Mathematical knowledge graph construction method based on big data

Abstract

The invention provides a mathematical knowledge graph construction method based on big data, and the method comprises the following steps: a plurality of data sources obtain data of a mathematical field, and the data is preprocessed through a natural language processing technology; extracting mathematical concepts, theorems, formulas and relationships among the mathematical concepts, the theorems and the formulas from the preprocessed data by using a deep learning model to form mathematical entities and association relationships thereof; constructing a mathematical knowledge graph by adopting a graph structure according to the extracted mathematical concepts and relationships; reasoning the constructed mathematical knowledge graph through a graph neural network, automatically deducing a new knowledge relationship based on the mathematical knowledge graph, and dynamically updating the mathematical knowledge graph based on knowledge extracted from new mathematical literatures and data. According to the method, the mathematical knowledge graph with self-learning and updating capabilities is constructed by collecting and processing large-scale data in combination with a graph structure and an inference technology, so that the efficiency of mathematical knowledge management can be greatly improved.

Description

Technical Field

[0001] The present invention belongs to the field of big data analysis and artificial intelligence technology, and specifically relates to a method for constructing a mathematical knowledge graph based on big data. Background Art

[0002] With the rapid development of the Internet and big data technology, the way of acquiring and expressing knowledge has undergone tremendous changes. As the foundation of science and technology, mathematical knowledge is highly logical and complex. The traditional mathematical knowledge management model cannot effectively handle massive amounts of data and complex relationships. As a semantic network structure, knowledge graphs can represent entities through nodes and the relationships between entities through edges. They have been widely used in various fields. Mathematical knowledge graphs help to systematically manage, retrieve and reason about mathematical knowledge, but existing methods have limitations in dealing with complex relationships between mathematical concepts and large-scale data.

[0003] The present invention proposes a method for constructing a mathematical knowledge graph based on big data, aiming to solve the problems of difficulty in graph construction and poor correlation of mathematical knowledge in the prior art, and to achieve efficient organization and automatic reasoning of mathematical knowledge by utilizing big data technology and intelligent algorithms. Summary of the invention

[0004] The purpose of this invention is to provide a method for constructing a mathematical knowledge graph based on big data, which combines large-scale data analysis technology and knowledge reasoning technology to automatically extract mathematical concepts and their relationships from massive mathematical data, construct an efficient mathematical knowledge graph, and improve the organization and reasoning ability of mathematical knowledge.

[0005] The technical solution of the present invention is as follows:

[0006] A method for constructing a mathematical knowledge graph based on big data includes the following steps:

[0007] Obtain data in the field of mathematics from multiple data sources and pre-process the data using natural language processing technology;

[0008] Use deep learning models to extract mathematical concepts, theorems, formulas and their relationships from preprocessed data to form mathematical entities and their associations;

[0009] Based on the extracted mathematical concepts and relationships, a mathematical knowledge graph is constructed using a graph structure;

[0010] The constructed mathematical knowledge graph is inferred through graph neural networks, new knowledge relationships are automatically derived based on the mathematical knowledge graph, and the mathematical knowledge graph is dynamically updated based on knowledge extracted from new mathematical literature and data.

[0011] Furthermore, specific mathematical keywords, keyword combinations, and contextual semantic matching rules are set to obtain data in the field of mathematics from multiple data sources through distributed crawler technology.

[0012] Furthermore, the data sources include mathematics literature, teaching materials, question banks and network resources.

[0013] Furthermore, the data preprocessing includes data deduplication, noise removal and synonym normalization of mathematical terms.

[0014] Furthermore, the natural language processing technology process is:

[0015] Use lexical analysis to divide mathematical texts into basic lexical units;

[0016] Structural extraction of mathematical concepts and their dependencies through syntactic analysis and dependency syntactic analysis;

[0017] Use statistical or deep learning-based entity recognition algorithms to extract mathematical concepts, theorems, and formula entities from sentences.

[0018] Furthermore, the deep learning model uses a BERT, GPT or LSTM model, which is fine-tuned on a pre-trained mathematical dataset to automatically extract mathematical entities and their relationships from text.

[0019] Furthermore, the mathematical knowledge graph is constructed by using a graph database for storage, the node set in the graph represents the mathematical knowledge unit, and the edge set represents the logical or inference relationship between the mathematical knowledge units.

[0020] Furthermore, the reasoning of the constructed mathematical knowledge graph through the graph neural network specifically includes:

[0021] Perform feature embedding on nodes in the knowledge graph to represent the mathematical properties of each node;

[0022] The adjacent relationship between nodes is used to propagate and update features, and new mathematical relationships are derived recursively;

[0023] The node embedding update formula in the graph neural network is:

[0024]

[0025] Among them, h(v i ) is the embedding representation of the node, N(v i ) is its neighbor node, W (l) is the weight matrix of the l-th layer network, and σ is the activation function.

