Text data mining is the process of discovering hidden information and new knowledge from a large amount of unstructured text. The commercial value of this method is high. It is closely related to natural language processing. The most critical of them is to extract helpful text features. Mining methods commonly include text classification, clustering, association analysis, and trend prediction. The maturity and perfection of statistical algorithms promote the continuous development of text mining technology. Computing text similarity is the key and foundation of mining other text data. It is getting more and more attention [1]. A translation is also a text. By comparing the similarity of translated texts, we can provide critical quantitative indicators for translation quality assessment and translation comparison.

The translation of English passive sentences is critical in developing online machine translation [2]. What is the similarity between online machine translation and human translation in translating English passive sentences into Chinese passive sentences? What method can be used to measure this similarity objectively and scientifically? These are the two research questions of this paper.

The method of text data mining may be desirable. Its commonly used methods include text classification, clustering, feature extraction, and information compression. The vector space model (VSM) is one of the most frequently used models. Information compression usually uses principal component analysis. This study attempts to combine VSM and PCA to measure and compare the similarity between online machine translation and human translation in the corresponding translated passive sentences. In this way, a new method can be found to quantify and measure the similarity of the translation of particular sentence patterns in different versions [3]. This study intends to build a parallel corpus. We use the method of data mining, combining quantitative and qualitative analysis to compare the similarity between online machine translation and human translation in the translation of passive sentences.

The corpus selected in this paper is the self-built one-to-five English-Chinese bilingual parallel corpus of Pride and Prejudice. The total storage capacity is about 1.1 million words. The oeuvre includes a completely original English text, an online machine translation, and four human translations [4]. The manual translators were Document A (Shanghai Translation Publishing House, 1980), Document B (Yilin Publishing House, 1985), Document C and Zhang Yanghe (1995 People's Literature Publishing House), and Document D (Zhejiang Literature and Art Publishing House, 2004). Baidu online translation was selected as the online translation in this study. We automatically generate it online through the website

The traditional VSM feature extraction is mainly based on the frequency of high-frequency words, which ignores the semantic and syntactic structure. The usual high-frequency words primarily function words such as auxiliary words. Corresponding translation studies of passive sentences need to integrate different vocabulary, syntax, and semantics. Therefore, the feature selection of this study corresponds to multiple types of passive marker words in translation [5]. We use the parallel retrieval software CUC_Paraconc3.0 to extract English passive sentences and their corresponding Chinese translations based on an English-Chinese bilingual parallel corpus. Remove undesired corpus from search results. In this way, a multi-version parallel corpus containing only passive sentences is constructed. We extract similar sentence pairs by editing the regular expressions of English passive sentences and then statistically compare the specific data of the corresponding translations in each translation. The article then explores the similarity between online and human translations. At the same time, we propose a similarity calculation formula that combines PCA and spatial vector distance. This paper also improves the traditional distance formula. This paper calculates the similarity between translations by a new space vector distance calculation formula. This way, an objective and quantitative description of the translation similarity of passive sentences between translations is achieved.

VSM is often used in the field of information retrieval. It has strong operability and computability. The main principle of VSM is to represent documents as vectors. We take the weights of the extracted feature items as each dimension of the vector. This paper calculates the similarity by word frequency statistics and vector dimensionality reduction. It is a standard measure of text similarity [6]. The cosine angle value usually expresses the vector similarity. The larger the matter, the smaller the angle. This indicates a higher similarity between the two. So VSM can generally be used to calculate the similarity between texts. The feature vector of each translation corresponds to a point in the space, and their relative positions determine the similarity between the two translations. Measure the cosine of the angle between different translation vectors. It can be used to characterize their similarity.

