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Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern Recognition, CVPR (2009) 2790-2797] to cluster noisy data, and develops some novel theory demonstrating its correctness. In particular, the theory uses ideas from geometric functional analysis to show that the algorithm can accurately recover the underlying subspaces under minimal requirements on their orientation, and on the number of samples per subspace. Synthetic as well as real data experiments complement our theoretical study, illustrating our approach and demonstrating its effectiveness.

This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance how many subspaces there are nor do we have any information about their dimensions. We develop a novel geometric analysis of an algorithm named sparse subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern Recognition, 2009. CVPR 2009 (2009) 2790-2797. IEEE], which significantly broadens the range of problems where it is provably effective. For instance, we show that SSC can recover multiple subspaces, each of dimension comparable to the ambient dimension. We also prove that SSC can correctly cluster data points even when the subspaces of interest intersect. Further, we develop an extension of SSC that succeeds when the data set is corrupted with possibly overwhelmingly many outliers. Underlying our analysis are clear geometric insights, which may bear on other sparse recovery problems. A numerical study complements our theoretical analysis and demonstrates the effectiveness of these methods.

With the emergence of new classroom teaching modes such as STEM education, traditional classroom teaching and student cultivation are facing many new challenges, so this paper explores the use of knowledge mapping in teaching classrooms based on the STEM education perspective. The article first analyzes the basic theory of knowledge graphs and designs a knowledge graph architecture based on the relevant basic theory. It also proposes a personalized learning path generation and recommendation algorithm. Finally, 38 students majoring in educational technology were surveyed to test and explore the knowledge mapping approach proposed in this paper for STEM education. The results of the study indicate that the fifth and sixth groups, which utilized the personalized recommendation algorithm proposed in this paper, achieved the highest learning gains of 0.531 and 0.756, respectively.

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors D is large, one encounters a daunting problem in attempting to estimate a D-dimensional surface based on limited data. Fortunately, in many applications, the support of the data is concentrated on a d-dimensional subspace with d « D. Manifold learning attempts to estimate this subspace. Our focus is on developing computationally tractable and theoretically supported Bayesian nonparametric regression methods in this context. When the subspace corresponds to a locally-Euclidean compact Riemannian manifold, we show that a Gaussian process regression approach can be applied that leads to the minimax optimal adaptive rate in estimating the regression function under some conditions. The proposed model bypasses the need to estimate the manifold, and can be implemented using standard algorithms for posterior computation in Gaussian processes. Finite sample performance is illustrated in a data analysis example.

At present, Chinese colleges and universities pursue “innovative talents” more strongly than ever. The status quo of creativity is closely related to the relatively low success rate of Chinese college students’ entrepreneurship. This paper combs the research results on the impact of creativity on college students’ entrepreneurial intention, and conducts a confirmatory analysis on the regulatory effect of creativity on entrepreneurial intention of Chinese vocational college students. This paper takes creativity as the independent variable, takes entrepreneurial intention as the dependent variable, makes an empirical analysis on the final sample data of 508 vocational college students, taking Chinese vocational college students as the survey objects. We find that creativity has a positive and distinctive impact on entrepreneurial intention of Chinese vocational college students. At the same time, we can see that there are obvious differences between entrepreneurial cultures of different countries and creativity of college students. It is suggested that the Chinese government should guide college students to cultivate entrepreneurial thinking, bring innovative thinking and adventurous spirit into their study and life, and actively advocate the establishment of a diversified and sustainable entrepreneurial ecology.

