DE202022106616U1 - A system for representing and classifying formulas for searching mathematical information - Google Patents

Abstract

A system for representing and ranking formulas for searching mathematical information, the system comprising:an input unit for receiving scientific document data and a user query;a document preprocessing unit for removing noise and extracting formulas from the scientific document data;a formula embedding processor having a Formula embedding unit for generating a binary vector using bit position information and an embedded formula indexer for generating an embedded formula index for the generated binary vectors;a formula generalization processor with a formula generalization unit for extracting all entities present in the formula, thereby converting them into a generalized vector, and a generalized formula indexer for generating a generalized formula index;a query embedding unit for extracting a set of entities from the user query and using bit position information for generating a query vector;a query generalization unit for converting the user query into a generalized query vector; anda search and ranking unit for receiving a generalized query vector of keywords, thereby generating a set of similarity and dissimilarity factors that help to retrieve the exact match formula, the subformula and the parent formula and to match each input keyword with each indexed context, whereby calculating the number of similar tokens between the query and the indexed context.

Description

FIELD OF THE INVENTION

The present disclosure relates to a system for representing and ranking formulas for searching mathematical information.

BACKGROUND OF THE INVENTION

Natural language processing (NLP) is an area of artificial intelligence (AI) concerned with the processing and analysis of human language. It automates the process of information extraction, management, translation, synthesis and generation. The Internet is considered to be a universal repository of knowledge, providing free or low-cost access to various information. However, the world of information is growing and finding the information you need quickly becomes an extremely complex task. The process of searching for information varies depending on the subject of the search. The search for text information differs quantitatively and qualitatively from the search for images, videos and mathematical notations. In general, Information Retrieval (IR) is an application of NLP that aims to have the generic IR system take the user's query as input, estimate similarity, and provide the rank of relevant search results. The majority of data available on the web is sequential text data, images and video. However, user requirements may change. Sometimes users are looking for images/videos based on a text-based query, or they are looking for text information using an image-based query, or videos based on an audio-based query.

The formulas are often more important than the text in conveying the idea of a scientific document. The Digital Mathematical Libraries (DMLs) required a system that would recognize and retrieve formulas in scientific documents. Traditional IR systems treat the formulas as text, but are unable to capture the structural and semantic meaning of the formulas. To fill this gap, the Mathematical Information Retrieval (MIR) system has come into the limelight and caught the attention of researchers. The main task of a MIR system is to find the scientific document/formula/source file that contains the queried formula or relevant information related to the user query. In MIR, users can express their information needs in the form of natural language text or mathematical formulas or a combination of both (text + formulas). In MIR, the meaning of the term "relevant" is a subjective matter and is defined in two ways: the first finds the structural similarities between the user query and the report information, the second finds the semantic similarities between the user query and the report information. These relevance criteria consider not only the exact match with the user's query, but also the information that partially matches the user's query.

The existing information retrieval and MIR system have some challenges including the mathematical formulas are recursive in structure while the textual information is linear in structure and the conventional search engines have no availability of math editor to query the formula-based.

In view of the preceding discussion, it is clear that a formula representation and ranking system is required for mathematical information retrieval.

SUMMARY OF THE INVENTION

The present disclosure aims to provide a system for representing and ranking formulas for searching mathematical information.

In one embodiment, a formula rendering and ranking system for mathematical information retrieval is disclosed. The system includes an input unit for receiving scientific document data and a user query. The system further includes a document pre-processing unit for removing noise and extracting formulas from the scientific document data. The system further includes a formula embedding processor having a formula embedding unit for generating a binary vector using bit position information and an embedded formula indexer for generating an embedded formula index for the generated binaries ren vectors. The system further includes a formula generalization processor having a formula generalization unit for extracting all entities present in the formula, thereby converting them into a generalized vector, and a generalized formula indexer for generating a generalized formula index. The system also includes a query embedding unit for extracting a set of entities from the user query and using bit position information to generate a query vector. The system also includes a query generalization unit for converting the user query into a generalized query vector. The system also includes a search and shunting unit for receiving the generalized query vector with its keywords, generating a set of similarity and dissimilarity factors that help retrieve the exact match formula, subformula, parent formula, and each entered keyword with each match the indexed context, which calculates the number of similar tokens between the query and the indexed context.

In another embodiment, the generalized formula index consists of four attributes selected from a set of vectors in generalized form, the context of a formula, the document ID from which the formula was extracted, and the formula in Presentation MathML format.

In another embodiment, the user query is a combination of mathematical formulas and textual keywords, the query set includes simple and complex queries that allow for efficient evaluation, each query having a unique ID that is used to identify the obtained result of a query with compared to the graded results stored in the gold record.