[0026] Compared with the prior art, the present invention has the following advantages:

[0027] The present invention provides a method for constructing a mathematical knowledge graph based on big data, which converts complex mathematical knowledge into a graph form for structured management through the automatic collection, processing and analysis of large-scale data. Mathematical concepts, theorems, formulas and their relationships are visualized as graph structures, making the hierarchy, relevance and logical deduction path of mathematical knowledge clearer and more intuitive. Compared with the traditional linear knowledge storage method, the knowledge graph can help users quickly locate and understand the upstream and downstream relationships of mathematical knowledge points, greatly improving the efficiency of knowledge management.

[0028] The present invention realizes the automatic knowledge reasoning function based on graph through graph neural network and logical reasoning algorithm. It can deduce hidden knowledge or automatically generate proof paths through the relationship between known mathematical concepts, theorems and formulas.

[0029] The present invention has a dynamic update mechanism, which can obtain the latest mathematical knowledge from sources such as mathematical literature, question banks, and teaching materials regularly or in real time, and automatically incorporate it into the existing knowledge graph. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The accompanying drawings generally illustrate various embodiments by way of example and not limitation, and together with the description and claims, serve to illustrate the embodiments of the invention. Where appropriate, the same reference numerals are used throughout the drawings to refer to the same or similar parts. Such embodiments are illustrative and are not intended to be exhaustive or exclusive embodiments of the present apparatus or method.

[0031] Figure 1 A schematic diagram of the method framework of the present invention is shown;

[0032] Figure 2 A schematic flow chart of a specific method of the present invention is shown. DETAILED DESCRIPTION

[0033] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0034] Example 1: Construction of knowledge graph of mathematics literature database based on big data

[0035] When implementing the present invention, the mathematical literature database is first used as the main data source, and the distributed crawler technology is used to collect data from mathematical literature from different sources. Mathematical literature includes academic journals, papers, monographs, etc. These documents cover a wide range of mathematical knowledge points, including basic mathematics, calculus, algebra, geometry, number theory and other fields. The crawler program will automatically capture content including mathematical formulas, theorems, proof processes, etc. according to preset keywords and regular expressions.

[0036] Step 1: Data collection and preprocessing

[0037] In mathematical literature, mathematical symbols, formulas, and theorems are usually expressed in professional formats, such as LaTeX or MathML. In order to standardize this information, the system needs to preprocess the crawled data. First, the document content will be parsed into plain text and structured data, including word segmentation, named entity recognition (NER), formula extraction, etc. The text is cleaned through the NLP model to remove redundant parts, such as author information, references, etc., and extract the real mathematical entities.

[0038] For example, entities that may appear in the document are:

[0039] Concepts: limit, derivative, function

[0040] Theorems: Fundamental Theorem of Calculus, Lagrange's Mean Value Theorem

[0041] formula:

[0042]

[0043] Through preprocessing, all text data will be converted into a series of mathematical entities and their properties. For example, the function f' x) is marked as "derivative formula" and Lagrange's mean value theorem is marked as "theorem". These processing results will serve as the basis for subsequent relationship extraction.

[0044] Step 2: Mathematical concepts and relation extraction

[0045] Next, we use natural language processing technology based on deep learning to conduct in-depth analysis on the preprocessed data. The model extracts features from mathematical texts using the pre-trained BERT (Bidirectional Encoder Representations from Transformers) model, which can identify the relationship between mathematical entities from complex syntactic structures. For example:

[0046] The relationship between functions and derivatives can be identified through semantic analysis as "the derivative is the rate of change of the function".

[0047] The relationship between Lagrange's mean value theorem and the fundamental theorem of calculus can be inferred from the text "Lagrange's mean value theorem is a special form of the fundamental theorem of calculus."

[0048] In order to better handle the characteristics of mathematical language, the present invention combines rule-based methods, such as qualitative rule analysis in the process of formula derivation, and discovering the dependency relationship between mathematical formulas through logical structure. Specifically, after identifying mathematical entities in the text, the system automatically generates relationship pairs (ei ,r k ,e j ), where e i and e j Represent mathematical concepts or theorems, r k Indicates the logical relationship between two things, such as "derived from", "equivalent to", etc.

[0049] The specific formula for relation extraction is:

[0050] P(r k |e i ,e j )=softmax(W·[h(e i );h(e j )])

[0051] Among them, W is the training parameter, h(e i ) and h(e j ) is the feature representation of the entity, and [·] represents the vector concatenation operation.

