引子

复杂网络    关系图   路径数    路径长度《阶数（节点数）》    关联度    关系     运算   

The concept of big data-driven and holistic mining of regularities for intelligent smartization is complex and multidimensional, encompassing the application of big data technology, the implementation of data mining techniques, and the enhancement of intelligent smartization levels. Big data provides a rich data foundation for decision-making, making the decision-making process more data-driven and scientific. By collecting, storing, processing, and analyzing vast amounts of data, it can reveal patterns and trends hidden behind the data, providing strong support for decision-making. Data mining is the process of extracting useful information from large amounts of data, including steps such as data cleaning, data transformation, data reduction, data mining implementation, and results analysis and presentation. Through the application of statistical methods, case-based reasoning, decision trees, rule-based reasoning, fuzzy sets, and other algorithms, hidden patterns, regularities, and knowledge can be mined from the data. Holistic mining not only focuses on the surface information of data but also delves into the inherent regularities and correlations within the data. It combines the scale and complexity of big data, utilizing advanced data mining techniques to achieve comprehensive, in-depth, and refined analysis of data. Building a stable and reliable big data infrastructure is the foundation for elevating the level of intelligent smartization. This includes the construction of high-speed networks, cloud computing platforms, data centers, and other facilities, providing basic support for the storage, transmission, and computation of big data. In the era of big data, data quality and data security are critical factors affecting the value and application of data. Enhancing data quality and strengthening data security protection can ensure the accuracy, integrity, and safety of data, providing reliable data support for intelligent smartization applications.Holographic observation technology is an observation method based on a holographic perspective (multi-dimensional, multi-temporal and spatial, full-factor, and full-process, etc.), featuring the characteristics of information integrity and extensive applicability.

Human-computer integration aims to achieve improved efficiency and quality in work by integrating the flexibility and creativity of the human brain with the high-speed computing, precise control, and other capabilities of computers. With the continuous development of computer technology, human-computer integration has evolved from being a simple auxiliary tool to a core force that profoundly impacts human life and work. As artificial intelligence technology continues to progress, human-computer integration will become more intelligent, allowing machines to better understand human needs and provide more personalized services.

PS:

Complex Network refers to a network that possesses some or all of the properties of self-organization, self-similarity, attractors, small-world, and scale-free characteristics. It is a network that exhibits high complexity, featuring the following attributes. Structural complexity: There is a significant number of nodes, and the network structure exhibits various distinct characteristics. Network evolution: Nodes or connections may emerge or disappear, for instance, web pages or links in a worldwide network may appear or disconnect at any time. Connectivity diversity: The connection weights between nodes differ, and directionality may exist. Dynamical complexity: Node sets may belong to non-linear dynamical systems, with the node states undergoing complex changes over time. Node diversity: Nodes in complex networks can represent anything, such as individuals in a complex network formed by human relationships, or different web pages in a complex network composed of the World Wide Web. Integration of multiple complexities: The above-mentioned multiple complexities interact, leading to more unpredictable outcomes.

Complex networks can be classified based on different criteria, such as regular networks, random networks, and network types that fall between the two. When the number of node types or edge types exceeds a certain threshold, it is called a heterogeneous network; otherwise, it is a homogeneous network. There are also sparse networks and dense networks, where the nodes in dense networks are a fractional multiple of the edges.

Generally, complex networks possess the following properties:

Small-world: Despite the large scale of the network, there is a relatively short path between any two nodes. Clustering coefficient: There are always some clustered small networks in the network, such as circles of acquaintances or friends in social networks. Power-law degree distribution: The connection distribution between nodes exhibits a power-law characteristic.

Complex networks have widespread applications in many fields, such as:

Social network analysis: Helps understand the connections between people and predict their behaviors. Financial networks: Analyze market risks, predict financial crises, and have great potential for risk assessment, financial regulation, and investment decision-making. Ecological networks: Understand the evolutionary laws of ecosystems, predict the dynamic changes of biological populations, and study biological migration paths.

Although complex networks provide new solutions, they also face many challenges, such as the dynamics and complexity of networks, ensuring the robustness and reliability of networks, and the challenges of data mining and analysis brought by large amounts of data. The research methods of complex networks include various algorithms and models, such as the self-contained GN algorithm, fast splitting algorithm, dissimilarity-based algorithm, extreme value optimization algorithm, Newman's fast algorithm, and the heap-structured greedy algorithm (CNM algorithm). These algorithms and models provide powerful tools for the analysis and research of complex networks. In summary, complex networks are a broad and in-depth field, covering knowledge from network science, graph theory, statistics, and other disciplines. With the development of technology and further research, complex networks will demonstrate their unique value and application potential in more areas.

The Relationship Diagram is a graphical tool used to represent the relationships between different entities (or referred to as nodes). It is commonly used to display the associations, dependencies, interactions, or connections between data. In a relationship diagram, nodes typically represent entities such as people, organizations, concepts, data items, and so on. The lines (or edges) connecting the nodes represent the relationships between these entities, which can be unidirectional or bidirectional. The relationship diagram is an intuitive and powerful tool that helps people better understand and analyze the relationships and interactions within complex systems. Through a relationship diagram, we can quickly identify the root causes of problems, assess potential impacts, plan action schemes, and make adjustments and optimizations when necessary.

The number of paths refers to the total possible paths from one node to another node. The number of paths can be calculated using the combination formula C(m+n,m) in combinatorial mathematics, where m and n represent the number of steps to the right and upward respectively. Path length refers to the number of edges (or steps) passed through from one node to another node. Path length is often used to measure the distance or cost from one node to another. In mathematics and computer science, the order usually refers to the number of nodes in a graph or the number of rows/columns in a matrix. It determines the scale and complexity of the graph, as well as the time and space complexity of executing algorithms on it. Degree of correlation is a measure of the correlation between two objects, referring to the degree of similarity between two functions in mathematics. It is usually obtained by calculating the average of correlation coefficients, where the correlation coefficient measures the relationship between the minimum and maximum absolute differences of the time series of the parent factor and the child factor at each moment. Degree of correlation has wide applications in fields such as grey system analysis, data mining, and prediction, used to evaluate the correlation between different factors.

Relations usually refer to binary relations, which are one of the fundamental concepts in mathematics. Based on sets, relations define an important concept that primarily reflects the connections and properties between elements. In computer science, the concept of relations also holds significant importance, often appearing in descriptions of finite automata and formal languages, compiler programming, information retrieval, data structures, as well as algorithm analysis and programming design. Relations and relational operations are basic concepts and tools in mathematics and computer science, playing a crucial role in data processing and analysis.

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