In another embodiment, the indexed formula similarity factor indicates how much the indexed formula is similar to the user query, while the indexed formula dissimilarity factor indicates how much the indexed formula differs from the user query.

In another embodiment, the user query is converted into a vector of 0s and 1s by the query embedding unit and the query generalization unit.

In another embodiment, the formula embedder is configured to retrieve the syntactically similar formula while formula generalization is used to retrieve the semantically similar formula in relation to the query entered by the user.

In another embodiment, the bit positions ranging from 0-25 and the lexical units at bit positions 150-201 are set to zero for the generalized vector form, and the formula generalization processor is configured to represent the semantically similar formula in a unified form.

In another embodiment, the query vector searches all formula vectors present in the index for the formula relevance score and the context relevance score.

An object of the present disclosure is to provide a formula representation and ranking system for searching mathematical information.

Another goal of the present disclosure is to find syntactically and semantically similar formulas, sub-formulae and super-formulae.

Another object of the present invention is to provide a fast and inexpensive approach to embedding and generalizing formulas using bit position information to improve the performance of MIR systems.

In order to further clarify the advantages and features of the present disclosure, a more detailed description of the invention is provided by reference to specific embodiments that are illustrated in the accompanying figures. It is understood that these figures represent only typical embodiments of the invention and therefore should not be considered as limiting the scope of the invention. The invention will be described and illustrated with additional specificity and detail with the accompanying figures.

character list

• 1 ein Blockdiagramm eines Systems zur Darstellung von Formeln und zur Einstufung für die Suche nach mathematischen Informationen gemäß einer Ausführungsform der vorliegenden Offenbarung zeigt;
• 2 eine Systemarchitektur des vorgeschlagenen Ansatzes in Übereinstimmung mit einer Ausführungsform der vorliegenden Offenbarung zeigt;
• 3 einen Vektor-Generierungsprozess Einbettung und Verallgemeinerung Modul mit Formel in Übereinstimmung mit einer Ausführungsform der vorliegenden Offenbarung veranschaulicht;
• 4 die Struktur eines eingebetteten Formelindexes gemäß einer Ausführungsform der vorliegenden Offenbarung zeigt;
• 5 veranschaulicht, dass Tabelle 1 Bitpositionsinformationen in Übereinstimmung mit einer Ausführungsform der vorliegenden Offenbarung darstellt;
• 6 veranschaulicht Tabelle 2, die die Werte der Bewertungsparameter für 40 Datenbankformel-Browsing-Aufgabenabfragen gemäß einer Ausführungsform der vorliegenden Offenbarung zeigt; und
• 7 zeigt Tabelle 3 mit den Werten der Bewertungsparameter für 30 Datenbank-Hauptaufgabenabfragen gemäß einer Ausführungsform der vorliegenden Offenbarung.

These and other features, aspects, and advantages of the present disclosure will be better understood when the following detailed description is read with reference to the accompanying figures, in which like characters represent like parts throughout the figures, wherein:

• 1 Figure 12 shows a block diagram of a formula representation and ranking system for searching mathematical information according to an embodiment of the present disclosure;
• 2 shows a system architecture of the proposed approach in accordance with an embodiment of the present disclosure;
• 3 illustrates a vector generation process embedding and generalization module with formula in accordance with an embodiment of the present disclosure;
• 4 Figure 12 shows the structure of an embedded formula index according to an embodiment of the present disclosure;
• 5 Illustrates that Table 1 presents bit position information in accordance with an embodiment of the present disclosure;
• 6 Table 2 illustrates the values of the evaluation parameters for 40 database formula browsing task queries according to an embodiment of the present disclosure; and
• 7 Table 3 shows the values of the evaluation parameters for 30 main database task queries according to an embodiment of the present disclosure.

Those skilled in the art will understand that the elements in the figures are presented for simplicity and are not necessarily drawn to scale. For example, the flow charts illustrate the method of key steps to enhance understanding of aspects of the present disclosure. In addition, one or more components of the device may be represented in the figures by conventional symbols, and the figures only show the specific details relevant to understanding the embodiments of the present disclosure, not to encircle the figures with details to overload, which are easily recognizable to those skilled in the art familiar with the present description.

DETAILED DESCRIPTION

For the purposes of promoting an understanding of the invention, reference will now be made to the embodiment illustrated in the figures and specific language will be used to describe the same. It should be understood, however, that no limitation on the scope of the invention is intended, and such alterations and further modifications to the illustrated system and such further applications of the principles of the invention set forth therein are contemplated as would occur to those skilled in the art invention would normally come to mind.

It will be understood by those skilled in the art that the foregoing general description and the following detailed description are exemplary and explanatory of the invention and are not intended to be limiting.

