The latent semantic analysis (LSA) is a mathematical/statistical way of discovering hidden concepts between terms and documents or within a document collection (i.e., a large corpus of text). Each document of the corpus and terms are expressed as a vector with elements corresponding to these concepts to form a term-document matrix. Then, the LSA uses a low-rank approximation to the term-document matrix in order to remove irrelevant information, to extract more important relations, and to reduce the computational time. The irrelevant information is called as “noise” and does not have a noteworthy effect on the meaning of the document collection. This is an essential step in the LSA. The singular value decomposition (SVD) has been the main tool obtaining the low-rank approximation in the LSA. Since the document collection is dynamic (i.e., the term-document matrix is subject to repeated updates), we need to renew the approximation. This can be done via recomputing the SVD or updating the SVD. However, the computational time of recomputing or updating the SVD of the term-document matrix is very high when adding new terms and/or documents to preexisting document collection. Therefore, this issue opened the door of using other matrix decompositions for the LSA as ULV- and URV-based decompositions. This study shows that the truncated ULV decomposition (TULVD) is a good alternative to the SVD in the LSA modeling.

Nowadays digital environment, the rapid duplication and unauthorized use of color images shared online have led to increasing concerns regarding copyright infringement and data security. Therefore, the development of effective and robust methods for protecting digital content has become critically important. In this study, an integrated digital watermarking method is proposed to ensure copyright protection and data security for both color and medical images. In the proposed approach, watermark embedding is performed by jointly applying Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD) on the blue (B) color channel of the cover image. The watermark image is preprocessed using a dimension reduction technique and optimized through the Grey Wolf Optimization (GWO) algorithm. The optimized watermark is then embedded into the cover image, and inverse transformations are applied to obtain the watermarked image. The performance of the proposed algorithm is evaluated on standard test images under various attack scenarios. Imperceptibility is assessed using Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), while robustness is measured using the Normalized Correlation (NC) and Bit Error Rate (BER) metrics. Experimental results demonstrate that the proposed method achieves high imperceptibility and successfully preserves watermark information under different attacks. Comparisons with related studies in the literature indicate that the proposed approach is competitive and, in some cases, superior in terms of both imperceptibility and robustness. Consequently, the proposed method provides an effective and reliable digital watermarking solution for color images.