Topic modeling stands as a well-explored and foundational challenge in the text mining domain. Traditional topic schemes based on word co-occurrences, aim to expose the latent semantic structure embedded in a document corpus. Nevertheless, the inherent brevity of short texts introduces data sparsity, hindering the effectiveness of conventional topic models and yielding suboptimal outcomes for such text. Typically, short texts encompass a restricted number of topics, necessitating a grasp of relevant background knowledge for a comprehensive understanding of semantic content. Motivated by the observed information, this research introduces a novel Deep Auto encoder Graph Regularized Non-negative Matrix Factorization algorithm (DAGR-NMF) to uncover significant and meaningful topics within short document contents. The three main phases of proposed work are preprocessing, feature extraction and topic modeling. Initially, the data are preprocessed using natural language preprocessing tasks such as stop word removal, stemming and lemmatizing. Then, feature extraction is performed using hybrid Absolute Deviation Factors-Class Term Frequency (ADF-CTF) to capture the most relevant information from the text. Finally, topic modeling task is executed using proposed DAGR-NMF approach. Experimental findings demonstrate that the introduced DAGR-NMF model outperforms all other techniques by achieving NMI values of 0.852, 0.857, 0.793, and 0.831 on associated press, political blog datasets, 20NewsGroups, and News category dataset, respectively.

The controlling and synchronizing chaotic systems (CSs) are crucial aspects of engineering, with broad applications across various applied sciences, such as secure communications, nonlinear circuit design, biomedical engineering, and image processing. This paper deals with the complex problem of achieving finite-time projective synchronization for uncertain CSs with incommensurate non-integer orders using adaptive fuzzy sliding-mode control (AFSMC). Specifically, we focus on practical projective synchronization, introducing two novel control approaches that effectively mitigate the chattering phenomenon, a common issue in conventional sliding mode control. To achieve this, two innovative non-singular sliding surfaces with finite-time properties are formulated. This type of sliding surface enhances projective synchronization accuracy, response speed, and robustness. The adaptive fuzzy logic systems, known for their universal approximation capability, are employed to estimate continuous functional uncertainties. We rigorously analyzed the stability of both approaches using Lyapunov’s direct method. Extensive simulations confirm the effectiveness and benefits of our proposed methods. These methods significantly reduce or eliminate chattering and achieve practical projective synchronization in a finite time. This makes them well-suited for real-world applications in complex CSs.