Diny Syarifah Sany
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Linear Algebra for Modern Statistics: Efficiency and Interpretability Challenges in Regression and PCA Khoerul Rahman; Diny Syarifah Sany
Jurnal Ilmiah Informatika dan Komputer Vol. 2 No. 1 (2025): June 2025
Publisher : CV.RIZANIA MEDIA PRATAMA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.69533/tsygq116

Abstract

The development of modern statistics faces the challenge of high-dimensional data complexity, which requires an efficient yet interpretable approach. Linear algebra offers a solution through matrix representation, but its limitations in non-linear contexts and high-dimensional interpretation need to be examined in greater depth. This study analyzes algebraic methods through case studies of linear regression (normal equation solutions) and PCA (eigen decomposition), tested on synthetic datasets and MNIST. The results show: (1) a 40% computational acceleration in matrix-based regression, (2) PCA successfully reduces the MNIST dimension to 3 main components (retaining 85% of the variance), but a survey reveals that 73% of practitioners have difficulty interpreting high-dimensional components. Despite its efficiency advantages, algebraic methods require further development through hybrid approaches (kernel PCA) and interpretable techniques to address limitations in linearity and high-dimensional complexity.
Matrix in Linear Algebra for Modern Computational Solutions Miral Setiawan; Diny Syarifah Sany
Jurnal Ilmiah Informatika dan Komputer Vol. 2 No. 1 (2025): June 2025
Publisher : CV.RIZANIA MEDIA PRATAMA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.69533/wcv24y31

Abstract

This study aims to examine the basic concepts of matrix in linear algebra through conceptual and computational approaches. Matrix are understood not only as computational tools, but also as representations of linear transformations and relationships in vector spaces. The method used is a combination of theoretical analysis and numerical experiments using NumPy and SymPy. A case study was conducted by constructing a distance matrix between 20 districts in Cianjur in the form of a 20x20 symmetric matrix. The results show that the determinant of the matrix reflects the stability of the spatial system, while the inverse is useful for solving systems of linear equations. Eigenvalue and eigenvector analysis identified the most strategically located districts within the network. Additionally, the farthest distance between districts was successfully determined and can be utilized for more efficient transportation route planning. In conclusion, a conceptual and computational understanding of matrix structure is crucial, not only in linear algebra theory but also in practical applications such as regional planning and transportation network management.
Generating Unimodular Matrix in Python for Solving Systems of Linear Equations Muhammad Irfan Mustakim; Diny Syarifah Sany
Jurnal Ilmiah Informatika dan Komputer Vol. 2 No. 2 (2025): Desember 2025
Publisher : CV.RIZANIA MEDIA PRATAMA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.69533/8k7k9p54

Abstract

Linear equation systems with integer solutions are widely used in modern computing fields such as cryptography and optimization, but conventional methods often produce inaccurate decimal solutions. To address this issue, this research developed a Python program based on NumPy that can efficiently generate unimodular matrices. The method involves three main stages: initializing an upper triangular matrix with diagonal elements of ±1, filling non-diagonal elements with random integers, and transforming the matrix through elementary row operations. Test results show that the program successfully generates unimodular matrices of sizes 4×4 to 9×9 with perfect accuracy (determinant exactly ±1), an average computation time of 0.5 seconds for a 4×4 matrix, and efficient memory usage (under 20 MB). The solutions to the linear equations are always exact integers, meeting the requirements for high-precision computation. This implementation not only provides a practical solution for integer linear equation systems but also opens up opportunities for applications in cryptographic algorithm development and optimization techniques that require absolute precision. The findings of this research confirm that numerical computation approaches can produce both accurate and efficient mathematical solutions.
Penerapan Algoritma A* Pathfinding dan Behavior Tree Pada Perilaku Non-Playable Character (NPC) pada Game Labirin “Dungeon Escape” Wildan Fadilah; Diny Syarifah Sany
SABER : Jurnal Teknik Informatika, Sains dan Ilmu Komunikasi Vol. 3 No. 4 (2025): Oktober: Jurnal Teknik Informatika, Sains dan Ilmu Komunikasi
Publisher : STIKes Ibnu Sina Ajibarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59841/saber.v3i4.3206

Abstract

This study focuses on the development of an intelligent enemy behavior system in the 2D maze game Dungeon Escape by combining the A* algorithm for pathfinding and a Behavior Tree (BT) structure for decision-making. The main objective is to enhance Non-Playable Character (NPC) intelligence, enabling more adaptive and realistic interactions with players. The A* algorithm is implemented to allow NPCs to pursue players through the shortest and most efficient paths while avoiding obstacles on a grid-based map. Meanwhile, the Behavior Tree framework is designed to manage NPC actions based on dynamic conditions, such as attacking when in close proximity, chasing players within a certain detection radius, and retreating to the original guard position when the player leaves the active zone. The research methodology involves a comprehensive literature review, system design, and implementation using the Unity game engine. Testing procedures consist of both white-box and black-box approaches to evaluate the correctness, functionality, and efficiency of the system. The results indicate that all major game features—including player navigation, combat mechanics, key collection, enemy pathfinding, and user interface interactions—operate smoothly as expected. Furthermore, NPCs exhibit adaptive behavior by dynamically switching between patrolling, chasing, and attacking modes depending on the player’s location and proximity. Performance testing shows that the integrated A* and BT system runs efficiently without significant delays or instability, even in higher-level stages with more complex layouts. The final game prototype includes seven progressively challenging levels, offering players an engaging and dynamic gameplay experience. This study demonstrates that the combination of pathfinding and decision-making algorithms provides an effective solution for designing intelligent NPCs, improving both realism and entertainment value in 2D games. The findings are expected to serve as a useful reference for future research and development in AI-based game design, particularly in the context of Unity game projects.