Comparisonof Matrix Decomposition in Null Space-Based LDA Method

Comparisonof Matrix Decomposition in Null Space-Based LDA Method

linear discriminant analysis; small sample size; null space;singular value decomposition (SVD);Cholesky decomposition; QRdecomposition

Problems with small sample sizesand high dimensionality are common in pattern recognition.Almost all machine learning algorithms degrade in high-dimensional data, so thatsingularities in the scatter matrices, the main problem of the Linear Discriminant Analysis (LDA) technique, might result.A null space-based LDA (NLDA) has been conceived to address the singularity issue. NLDA aims to maximize the distance between classesin the null space of the within-class scatter matrix.In the earliest research, the NLDA method was performed by computing eigenvalue decomposition and singular value decomposition (SVD). This research led to several new implementations of the NLDA method using other matrix decompositions.The new implementations include NLDA using Cholesky decomposition and NLDA using QR decomposition. This paper compares the performance of three NLDA methods using different matrix decompositions, namely SVD, Cholesky decomposition, and QR decomposition.Two sets of data were used in the experiments that used three different NLDA algorithms.To determine the performance of the NLDA methods, the classification accuracy of the three methods was measuredusing the Confusion Matrix. The results show that the NLDA method using SVD has the best performance when compared to the other two methods, achieving 77.8% accuracy for the Colon dataset and 98.8% accuracy for the TKI-resistance dataset

Carissa Devina Usman1,Farikhin2, Titi Udjiani

https://jurnal.iaii.or.id/index.php/RESTI/article/view/5637/937

Departmentof Mathematics, Facultyof Science and Mathematics, Diponegoro University, Semarang, Indonesia

05-06-2024

FAJAR BAGUS W

PDF

ENGLISH

TEXT