When this specification refers to "an aspect," "another aspect," or the like, it means that a particular feature, structure, or characteristic described in connection with the embodiment is present in at least one embodiment included in the present disclosure. Therefore, the phrases "in one embodiment," "in another embodiment," and similar phrases throughout this specification may or may not all refer to the same embodiment.

The terms "comprises,""including," or other variations thereof are intended to cover non-exclusive inclusion, such that a method or method that includes a list of steps includes not only those steps, but may also include other steps that are not expressly stated or pertaining to any such process or method. Likewise, any device or subsystem or element or structure or component preceded by "comprises...a" does not, without further limitation, exclude the existence of other devices or other subsystem or other element or other structure or other component or additional devices, or additional subsystems, or additional elements, or additional structures, or additional components.

Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one skilled in the art to which this invention pertains. The system, methods, and examples provided herein are for purposes of illustration only and are not intended to be limiting.

Embodiments of the present disclosure are described in detail below with reference to the attached figures.

1 12 shows a block diagram of a system for representing formulas and ranking for searching mathematical information according to an embodiment of the present disclosure. The system 100 includes an input unit 102 for receiving scientific document data and a user query.

In one embodiment, a document pre-processing unit 104 is connected to an input unit 102 to remove noise and extract formulas from the scientific document data.

In another embodiment, a formula embedding processor 106 is coupled to a document preprocessing unit 104 and has a formula embedding unit 108 used to generate a binary vector using bit position information and an embedded formula indexer 110 used to generate an embedded formula index for the generated binary vectors is used.

In another embodiment, a formula generalization processor 112 is connected to a formula embedding processor 106, which has a formula generalization unit 114, which is connected to a formula generalization processor 112 to extract all entities present in the formula and thereby convert it into a generalized vector, and a generalized formula indexer 116 is connected to a formula generalization unit 114 to generate a generalized formula index.

In another embodiment, a query embedding unit 118 is coupled to a formula embedding processor 106 to extract a set of entities from the user query and use bit position information to generate a query vector.

In another embodiment, a query generalization unit 120 is coupled to a formula generalization processor 112 to convert the user query into a generalized query vector.

In another embodiment, a search and ranking unit 122 is employed to receive a generalized query vector of keywords, thereby generating a set of similarity and dissimilarity factors that help retrieve the exact match formula, subformula, and parent formula and each match the entered keyword against each indexed context, thereby calculating the number of similar tokens between the query and the indexed context.

In another embodiment, the generalized formula index consists of four attributes selected from a set of vectors in generalized form, the context of a formula, the document ID from which the formula was extracted, and the formula in Presentation MathML format.

In another embodiment, the user query is a combination of mathematical formulas and textual keywords, the query set includes simple and complex queries that allow for efficient evaluation, each query having a unique ID that is used to identify the obtained result of a query with compared to the graded results stored in the gold record.

In another embodiment, the indexed formula similarity factor indicates how much the indexed formula is similar to the user query, while the indexed formula dissimilarity factor indicates how much the indexed formula differs from the user query.

In another embodiment, the user query is converted into a vector of 0's and 1's by query embedding unit 118 and query generalization unit 120 .

In another embodiment, the formula embedder 108 is configured to retrieve the syntactically similar formula while using formula generalization to retrieve the semantically similar formula in relation to the query entered by the user.

In another embodiment, the bit positions ranging from 0-25 and the lexical units at bit positions 150-201 are set to zero for the generalized vector form, and the formula generalization processor 112 is configured to represent the semantically similar formula in a unified form.

2 12 shows the system architecture of the proposed approach in accordance with an embodiment of the present disclosure. The proposed approach was tested using NTCIR-12's MathTag Articles of database corpus. It contained 31,839 scientific articles containing 579,608 formulas in three different formats namely LATEX, Presentation MathML and Content MathML. Math Tag Articles documents contain both textual and mathematical information, and each of the documents contains at least one formula.

The performance of the proposed approach was evaluated using 70 mathematical queries presented in Presentation MathML format. These 70 queries include 40 formula-based queries selected from the database formula browsing task and 30 queries containing both formulas and text selected from the main database task. These queries were provided by the organizer of the NTCIR-12 MathIR task. The query set includes simple and complex queries that allow efficient evaluation of the proposed approach. Each query has a unique ID that is used to compare the result of a query against the results stored in the gold record.