First, n features are extracted in each document. These n features form a feature space, and each text can be represented as a dimensional vector. Each dimension in the vector represents the weight of the corresponding component in the text. Assuming that the feature space vector of one text is _{1} _{2} ⋯ _{N}_{1} _{2} ⋯ _{N}

Where 〈 〉 represents the inner product operation. | | represents the length of the vector. The cosine of the angle between the vectors is equal to the inner product of the unit vectors of the two vectors _{c}

Euclidean distance (ED) refers to the absolute distance between two points in space. It is determined by where each point is located. It can reflect the fundamental difference of numerical values, which aligns with the traditional cognitive concept of distance [8]. Accordingly, we use ED to estimate the similarity between the two translations. Assuming two text vectors are _{1} _{2} ⋯ _{N}_{1} _{2} ⋯ _{N}

The larger the value of the Euclidean distance _{e}

The vector CD can represent the distance in the two vector directions, while the ED can reflect the length [9]. We need to include both direction and altitude. Therefore, this study proposes a method that combines the two distances.

Because the vectors CD and ED dimensions are different, we must first normalize the two distances. Obtain the normalized CD as _{cn}_{en}

We perform a weighted average of the two distances. At this point, we construct a new distance formula as follows:

Suppose there are _{1} _{2} ⋯ _{M}]. Each sample extracts features, denoting as _{i} = [_{i}_{1} _{i}_{2} ⋯ _{iN}]^{N}. where [ ]^{T} stands for transpose. The basic process of PCA is as follows:

Since the data features we extract may have different dimensions, their numerical values are quite different and will affect the results. So we need to eliminate orders of magnitude from the original data and normalize the data. i.e., we transform it into normalized data with mean 0 and variance 1. When the dimensions of the original data are the same or the value difference is slight, we only need to perform the zero-mean operation.

We calculate its eigenvalues _{i}_{x}_{1} ≥ _{2} ≥ ⋯ ≥ _{N}_{x}_{1}, _{2}, ⋯, _{N}_{1}, _{2}, ⋯, _{N}

The principal component is the projection of the original data on the new coordinate system according to the principle of maximum variance, and the eigenvalue reflects its disagreement [10]. We introduce the cumulative contribution of eigenvalues. Its calculation formula is as follows:

We set _{p}

The principal components we extract can be obtained by projecting the zero-mean data on the coordinates of the first _{p}_{1} _{2} ⋯ _{p}

The principal components extracted by PCA are also applicable to the vector space model. Therefore, the translated text vector can be reduced to the primary component feature vector [11]. We use the vector distance formula (6) to calculate the actual distance between the two translations. In this way, we can comprehensively measure the translation similarity between the two.

After the above steps, we finally extracted 1524 sentences of passive structure in the valid English original text. However, the number of passive sentences in the Chinese translation is far apart. The number of passive sentences in English and Chinese is not equal and asymmetrical. It is known from research that only some English passive sentences are processed into Chinese passive sentences with passive markers. From this point of view, it is an excellent strategy to translate English passive sentences into Chinese passive sentences. It can reflect different translation characteristics.

In this study, 18 types of corresponding translated Chinese passive sentences were extracted. The specific data are shown in Table 1. We treat each translation as an 18-dimensional text vector. This enables translation vectorization. After that, the eigenvalues and eigenvectors are obtained by principal component analysis. We arrange the eigenvalues in descending order, calculate the cumulative amount of information, and finally extract the first few main components contributing more. Under normal circumstances, the cumulative contribution rate of the principal components needs to reach more than 85%. The purpose of taking the threshold of 90% in this paper is to retain more information. The variance contribution rate of the first principal component is 87.77%, and the second main component is 11.59%. The cumulative variance contribution rate of the first two principal components reaches 99.36%. This method preserves most of the information content of the original text vector. So we can replace the actual 18 dimensions with two new principal components. The correlation coefficient between the two new main components is 0, indicating that the two are mutually orthogonal. This removes the correlation and collinearity among the original features. It also shows the correctness of the algorithm. This paper uses these two principal components to establish a new two-dimensional orthogonal coordinate system, and the spatial position of each translation is shown in Figure 1.