[0052] For example, the present invention can automatically identify the following mathematical entity relationships:

[0053] The relationship between the derivative formula and Lagrange's mean value theorem is: the derivative formula can be derived through the mean value theorem.

[0054] The relationship between limits and differentials is that differential operations depend on limit operations.

[0055] Step 3: Construction of Mathematical Knowledge Graph

[0056] After the relationship extraction is completed, the system will store all mathematical entities and their relationships in the graph database. The structure of the knowledge graph is implemented through RDF (Resource Description Framework) or other graph structures to form a complete mathematical knowledge graph G = (V, E), where V represents the node set, including all mathematical concepts, theorems, formulas, etc., and E represents the edge set, representing the relationship between different mathematical knowledge units.

[0057] In this graph, each node represents a specific mathematical concept or formula, for example, "derivative" is node v1, "limit" is node v2, and the edge between them represents "derivative is defined based on limit". This graph structure fully demonstrates the hierarchy and relevance of mathematical knowledge, making it easier for users to search and reason efficiently.

[0058] For example, in the knowledge graph, you can quickly get all theorems, formulas and derivation relationships related to a mathematical concept by querying the upstream and downstream nodes of the concept. When using the graph system, users only need to enter "the fundamental theorem of calculus" to automatically display the related mathematical knowledge network, including the mean value theorem, derivative formula, application of integrals, etc.

[0059] Step 4: Inference and Dynamic Update

[0060] After the mathematical knowledge graph is built, the system also supports reasoning and dynamic updating based on the graph structure. Using the graph neural network (GNN), the system can embed features of nodes in the graph and vectorize the semantic information of each mathematical entity. This representation method can realize automatic reasoning of knowledge through the propagation mechanism between nodes.

[0061] For example, if the relationship between Theorem A and Theorem B is stored in the graph, the system can automatically deduce that Theorem C is the combination of Theorem A and Theorem B through logical reasoning or a propagation model based on a graph network. In addition, the system also supports generating proof steps based on user needs and automatically provides solutions to math problems.

[0062] The specific reasoning process is as follows:

[0063] Assume that there is v in the current graph i and v j The two nodes represent two mathematical theorems. Using the propagation rules of graph neural networks, the feature embedding of new nodes can be derived through the influence of neighboring nodes:

[0064]

[0065] Among them, h(v i ) is the embedding representation of the node, N(v i ) is its neighbor node, W (l) is the weight matrix of the l-th layer network, and σ is the activation function. In this way, the hidden knowledge related to a theorem or concept can be automatically inferred.

[0066] When training a graph neural network, the following loss functions can be used to optimize the embedding of nodes:

[0067]

[0068] Among them, S is the set of positive sample pairs, is a set of negative sample pairs, σ(x) is the Sigmoid function, h i represents the feature embedding of node i, h j Represents the feature embedding of node j

[0069] The present invention also has a dynamic update mechanism, that is, it regularly crawls and analyzes new mathematical literature and databases, and automatically incorporates new mathematical knowledge into the existing knowledge graph. For example, when a new mathematical theorem or formula is published, it will be automatically identified and added to the graph, and the reasoning chain related to the new knowledge will be derived based on the existing mathematical relationship. This dynamic update mechanism ensures the cutting-edge and real-time nature of the mathematical knowledge graph.

[0070] Example 2: Application in the Intelligent Education Platform

[0071] In the intelligent education platform, the mathematical knowledge graph construction method of the present invention also has a wide range of applications. For example, in the study of mathematics courses, students often need to have an in-depth understanding and flexible application of various mathematical concepts, theorems and formulas. Traditional textbook content is often linear, while the knowledge graph provides a multi-dimensional learning path that can help students understand the relationship between knowledge points from different perspectives.

[0072] Step 1: Knowledge point extraction and annotation

[0073] Automatically extract mathematical knowledge points from course handouts, exercise banks and other data on the intelligent education platform, and construct corresponding mathematical knowledge graphs. After preprocessing the handout content, identify knowledge points, such as:

[0074] Function: Description of function definition, properties, extreme values, etc.

[0075] Derivative: definition, physical meaning and law of derivative.

[0076] Limit: Operation rules of limit and common examples.

[0077] These knowledge points will serve as nodes in the graph, and the system can automatically link the knowledge points in each chapter to generate a complete learning path. For example, students can view the derivation process of a theorem through the knowledge graph and understand the source and application scenarios of the formula.