In order to validate the performance of the proposed approach in a realistic manner, the organizer of the NTCIR-12 MathIR Task provided the Gold dataset, which strictly follows the Text REtrieval Conference (TREC) qrel format. The first field is 'QueryID' which is used to identify a specific query of a query set. The second field, Iteration, is set to 0 and is ignored by the TREC. The third field is "Document#" which indicates the name/title of the document and the fourth attribute is "Relevance" which indicates a human's opinion of the information sought, classified as a binary category of relevant (1) or not relevant (0) is expressed.

The search results obtained with the proposed approach correspond to the TREC format. The result set includes six attributes, three of which (QuerylD, Document, and Relevance Score) were scored while the remaining three (Iteration, Rank, and RunID) were ignored. The proposed MIR approach successfully finds 800 scientific documents for the 40 mathematical queries. For each query, the proposed approach found the top 20 scientific documents, each of which contains at least one mathematical formula as the answer to the queried formula.

The system architecture is in displayed, with each module working cooperatively to obtain the relevant search results. The embedding and generalization of formulas are the two most important modules of the proposed system architecture. The main task of the formula embedding module is to find the syntactically similar formulas, while formula generalization is to find the semantically similar formulas with respect to the query entered by the user. The individual modules of the system architecture are described in the following subsections.

The mathematical articles in the database corpus contain both textual and mathematical content. The mathematical formulas in the articles are written in three different forms: Presentation MathML, Content MathML, and LATE X. The document preprocessor module of the proposed architecture extracts the mathematical notations marked with "<math>"&"</math>". , and the text surrounding them, specifically the titles marked "<title>"&"</title>", the headings "<h@>"&"</h@>", where @ stands for 1, 2, 3 ,...n and the context of each formula. the context of the formula is a small window that captures the 10 surrounding unique words of each formula. In this snippet, the document preprocessor engine extracts the math equation with the title, the caption, and the 10 surrounding vocabularies.

3 FIG. 12 shows a module for embedding and generalizing a vector generation process using a formula, according to an embodiment of the present disclosure. The formula embedding module of a system architecture uses the bit position information of Table 1 to generate a binary vector. This module converts the formula into a binary vector of size 202, where 1 represents the presence and 0 represents the absence of a specific unit in a formula. For example, consider a mathematical formula x2 - 2y + 1, which contains 2 variables, namely x and y, 2 operators, namely - and +, 1 numeric unit and 1 superscript. The process of formula embedding is in shown.

To search for a semantically similar formula, the formula generalization module was used in the proposed system architecture. The formula generalization engine extracts all entities present in the formula and converts them into a generalized vector of size 202, where 1 represents the presence and 0 represents the absence of a given entity in a formula. For the generalized vector form, bit positions 0-25 and the lexical entities present at bit positions 150-201 are set to "0". The main task of the formula generalization approach is to represent the semantically similar formulas in a unified form. For example, a2 + b2 and x2 + y2 are represented as 02 + 02, respectively. The process of formula generalization is in shown.

4 FIG. 1 shows the structure of an embedded formula index according to an embodiment of the present disclosure. The indexing module of the formula embedding approach creates the index for the vectors generated by the formula embedding module. Each index corresponds to the four fields: vector representation of the formula, the context of a formula, the document ID in which the formula was originally created, and the formula in Presentation MathML format. The indexer creates the index for the 579,608 formulas extracted from the 31,839 documents. The total size of the index is 787.6 MB, which is ~37% of the corpus size. The structure of the embedded formula index is in shown. Similar to the embedded formula indexer, the generalized formula indexer 116 creates the index for a pre-processed generalized formula in a scientific document. The index for generalized formulas contained 579,608 generalized vectors from 31,839 documents with a size of 787.6 MB, which is -37% of the corpus size. Like the embedded formula index, the generalized formula index consists of four attributes: vector in generalized form, the context of a formula, the document ID from which the formula was extracted, and the formula in Presentation MathML format. The user query is a combination of mathematical formulas and textual keywords. The query embedder extracts the entities present in the user query and uses the bit position information from Table 1 to generate a query vector, where 1 represents the presence and 0 represents the absence of a specific entity in a user query. After the query vector has been successfully generated, the query vector with its keywords is fed into the search and ranking module. Similar to the formula generalizer, the query generalizer transforms the user query into a generalized query vector. Then the query vector with the keywords is sent to the searcher and ranking module of the proposed approach. The query generalization engine replaces all entities between bit positions 0-25 and lexical entities in bit positions 150-201 with "0".