Various Chinese passive sentences translated into English passive sentence pairs

Serial number | Literature A | Literature B | Literature C | Literature D | Artificial average | Online machine translation |
---|---|---|---|---|---|---|

1 | 27 | 23 | 18 | 28 | 24 | 247 |

2 | 6 | 2 | 0 | 5 | 3.25 | 0 |

3 | 16 | 29 | 32 | 16 | 23.25 | 2 |

4 | 21 | 23 | 21 | 1 | 16.5 | 4 |

5 | 5 | 4 | 5 | 2 | 4 | 1 |

6 | 27 | 26 | 25 | 11 | 22.25 | 10 |

7 | 1 | 1 | 0 | 1 | 0.75 | 1 |

8 | 17 | 13 | 19 | 7 | 14 | 28 |

9 | 3 | 3 | 6 | 1 | 3.25 | 2 |

10 | 36 | 33 | 44 | 22 | 33.75 | 18 |

11 | 5 | 2 | 3 | 1 | 2.75 | 0 |

12 | 4 | 1 | 2 | 0 | 1.75 | 0 |

13 | 1 | 3 | 2 | 0 | 1.5 | 0 |

14 | 0 | 0 | 0 | 0 | 0 | 9 |

15 | 3 | 4 | 2 | 0 | 2.25 | 1 |

16 | 4 | 7 | 8 | 3 | 5.5 | 8 |

17 | 4 | 3 | 4 | 4 | 3.75 | 2 |

18 | 19 | 11 | 11 | 12 | 13.25 | 2 |

199 | 188 | 202 | 114 | 175.75 | 175.75 |

Their respective spatial locations determine the distance between the translations. It can be seen from Figure 1 that the four artificial translations are relatively concentrated in space. This shows that the classification and clustering of the two types of translations can be successfully achieved using principal component analysis. The line connecting the position of each translation and the origin constitutes the text vector of the translation. It can be seen that the distance and the included angle between the four artificial translations are minimal. This shows that the similarity of human translation is high. However, the distance between the human translation and the online machine translation is relatively far, and the angle is large. This shows that there is still a big gap between online machine translation and manual translation. Therefore, we use principal component analysis to study the characteristics of the corresponding translations of passive sentences in each translation. We can distinguish and classify human translations and online machine translations. This shows a significant difference between online machine translation and manual translation in the corresponding translation of English passive sentences.

We have extracted two principal components by dimensionality reduction. Its cumulative contribution rate reached 99.36%. This explains the vast majority of the amount of information. Therefore, we can project the original 18-dimensional text vector into a 2-dimensional space, and each translation can be reduced to a two-dimensional vector (Table 2).

Principal component eigenvectors

Literature A | Literature B | Literature C | Literature D | Artificial average | Online machine translation |
---|---|---|---|---|---|

21.6985 | 18.992 | 13.8412 | 24.944 | 19.5938 | 236.525 |

38.9658 | 41.4521 | 49.8598 | 22.1225 | 38.3195 | −14.8382 |

We pass the eigenvectors composed of two principal components and use the modified vector distance formula (6). In this way, the actual vector distances between the translations are obtained (Table 3).

Distances between passive sentence vectors in each translation

Literature A | Literature B | Literature C | Literature D | Artificial average | Online machine translation | |
---|---|---|---|---|---|---|

Literature A | 0 | |||||

Literature B | 0.0147 | 0 | ||||

Literature C | 0.0502 | 0.0147 | 0 | |||

Literature D | 0.0725 | 0.0502 | 0.0263 | 0 | ||

Artificial average | 0.0051 | 0.0113 | 0.044 | 0.0907 | 0 | |

Online machine translation | 0.7276 | 0.9017 | 1 | 0.6271 | 0.753 | 0 |

The vector distance values are all between 0 and 1. The larger the deal, the farther the distance is, and the less similar the corresponding translations of the passive sentence are. Distances are symmetrical. The text vector sum is the same distance as the sum. Therefore, only the left half of the distance values are listed in Table 3. It can be seen from Table 3 that the distance between the online translation and the manual translation is above 0.6. The cosine distance between human translations is basically below 0.2. This shows a big difference between online machine translation and human translation. In addition, the vector distance between the translation of document B and the translation of document A is only 0.0147. This shows that the two translators have the highest similarity in the translation of passive sentences. From Table 1, it can be roughly seen that the data structures and changes of the two translations are also relatively consistent.

