Formulasi Optimasi Diskrit untuk Penyelesaian Permasalahan Visualisasi Data

Abstract

The rapid development of computer technology has led to the accumulation of large amounts of high-dimensional data, creating challenges in analysis and visualization. Data visualization plays an important role in revealing patterns and relationships between variables, but the complexity of high-dimensional data often causes several problems, such as overlap, uneven data density, and difficult separation between clusters. Multidimensional Scaling (MDS) technique is one of the commonly used methods for dimensionality reduction, but it still has limitations in maintaining global structure and handling non-ideal data distribution. Therefore, this study proposes an MDS-based optimization formulation that aims to improve the quality of data visualization by minimizing distance distortion, improving local distribution, and sharpening the separation between clusters. This approach is developed based on a review of MDS+, MSSPD, Geometric MDS, and UAMDS techniques, which have demonstrated advantages in handling high-dimensional data. With this optimization formulation, data representation in a low-dimensional space is expected to be clearer, more informative, and adaptive to data noise and the addition of new data. In addition, this method can be applied in various fields that require complex data analysis, such as big data visualization, image processing, and data-based decision making. The results of this research are expected to make a significant contribution to the development of more efficient and accurate data visualization techniques, so as to improve data exploration and interpretation more optimally.