The formula relevance measurement approach considers the similarity and dissimilarity factors of indexed formulas in relation to the user query. The indexed formula similarity factor indicates how similar the indexed formula is to the user query, while the indexed formula dissimilarity factor indicates how much the indexed formula differs from the user query. Both similarity and dissimilarity contribute equally to finding the exact matching formula, subformula, and parent formula. The process of query transformation, as described in Sections 3.5.6 and 3.5.7, in which the user query is transformed into a vector of 0s and 1s by the query embedding and generalization engine. To evaluate formula relevance, the query vector searches all formula vectors in the index. For each formula vector present in the index, similarity and dissimilarity are calculated according to Equation 1. The proposed technique for measuring the relevance of formulas acts as a balancing factor in the ranking mechanism of mathematical information retrieval. To assess context relevance, the proposed approach compares each input keyword to each indexed context and calculates the Number of similar tokens between the request and the indexed context. The final relevance score combines the formula and context relevance score into a single metric, as defined in Equation 2. $$\begin{array}{l}\text{Formula relevance rating}\left(\text{f},\text{q}\right)=(\ddot{\text{A}}\text{resemblance}\left(\text{f},\text{q}\right))-\\ (\text{U.N}\ddot{\text{a}}\text{resemblance}\left(\text{f},\text{q}\right))\end{array}$$

where f represents the formula in a document and q represents a user query. Similarity(f,q) and Dissimilarity(f,q) calculate the number of similar and dissimilar bits, respectively, in a formula related to a user query. $$\begin{array}{l}\text{final}\ddot{\text{and}}\text{current relevance rating}\left(\text{f},\text{q}\right)=(\text{formula relevance assessment}(\text{f},\\ \text{q}))+(\text{Context Relevance Score}\left(\text{f},\text{q}\right))\end{array}$$

The formula relevance score (f, q) calculates the relevance between the formula vector and the query vector. Context relevance score(f, q) calculates the similarity between the indexed context of the formula and the keywords contained in the user query.

• • Bei der Berechnung der Formelähnlichkeit haben die Entitäten an den Bitpositionen 0-25 und 150-201 der Tabelle 1 eine geringere Priorität als andere Entitäten an den Bitpositionen 26-149.
• • Die Anzahl der ähnlichen und unähnlichen Bits in einer Formel f ist in Bezug auf die Benutzeranfrage q gleich. Daher gewährleistet der vorgeschlagene Ansatz zur Relevanzmessung die symmetrische Eigenschaft der Gleichheit. Diese Eigenschaft beweist, dass die Unähnlichkeit zwischen der Formel und der Abfrage im Vergleich zur Ähnlichkeit die gleiche Bedeutung hat.
• • Für die normalisierte Relevanzbewertung wird die Unähnlichkeitsbewertung zwischen der Formel und der Abfrage von der Ähnlichkeitsbewertung abgezogen. Die normalisierte Relevanzbewertung wird als Relevanzbewertung für ein bestimmtes Dokument in Bezug auf die Benutzeranfrage betrachtet.
• • Der Bereich der Relevanzbewertung ist nicht definiert; es kann sich um einen positiven oder negativen Wert handeln. Nach erfolgreicher Berechnung der Relevanzbewertung kombiniert das Rangfolgemodul die abgerufenen Dokumente aus beiden Ansätzen, d.h. aus dem Formel-Einbettungsansatz und dem Formel-Verallgemeinerungsansatz. Das Hauptziel des Ranker-Moduls ist es, die Dokumente auf der Grundlage des jeweiligen Suchansatzes zu ordnen. Die Dokumente, die mit beiden Ansätzen (Formel-Einbettung und Formel-Verallgemeinerung) abgerufen werden, haben eine höhere Priorität als ein einzelnes Dokument. Die Prioritäten gehen dann an die Dokumente, die mit dem Formel-Einbettungs-Ansatz gefunden wurden. Die Dokumente, die mit dem Formelverallgemeinerungsansatz gefunden werden, haben eine geringere Priorität als der kombinierte Ansatz und der Formel-Einbettungsansatz. Als endgültiges Suchergebnis gibt das Ranglistenmodul die 25 besten Dokumente zurück, die in Bezug auf die vom Benutzer eingegebene Suchanfrage gefunden wurden.

Below are the main cornerstones of calculating the relevance score between the documents and the user query:

• • When calculating formula similarity, the entities at bit positions 0-25 and 150-201 of Table 1 have lower priority than other entities at bit positions 26-149.
• • The number of similar and dissimilar bits in a formula f is the same with respect to the user query q. Therefore, the proposed approach to relevance measurement ensures the symmetrical property of equality. This property proves that the dissimilarity between the formula and the query has the same meaning compared to the similarity.
• • For the normalized relevance score, the dissimilarity score between the formula and the query is subtracted from the similarity score. The normalized relevance score is considered a relevance score for a particular document in relation to the user query.
• • The scope of the relevance assessment is not defined; it can be a positive or negative value. After successfully calculating the relevance score, the ranking engine combines the retrieved documents from both approaches, ie from the formula embedding approach and the formula generalization approach. The main goal of the Ranker module is to rank the documents based on the specific search approach. The documents retrieved using both approaches (formula embedding and formula generalization) have a higher priority than a single document. Priorities then go to the documents found using the formula embedding approach. The documents found with the formula generalization approach have a lower priority than the combined approach and the formula embedding approach. As a final search result, the ranking module returns the top 25 documents found in relation to the search query entered by the user.