The distance between the document D version and the online version is 0.6271. This is the minimum distance between a human translation and an online translation. The maximum value of the distance between human translations is 0.1866. The difference between the two values is about three times, which indicates that the similarity between the online version and the human understanding is less, and the similarity between the human versions is higher. Online machine translation relies on the limitation of bilingual corpus and statistical rules, making it incapable of being as flexible as human translation when translating passive English sentences. This will produce a large number of single “be” words. And some of the “big” words in the machine translation do not conform to the pragmatic color of Chinese. It is less readable, which suggests that machine translation needs more improvement. The human translators are very close to document A version. Therefore, the average artificial translation is also the most relative to Document A. We can also see from the line distances and trends of the corresponding translations in Figure 2. The point corresponding to the distance between Document D and the online machine translation of 0.6271 is a central turning point. This shows that the similarity between the two in passive sentence translation is significantly higher than that between other human translators and machine translation. Similarly, document C has the farthest distance from the machine translation (space is 1). This shows that the passive sentence translations of the two are the least similar.

This study proposes a vector distance measurement method that combines a vector space model and principal component analysis based on corpus translation studies and text data mining methods. The study found that Chinese passive sentences are significantly less than English ones. There is a significant asymmetry in the translation of English-Chinese passive sentences. We use the method of text data mining to compare the similarity of the translation features of the passive sentences of the two types of translations. The results show that the distance between the manual and online translations is more significant, and the distance between the manual translations is smaller. This indicates that there is still a big gap between online translation and manual translation quality.

#### Principal component eigenvectors

Literature A | Literature B | Literature C | Literature D | Artificial average | Online machine translation |
---|---|---|---|---|---|

21.6985 | 18.992 | 13.8412 | 24.944 | 19.5938 | 236.525 |

38.9658 | 41.4521 | 49.8598 | 22.1225 | 38.3195 | −14.8382 |

#### Various Chinese passive sentences translated into English passive sentence pairs

Serial number | Literature A | Literature B | Literature C | Literature D | Artificial average | Online machine translation |
---|---|---|---|---|---|---|

1 | 27 | 23 | 18 | 28 | 24 | 247 |

2 | 6 | 2 | 0 | 5 | 3.25 | 0 |

3 | 16 | 29 | 32 | 16 | 23.25 | 2 |

4 | 21 | 23 | 21 | 1 | 16.5 | 4 |

5 | 5 | 4 | 5 | 2 | 4 | 1 |

6 | 27 | 26 | 25 | 11 | 22.25 | 10 |

7 | 1 | 1 | 0 | 1 | 0.75 | 1 |

8 | 17 | 13 | 19 | 7 | 14 | 28 |

9 | 3 | 3 | 6 | 1 | 3.25 | 2 |

10 | 36 | 33 | 44 | 22 | 33.75 | 18 |

11 | 5 | 2 | 3 | 1 | 2.75 | 0 |

12 | 4 | 1 | 2 | 0 | 1.75 | 0 |

13 | 1 | 3 | 2 | 0 | 1.5 | 0 |

14 | 0 | 0 | 0 | 0 | 0 | 9 |

15 | 3 | 4 | 2 | 0 | 2.25 | 1 |

16 | 4 | 7 | 8 | 3 | 5.5 | 8 |

17 | 4 | 3 | 4 | 4 | 3.75 | 2 |

18 | 19 | 11 | 11 | 12 | 13.25 | 2 |

199 | 188 | 202 | 114 | 175.75 | 175.75 |

#### Distances between passive sentence vectors in each translation

Literature A | Literature B | Literature C | Literature D | Artificial average | Online machine translation | |
---|---|---|---|---|---|---|

Literature A | 0 | |||||

Literature B | 0.0147 | 0 | ||||

Literature C | 0.0502 | 0.0147 | 0 | |||

Literature D | 0.0725 | 0.0502 | 0.0263 | 0 | ||

Artificial average | 0.0051 | 0.0113 | 0.044 | 0.0907 | 0 | |

Online machine translation | 0.7276 | 0.9017 | 1 | 0.6271 | 0.753 | 0 |

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Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability 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Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model