The current research methods of machine translation mainly include rule-based methods, statistics-based methods, and instance-based methods. Statistics-based methods are increasingly becoming a hotspot in machine translation research—this paper studies Chinese-English machine translation based on Lagrangian mathematical algorithm. We have studied and improved Och's Lagrangian algorithm [1]. When the article expands the node, it expands on the inspiration node and expands on other nodes. This avoids removing assumptions with flawed heuristics but more reasonable ones. We apply this improved algorithm to the Chinese-English translation system. The experimental results show that the enhanced Lagrangian algorithm can obtain better translation results and search efficiency in the system.

The current statistical machine-translation method refers to the statistical machine-translation method based on the source-channel model [2]. The source-channel model treats the translation problem as restoring the signal from a noisy channel. It translates a given source language text (word sequence)

We study Chinese-English statistical machine translation based on Lagrangian mathematical algorithm. We adopt Lagrangian for two main reasons: 1) Compared with other alignment models, the alignment effect of Model 4 is better. 2) The dependence of the model on the warp rate in the target language can integrate n-gram language models during the search process.

We compute the parts of speech for Chinese and English based on Lagrangian. We first use MKCLS to generate parts of speech; then use GIZA++ to train these corpora to obtain Lagrangian parameters (Table 1).

Parameter information and scale of translation models

Parameter | Number |
---|---|

English part of speech C(e) | 129786 |

Chinese part of speech C(c) | 145083 |

P(count, C(e), C(c)) twist rate | 73888 |

P(e|c) back translation rate | 331796 |

P(c|e) translation rate | 331796 |

P(⊄ |e) reproduction rate | 129775 |

The English corpus is used as the training corpus for our language model in Chinese-English translation [4]. We use the CMU training corpus. This paper uses the ternary language model to obtain the data shown in Table 2.

Parameters and scale of language models

Parameter | Unary model parameters | Binary model parameters | Ternary model parameters |
---|---|---|---|

Number | 20000 | 173894 | 355043 |

This section will construct the Boussineq equation with perturbation term using the partial Lagrangian method [5]. The allowed Lagrangian functions are

The approximate Euler-Lagrange-type equation is

The determination equation of _{0} + _{1} is:

In

Each node is a hypothesis H about translation at a particular moment, and H can be described as follows [6]. The length of the target sentence is l; the prefix word _{1}, _{2} ⋯ _{k}_{1}, _{2} ⋯ _{k}_{1}, _{2} ⋯ _{k}_{k}_{+1}, _{k}_{+2} ⋯ _{1}.

(1) Prefix score

We build on Lagrangian mathematical algorithms and ternary language models:

Where

(2) Suffix score

Where

The presence of

If only the twist rate is considered,

The following takes Chinese-English translation as an example to describe the search process. The search target is _{1}, _{2}, ⋯, _{J}

While all words in the English vocabulary could be marked as candidates for each _{j}_{i}_{j}_{i}_{j}_{i}_{j}_{i}_{i}_{j}_{i}

The steps of the Lagrangian algorithm search are as follows: 1) Expand the optimal node according to the score. This score includes the prefix score and the heuristic score. 2) Without considering the heuristic score, expand other nodes according to the size of the prefix score.

When expanding, we expand the node with the best score and extend the node at the same level in the search graph [8]. The number of Chinese words they cover is the same as the optimal node. Better hypotheses can be found by doing a partial width search. The search algorithm is as follows:

The Open queue and Closed queue are initialized to empty. C(n) is the position set of covered Chinese words

(1) Initialize the hypothesis queue

_{j} Forall_{i}do

We create new hypotheses. We put it into the Open queue. The position of the previous translated Chinese word is set to

We calculate the prefix score

(2) Start searching

1) Expand the optimal node. We assume that the maximum score in the Open queue is m. We'll label it Closed.

We connect each candidate word _{i}_{j}

The calculated prefix score is

2) Partial width search

Please create a new hypothesis and mark it as Open.

3) Determine whether to terminate

Then search for Break. We output the hypothesis with the most significant score in |

At this point, we output the English translation.

4) All hypotheses marked as Open are sorted in descending order of their scores.

We verify the algorithm through experiments. The evaluation of the experimental results in this paper is done manually [9]. The evaluation standard is whether the translation result can convey the original text's meaning.

We selected 500 Chinese sentences with grammatical norms. The average number of words is 6.3. Test the effect of the maximum number of hypotheses acceptable in the hypotheses cohort on translation performance under normal circumstances [10]. The test data are shown in Table 3 (c=0.25, n=10, d=5).

Hypothetical effect of column size L on translation

Suppose the maximum length of the queue is N | 500 | 1000 | 1500 | 2000 |

Time spent translating a sentence | 11.34s | 14.65s | 24.89s | 39.64s |

Evaluation results | 40% | 50.50% | 50.56% | 50.56% |

The heuristic we employ is guaranteed to overestimate the remaining cost. We see that when L=1000 is a more appropriate setting.