1. i. Die Bitpositionen 0-25, 57-65 und 71-100 sind mit dem Inhalt des <mi>-Tags verknüpft, die Bitpositionen 26-45, 66-70 und 101-149 mit dem Inhalt des <mo>-Tags und die Bitpositionen 46-56 mit dem MathML-Tag. Diese Bitpositionen tragen zur semantischen Formel bei. Die Bitpositionen 150-175 und 176-201 wiederum stehen für die lexikalischen Einheiten in hoch- und tiefgestellter Form.
2. ii. Es gibt keinen Unterschied zwischen den Entitäten, die eine semantische Ähnlichkeit aufweisen, wie z. B. „log“ und „In“, die derselben Bitposition zugeordnet sind. Ebenso werden „exp“ und „e“ der gleichen Bitposition zugeordnet. Variablen sind unabhängig von der Groß-/Kleinschreibung, d. h. es gibt keinen Unterschied zwischen den Groß-/Kleinschreibungsvariablen, und werden der gleichen Bitposition zugewiesen. So werden z. B. ‚A‘ und ‚a‘ derselben Bitposition zugewiesen.
3. iii. Wenn die Entität mehr als einmal auftritt, wird nur ein Auftreten dieser Entität für die Vektorgenerierung berücksichtigt.
4. iv. Die trigonometrischen Funktionen werden der gleichen Bitposition zugewiesen, um ein verallgemeinertes Ergebnis zu erhalten.
5. v. Bitposition 65 ist als Mehrzweckvariable gekennzeichnet, deren Rolle nicht vordefiniert ist, wie z.B. log, lim, usw.

The following points are relevant to the vector generation process and the Bit Position Information Table (BPIT):

1. i. Bit positions 0-25, 57-65 and 71-100 are linked to the content of the <mi> tag, bit positions 26-45, 66-70 and 101-149 are linked to the content of the <mo> tag and the bit positions 46-56 with the MathML tag. These bit positions contribute to the semantic formula. Bit positions 150-175 and 176-201 in turn represent the lexical units in superscript and subscript form.
2. ii. There is no difference between the entities that share a semantic similarity, such as B. "log" and "In" mapped to the same bit position. Likewise, "exp" and "e" are mapped to the same bit position. Variables are case-insensitive, ie there is no difference between upper and lower case variables, and are assigned the same bit position. So e.g. For example, 'A' and 'a' are assigned to the same bit position.
3. iii. If the entity occurs more than once, only one occurrence of that entity is considered for vector generation.
4. IV. The trigonometric functions are assigned the same bit position to get a generalized result.
5. v. Bit position 65 is marked as a general purpose variable whose role is not predefined, such as log, lim, etc.

5 FIG. 1 illustrates that Table 1 presents bit position information in accordance with an embodiment of the present disclosure.

6 Table 2 shows the values of the evaluation parameters for 40 database formula browsing task queries according to an embodiment of the present disclosure.

7 Table 3 shows the values of the evaluation parameters for 30 main database task queries according to an embodiment of the present disclosure.

Query set description

To evaluate the performance of the proposed approach, 70 mathematical queries presented in Presentation MathML format were used. The query set consists of both simple and complex queries, resulting in an efficient assessment of the performance of the proposed approach. Of the above 70 queries, 30 queries were obtained from the main Wikipedia task and 40 from the NTCIR-12 Wikipedia formula browsing task. Each query has a unique ID that allows the result of a query to be compared to the scored results in the gold dataset.

Gold record description

The Gold dataset is used to measure the effectiveness of the proposed approach in a standardized way. The structure of the Gold dataset strictly follows the Text REtrieval Conference (TREC) qrel format, which consists of four attributes. The first attribute is QueryID, which defines the ID of a specific query in a query set. The second attribute is Iteration, which is set to 0 and is pushed aside by the TREC. The third attribute is "Document#" which defines the name/title of the document and the fourth attribute is "Relevance" which defines a human's assessment in relation to the user's information needs and the assessment is defined as a binary classification of either indicated as relevant (1) or not relevant (0).