When the traditional poetry translation model can not be applied to the translation requirements of poetry context, it is necessary to improve the backward translation model. To address the issues in the traditional translation model, this paper utilizes the error in the translation model of the improved clustering algorithm for correction. The poetry translation model’s overall framework is explained in detail, and each module code is analyzed. After optimizing the data in the model, the reasons for the model translation error are analyzed and corrected to achieve a perfect fit between the Chinese and English translations of the poems. The results of the study show that the errors in poetry translation are mainly caused by words and sentences, as analyzed in this paper. This paper also corrects the clustering algorithm for related errors and proposes a model for correcting translation errors in the Logistics Chaos Model. Finally, it is concluded that words and sentences are the key factors that affect the English translation of poetry. Compared with SDPS, LDifC, WFBC, LDivC, and FC, its correctness rate reaches more than 96%, 93%, 92%, 92%, and 95% after correction, respectively. Compared with the pre-correction, their accuracy increased by 0-3.06%, 3.06%-21.05%, 2.11%-10.2%, 4.35%-9.68%, and 0-8.25%, respectively. It can be seen that the translation model with an improved clustering algorithm proposed in this paper is of great significance for the improvement of the accuracy of the DWMA translation text model for an English translation of poetry.

In the evolving landscape of library services, propelled by advancements in Internet technology and service paradigms, this study utilizes cloud-based lending data from college libraries to improve user profiling and subject-specific lending. Integrating the K-means algorithm with a Boolean matrix-enhanced Apriori algorithm, we devise a data mining model that fine-tunes detecting patterns in user borrowing behaviors. This approach distinguishes five distinct subject areas: energy, computing, electronic communication, machinery, and environmental chemistry. The outcome reveals a bibliographic association rule mining confidence of up to 79.38%, a 30% increase over conventional methods. Moreover, it generates three notable 2-item sets. Our model introduces a groundbreaking way to offer personalized library services, significantly enriching the user experience with tailored subject information.

The need for advanced detection methods has become more critical in light of the increasing prevalence of network security incidents. This study proposes a novel approach to network security detection using a fuzzy data mining algorithm, addressing the rising challenges in big data processing and network security. The paper outlines the evolution of big data analytics by exploring the integration of network security detection, data mining, and structural feature analysis. Data for this research was collected using a sniffer device and underwent extensive preprocessing to ensure diversity and applicability. To overcome the limitations of traditional data mining, such as the issue of sharp boundaries, this method combines fuzzy logic with data mining techniques, enhancing conventional network security protocols. Simulation experiments demonstrate the efficacy of this fuzzy mining-based approach, with results showing 987,238 predicted positive cases, 93,951 of which were accurate. The method achieves an impressive 93.65% accuracy and 92.55% recall rate, proving its capability to promptly identify and mitigate suspicious network activities.

Education evolves with the times, and innovation in educational philosophy is a prerequisite for efficient teaching. The birth and development of big data have further expanded and deepened the vision of art education, and its application aims not only to understand individual interests and hobbies but, more importantly, to control the learning and development tendencies of the group from the macro context and to provide all-round support for the digitization of art education. This paper proposes a new pedagogical model, ROF-LGB, based on the LightGBM model and the rotating forest. 30 ten-fold hierarchical cross-validation analyses of the four models are then conducted. The ROF-LGB model has nearly 7% more micro-averages and 10% more macro-averages than the other three models. When all datasets were compared, the ROF-LGB model outperformed in both metrics by as much as 65.2% of the datasets and in the comparison of accuracy by 82.6%. Therefore, the ROF-LGB model has greatly improved the accuracy rate based on the rotating forest and LightGBM, making this system a good aid for innovative art education.

This paper aims to study how to innovate and develop the culture of the old industrial base of Northeast China in the environment of big data. In this paper, based on sorting out the big data processing process, a data mining model based on the Bayesian network is established, parameter learning is performed using great likelihood estimation, and the Bayes-Dilley scoring function is obtained by structure learning. Then, based on the trained network, the big data mining analysis is performed on the cultural industry of the old industrial base of northeast China and the northeast China cultural impression words on social networks. From 2018 to 2021, the successive annual growth values of the cultural industry of the old industrial base of northeast China are 119.835 billion yuan, 120.345 billion yuan, 115.764 billion yuan, 116.001 billion yuan, and the proportion of GDP increased from 2.11% raised to 2.38%. Among them, Jilin was raised from 2.14% to 2.46%, Heilongjiang from 2.65% to 2.72%, and Liaoning from 1.03% to 1.52%. The cultural innovation of the old industrial base in Northeast China under the environment of big data should abandon the traditional culture, find the cultural positioning, break through the thinking stereotype, create a new advanced culture, and change the ideology.