In Chinese-English translation, we need to set the size of the parameter when selecting candidate English words for each Chinese word [11]. We tested 5000 grammatically canonical Chinese sentences. The average number of words included is 6.7. The experimental results are shown in Table 4 and Table 5 (L=1000, d=5).

When n=20, the effect of the size of c on translation

The multiple c of the maximum back translation rate | 0.01 | 0.1 | 0.2 | 0.25 | 0.3 |

Average time spent per sentence | 18.65s | 17.25s | 14.76s | 14.68s | 13.12s |

Evaluation results | 43.30% | 50.18% | 50.25% | 50.40% | 50.10% |

When n=10, the effect of the size of c on translation

The multiple c of the maximum back translation rate | 0.01 | 0.1 | 0.2 | 0.25 | 0.3 |

Average time spent per sentence | 18.35s | 17.15s | 14.73s | 14.62s | 13.08s |

Evaluation results | 44.60% | 50.20% | 50.34% | 50.40% | 50.10% |

In Chinese-English translation, a Chinese word _{j}_{i}

Chinese and English are very different languages. Although we can filter out most of the completely wrong translations for each Chinese word through Experiment 2, other differences are not well resolved by the heuristic function alone. So we added extended nodes to make the system full of options [12]. The corpus we selected is the same as in Experiment 2. The experimental results are shown in Table 6 (L=1000, c=0.25, n=10).

The effect of increasing the number of extended nodes d on translation

Increase the number of extension nodes d | 0 (only the best node) | 5 | 10 |
---|---|---|---|

Average time spent per sentence | 6.02s | 14.65s | 22.87s |

Evaluation results | 40.10% | 50.40% | 49.80% |

Some hypotheses have high heuristic scores, but the translations obtained by searching in this direction are not good. For example, the correct word translation rate in a particular translation obtained may be relatively high [13]. The order between words is far from what is expected. This happens because the heuristic we use always overestimates the remaining cost. We always estimate where the distortion is most significant for the distorted case. Sometimes, there is not such a significant distortion. Therefore, the translation obtained by searching in this direction may be far from the correct result.

Consequently, ly expand the optimal noandlso expand other nodes according to the prefix score. This gives search more options. This will alleviate the above situation. If too many nodes are developed, the search time will be prolonged. Too few, and you may miss better hypotheses. We see that scaling up to five nodes is a good choice with a limited hypothetical number of 1000.

We have studied and improved a Lagrangian search algorithm based on a Lagrangian mathematical algorithm. We apply the improved algorithm to Chinese-English machine translation. In the experiment, we found that statistical machine translation has higher accuracy in finding the target word because it considers the relationship between words. Since better translations may be missed by the heuristic search alone, we conduct a partial width search along with the Lagrangian tracking. Experiments show that the quality and efficiency of translation are relatively more satisfactory. Through experiments, we realize that statistical machine translation is somewhat dependent on a corpus, consuming a lot of time and space. Therefore, we spend more time on word reorganization in the search.

#### When n=20, the effect of the size of c on translation

The multiple c of the maximum back translation rate | 0.01 | 0.1 | 0.2 | 0.25 | 0.3 |

Average time spent per sentence | 18.65s | 17.25s | 14.76s | 14.68s | 13.12s |

Evaluation results | 43.30% | 50.18% | 50.25% | 50.40% | 50.10% |

#### Hypothetical effect of column size L on translation

Suppose the maximum length of the queue is N | 500 | 1000 | 1500 | 2000 |

Time spent translating a sentence | 11.34s | 14.65s | 24.89s | 39.64s |

Evaluation results | 40% | 50.50% | 50.56% | 50.56% |

#### When n=10, the effect of the size of c on translation

The multiple c of the maximum back translation rate | 0.01 | 0.1 | 0.2 | 0.25 | 0.3 |

Average time spent per sentence | 18.35s | 17.15s | 14.73s | 14.62s | 13.08s |

Evaluation results | 44.60% | 50.20% | 50.34% | 50.40% | 50.10% |

#### Parameters and scale of language models

Parameter | Unary model parameters | Binary model parameters | Ternary model parameters |
---|---|---|---|

Number | 20000 | 173894 | 355043 |

#### Parameter information and scale of translation models

Parameter | Number |
---|---|

English part of speech C(e) | 129786 |

Chinese part of speech C(c) | 145083 |

P(count, C(e), C(c)) twist rate | 73888 |

P(e|c) back translation rate | 331796 |

P(c|e) translation rate | 331796 |

P(⊄ |e) reproduction rate | 129775 |

#### The effect of increasing the number of extended nodes d on translation

Increase the number of extension nodes d | 0 (only the best node) | 5 | 10 |
---|---|---|---|

Average time spent per sentence | 6.02s | 14.65s | 22.87s |

Evaluation results | 40.10% | 50.40% | 49.80% |

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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 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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