Structure of the result set

With the proposed approach, 1400 documents for 70 MathML queries were retrieved from the queryset. The result set contains 6 attributes, three of which (QueryID, Document, and Relevance Score) were examined by a scoring tool, while the remaining three (Iteration, Rank, and RunID) were left aside.

rating parameters

Information retrieval system performance is measured by the number of documents retrieved from the system. For each user query, the retrieval system creates a list of documents, and then the average is taken to measure the overall performance of the retrieval system. This performance measurement framework includes the parameters that assess the effectiveness of the retrieval system. In this work, to measure the performance of the proposed approach, the parameter P K is used, which calculates the number of relevant 401 documents from the top K retrieved documents, where K=5, 10, 15, and 20. All these measures are first calculated for each Query is calculated, and the results are then averaged across all queries with equal posts.

Comparative Analysis

The formula embedding and generalization modules of the proposed approach effectively find the syntactically and semantically similar formulas, subformulas, and parent formulas. The performance results of the proposed approach are presented in Tables 2 and 3. It turns out that the approach of considering the context of the formula and the dissimilarity factor when measuring the relevance score leads to more relevant results. The results obtained for 40 Wikipedia Formula browsing tasks are compared to the state of the art, i.e. a text-based search engine implemented using the Apache Nutch4 platform, using MIaS, the formula embedding approach, the official treceval results of the MCAT math retrieval system and the Tangent 3 system of the RITUW. The graphical and tabular representation of the results is shown in Table 2. Likewise, the achieved results for 30 database main task queries are compared with the official task results of the NTCIR-12 participants, i.e. Team FSE, WikiMir system by ICST, Team MCAT, MIaS system by Team MIRMU, Tangent-3 system by Team RITUW and Team SMSG5. The graphical and tabular representation of the results is shown in Table 3. The remarkable difference in the metrics of these existing state-of-the-art MIR approaches has shown that the combined approach of formula embedding and generalization leads to more relevant search results. From the comparison of the approaches mentioned, it can be deduced that the dissimilarity factor represents a significant additional value when measuring the relevance rating. Interestingly, the result of the proposed approach shows that the exact match ranks first in the ranking of retrieved documents compared to parent formulas and subformulae. The approach of considering the formula context and the dissimilarity factor when calculating the relevance score results in qualitatively and qualitatively effective search results.

• Erstens integriert der vorgeschlagene Ansatz Ergebnisse aus verschiedenen Modulen, die für die Bewältigung unterschiedlicher Herausforderungen konzipiert sind. Den Suchergebnissen, die Text und Mathematik enthalten, die sehr erwünscht sind, wird die höchste Präferenz zugewiesen. Diese Beispielergebnisse zeigen, dass es erfolgreich Suchergebnisse findet, die ähnliche Formeln, Unterformeln, übergeordnete Formeln und solche, die sowohl Text als auch Formeln enthalten. Zweitens verwendet das leistungsstärkste ICST Math Retrieval System des NTCIR die Technik der semantischen Anreicherung, um strukturelle und semantische Informationen aus dem Layout der Formeln zu extrahieren. Das ICST-System verwendet jedoch nur wenige der Dateien für Experimente. Außerdem kann es die Korrelation zwischen Textabfragen und indizierten mathematischen Inhalten nicht verarbeiten. Drittens verwendet das MCAT-Mathe-Retrieval-System die Dependency-Graph-Methode, um die Textinformationen anzureichern und die Suche durchzuführen. Das Scheitern der Dependency-Graph-Methode von MCAT ist jedoch der Tatsache geschuldet, dass die Mehrzahl der in der Abfrage enthaltenen Textschlüsselwörter Stopp-Wörtern ähneln und ihre Anreicherung daher nicht von Vorteil ist. Nur 5 von 30 Abfragen enthalten Schlüsselwörter, die ungewöhnlich und spezifisch für die Formel sind. Viertens berücksichtigt das TANGENT-System auch nicht die Beziehungen zwischen Text und Mathematik und verwendet keine Textmerkmale oder Kontexte, die mit der Formel verbunden sind. Fünftens berücksichtigt der auf der Borda-Anzahl basierende Ranking-Mechanismus, der vom SMSGS-System verwendet wird, verschiedene Wissensdatenbanken, weist aber den Ergebnissen aus diesen Wissensdatenbanken die gleiche Gewichtung zu, was für die Mehrheit der Abfragen nicht gut funktioniert.

