | 0.2838 | 0.3828 | 0.5405 |

Algorithm in Gao et al. [11] | 0.2432 | 0.3468 | 0.4703 |

Algorithm in Zhu et al. [16] | 0.2568 | 0.3604 | 0.5081 |

Algorithm in Zhu et al. [17] | 0.2703 | 0.3649 | 0.5135 |

**Table 4.**The experiment data of ontology mapping on sponge city rainwater treatment system ontologies using big smaple data ${S}_{4}$.

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**MDPI and ACS Style**

Wu, J.; Sangaiah, A.K.; Gao, W.
Graph Learning-Based Ontology Sparse Vector Computing. *Symmetry* **2020**, *12*, 1562.
https://doi.org/10.3390/sym12091562

**AMA Style**

Wu J, Sangaiah AK, Gao W.
Graph Learning-Based Ontology Sparse Vector Computing. *Symmetry*. 2020; 12(9):1562.
https://doi.org/10.3390/sym12091562

**Chicago/Turabian Style**

Wu, Jianzhang, Arun Kumar Sangaiah, and Wei Gao.
2020. "Graph Learning-Based Ontology Sparse Vector Computing" *Symmetry* 12, no. 9: 1562.
https://doi.org/10.3390/sym12091562