[0078] Step 2: Automatic reasoning and exercise recommendation

[0079] After the knowledge graph is built, the personalized exercise recommendation function can be realized based on the graph. According to the student's learning progress, the questions that match their current knowledge status will be automatically selected from the question bank. For example, when students have mastered the basic knowledge of derivatives, they can automatically infer related high-level questions and give appropriate prompts based on the related knowledge points in the knowledge graph.

[0080] Suppose a student is currently learning the "definition of derivatives", he or she can automatically find topics related to this concept through the knowledge graph, such as "using derivatives to find the extreme points of a function" or "applications of derivatives in physics". This automatic reasoning mechanism can not only improve students' learning efficiency, but also help teachers generate personalized learning paths and recommended resources.

[0081] Step 3: Dynamic updates and student progress tracking

[0082] The knowledge graph system in the intelligent education platform can also be updated dynamically, adjusting the recommended content based on the student's learning performance. The system will record each student's mastery of different knowledge points, update the node weights in the graph, and dynamically adjust the learning path. For example, when a student encounters difficulties with a certain knowledge point many times, the system will automatically recommend related basic knowledge to help students consolidate what they have learned.

[0083] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for constructing a mathematical knowledge graph based on big data, characterized in that: The following steps are involved: Obtain data in the field of mathematics from multiple data sources and pre-process the data using natural language processing technology; Use deep learning models to extract mathematical concepts, theorems, formulas and their relationships from preprocessed data to form mathematical entities and their associations; Based on the extracted mathematical concepts and relationships, a mathematical knowledge graph is constructed using a graph structure; The constructed mathematical knowledge graph is inferred through graph neural networks, new knowledge relationships are automatically derived based on the mathematical knowledge graph, and the mathematical knowledge graph is dynamically updated based on knowledge extracted from new mathematical literature and data.

2. The method for constructing a mathematical knowledge graph based on big data according to claim 1, characterized in that: Set specific mathematical keywords, keyword combinations, and contextual semantic matching rules, and obtain mathematical data from multiple data sources through distributed crawler technology.

3. The method for constructing a mathematical knowledge graph based on big data according to claim 1 or 2, characterized in that: The data sources include mathematics literature, teaching materials, question banks and network resources.

4. The method for constructing a mathematical knowledge graph based on big data according to claim 1, characterized in that: The formula for extracting mathematical concepts, theorems, formulas and their relationships from preprocessed data using a deep learning model is: P(r k |e i ,e j )=softmax(W·[h(e i );h(e j )]) Among them, W is the training parameter, h(e i ) and h(e j ) is the feature representation of the entity, and [·] represents the vector concatenation operation.

5. The method for constructing a mathematical knowledge graph based on big data according to claim 1, characterized in that: The data preprocessing includes data deduplication, noise removal and synonym normalization of mathematical terms.

6. The method for constructing a mathematical knowledge graph based on big data according to claim 1, characterized in that: The natural language processing technology process is: Use lexical analysis to divide mathematical texts into basic lexical units; Structural extraction of mathematical concepts and their dependencies through syntactic analysis and dependency syntactic analysis; Use statistical or deep learning-based entity recognition algorithms to extract mathematical concepts, theorems, and formula entities from sentences.

7. The method for constructing a mathematical knowledge graph based on big data according to claim 1, characterized in that: The deep learning model uses a BERT, GPT or LSTM model, fine-tuned on a pre-trained mathematical dataset, to automatically extract mathematical entities and their relationships from text.

8. The method for constructing a mathematical knowledge graph based on big data according to claim 1, characterized in that: The mathematical knowledge graph is constructed by using a graph database for storage. The node set in the graph represents the mathematical knowledge unit, and the edge set represents the logical or inference relationship between the mathematical knowledge units.

9. The method for constructing a mathematical knowledge graph based on big data according to claim 1, characterized in that: The specific reasoning of the constructed mathematical knowledge graph through the graph neural network includes: Perform feature embedding on nodes in the knowledge graph to represent the mathematical properties of each node; The adjacent relationship between nodes is used to propagate and update features, and new mathematical relationships are derived recursively; The node embedding update formula in the graph neural network is: Among them, h(v i ) is the embedding representation of the node, N(v i ) is its neighbor node, W (l) is the weight matrix of the ,th layer network, and σ is the activation function.

10. The method for constructing a mathematical knowledge graph based on big data according to claim 1, characterized in that: When training a graph neural network, the following loss functions can be used to optimize the embedding of nodes: Among them, S is the set of positive sample pairs, is a set of negative sample pairs, σ(x) is the Sigmoid function, h i represents the feature embedding of node i, h j represents the feature embedding of node j.

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