The following differences between the proposed approach and the existing MIR systems as well as the limitations of the existing MIR systems are also worth noting:

• First, the proposed approach integrates results from different modules designed to address different challenges. The search results that contain text and math, which are highly desirable, are assigned the highest preference. These sample results show that it successfully finds search results that contain similar formulas, subformulas, parent formulas, and those that contain both text and formulas. Second, NTCIR's most powerful ICST Math Retrieval System uses the technique of semantic enrichment to extract structural and semantic information from the layout of the formulas. However, the ICST system uses few of the files for experiments. Also, it cannot handle the correlation between text queries and indexed math content. Third, the MCAT math retrieval system uses the dependency graph method to enrich the text information and perform the search. However, the failure of MCAT's Dependency Graph method is due to the fact that the majority of the text keywords included in the query resemble stop words and their enrichment is therefore not beneficial. Only 5 out of 30 queries contain keywords that are uncommon and specific to the formula. Fourth, the TANGENT system also does not consider the relationships between text and mathematics and does not use textual features or context associated with the formula. Fifth, the Borda count-based ranking mechanism used by the SMSGS system considers different knowledge bases, but assigns the same weight to the results from those knowledge bases, which does not work well for the majority of queries.

The figures and the preceding description give examples of embodiments. Those skilled in the art will understand that one or more of the elements described may well be combined into a single functional element. Alternatively, certain elements can be broken down into multiple functional elements. Elements from one embodiment may be added to another embodiment. For example, the order of the processes described herein may be changed and is not limited to the manner described herein. Additionally, the actions of a flowchart need not be performed in the order shown; Also, not all actions have to be carried out. Also, the actions that are not dependent on other actions can be performed in parallel with the other actions. The scope of the embodiments is in no way limited by these specific examples. Numerous variations are possible, regardless of whether they are explicitly mentioned in the description or not, e.g. B. Differences in structure, dimensions and use of materials. The scope of the embodiments is at least as broad as indicated in the following claims.

Advantages, other benefits, and solutions to problems have been described above with respect to particular embodiments. However, the benefits, advantages, problem solutions, and components that can cause an advantage, benefit, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential feature or component of any or all claims.

Reference List

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A formula display and ranking system for mathematical information retrieval.

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input unit

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Preprocessing unit for documents

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Formula embedding processor

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Unit for embedding formulas

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Indexer for embedded formulas

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Formula Generalization Processor

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Unit for formula generalization

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Indexer for generalized formulas

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Unit for embedding queries

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Unit for query generalization

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Seeker and ranking unit

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Scientific Documents

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Document Preprocessor

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Module for embedding formulas

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Formula indexer to embed

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Embed formula index

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Formula generalization module

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Generalization Formula Indexer

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Generalization Formula Index

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Formula embedding approach

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Formula Generalization Approach

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Results

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query

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search results

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ranking

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Relevance Rating

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similarity

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dissimilarity

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Seeker and ranking module

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Module for embedding search queries

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Module for generalizing search queries

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user query

Claims (8)

A system for representing and ranking formulas for searching mathematical information, the system comprising: an input unit for receiving scientific document data and a user query; a document pre-processing unit for removing noise and extracting formulas from the scientific document data; a formula embedding processor having a formula embedding unit for generating a binary vector using bit position information and an embedded formula indexer for generating an embedded formula index for the generated binary vectors; a formula generalization processor having a formula generalization unit for extracting all entities present in the formula, thereby converting them into a generalized vector, and a generalized formula indexer for generating a generalized formula index; a query embedding unit for extracting a set of entities from the user query and using bit position information to generate a query vector; a query generalization unit for converting the user query into a generalized query vector; and a search and ranking unit for receiving a generalized query vector of keywords, thereby generating a set of similarity and dissimilarity factors that help retrieve the exact match formula, subformula and parent formula and match each input keyword to each indexed context, which calculates the number of similar tokens between the query and the indexed context. system after claim 1 , where the generalized formula index forms four attributes selected from a set of vectors in generalized form, the context of a formula, the document ID from which the formula was extracted, and the formula in Presentation MathML format. system after claim 1 , where the user query is a combination of mathematical formulas and textual keywords, where the query set contains simple and complex queries that allow for efficient evaluation, where each query has a unique ID that is used to compare the obtained result of a query with the in compare assessed results stored with the gold record. system after claim 1 , where the indexed formula similarity factor represents how closely the indexed formula is similar to the user query, while the indexed formula dissimilarity factor represents how closely the indexed formula differs from the user query. system after claim 1 , where the user query is transformed into a vector of 0s and 1s by a query embedding unit and a query generalization unit. system after claim 1 , wherein the formula embedder is configured to retrieve the syntactically similar formula while using the formula generalization to retrieve the semantically similar formula in relation to the query entered by the user. system after claim 1 , where the bit positions are in the range 0-25 and lexical units present at bit positions 150-201 are set to zero for the generalized vector form, the formula generalization processor being configured to unify the semantically similar formula into a represents shape. system after claim 1 , where the query vector searches all formula vectors present in the index for formula relevance score and context relevance score.

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