Comparison of Matrix Decomposition in Null Space-Based LDA Method
Problems with small sample sizes and high dimensionality are common in pattern recognition. Almost all machine learning algorithms degrade in high-dimensional data, so that singularities in the scatter matrices, the main problem of the Linear Discriminant Analysis (LDA) technique, might result. A nu...
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Ikatan Ahli Informatika Indonesia
2024-06-01
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| Series: | Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi) |
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| Online Access: | https://jurnal.iaii.or.id/index.php/RESTI/article/view/5637 |
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| author | Carissa Devina Usman Farikhin Titi Udjiani |
| author_facet | Carissa Devina Usman Farikhin Titi Udjiani |
| author_sort | Carissa Devina Usman |
| collection | DOAJ |
| description | Problems with small sample sizes and high dimensionality are common in pattern recognition. Almost all machine learning algorithms degrade in high-dimensional data, so that singularities 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 classes in the null space of the within-class scatter matrix. In the first research, the NLDA method was performed by computing the eigenvalue decomposition and singular value decomposition (SVD). This research led to several new implementations of the NLDA method that use 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 that use 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 measured using the confusion matrix. The results show that the NLDA method using SVD has the best performance when compared to the other two methods, achieving a precision of 77.8% accuracy for the Colon dataset and a precision of 98.8% accuracy for the TKI-resistance dataset. |
| format | Article |
| id | doaj-art-ff34df8498fe43a9b96df6747baf3537 |
| institution | Kabale University |
| issn | 2580-0760 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Ikatan Ahli Informatika Indonesia |
| record_format | Article |
| series | Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi) |
| spelling | doaj-art-ff34df8498fe43a9b96df6747baf35372025-01-13T03:33:46ZengIkatan Ahli Informatika IndonesiaJurnal RESTI (Rekayasa Sistem dan Teknologi Informasi)2580-07602024-06-018336136710.29207/resti.v8i3.56375637Comparison of Matrix Decomposition in Null Space-Based LDA MethodCarissa Devina Usman0Farikhin1Titi Udjiani2Diponegoro UniversityDiponegoro UniversityDiponegoro UniversityProblems with small sample sizes and high dimensionality are common in pattern recognition. Almost all machine learning algorithms degrade in high-dimensional data, so that singularities 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 classes in the null space of the within-class scatter matrix. In the first research, the NLDA method was performed by computing the eigenvalue decomposition and singular value decomposition (SVD). This research led to several new implementations of the NLDA method that use 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 that use 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 measured using the confusion matrix. The results show that the NLDA method using SVD has the best performance when compared to the other two methods, achieving a precision of 77.8% accuracy for the Colon dataset and a precision of 98.8% accuracy for the TKI-resistance dataset.https://jurnal.iaii.or.id/index.php/RESTI/article/view/5637linear discriminant analysissmall sample sizesingular value decomposition (svd)cholesky decompositionqr decomposition |
| spellingShingle | Carissa Devina Usman Farikhin Titi Udjiani Comparison of Matrix Decomposition in Null Space-Based LDA Method Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi) linear discriminant analysis small sample size singular value decomposition (svd) cholesky decomposition qr decomposition |
| title | Comparison of Matrix Decomposition in Null Space-Based LDA Method |
| title_full | Comparison of Matrix Decomposition in Null Space-Based LDA Method |
| title_fullStr | Comparison of Matrix Decomposition in Null Space-Based LDA Method |
| title_full_unstemmed | Comparison of Matrix Decomposition in Null Space-Based LDA Method |
| title_short | Comparison of Matrix Decomposition in Null Space-Based LDA Method |
| title_sort | comparison of matrix decomposition in null space based lda method |
| topic | linear discriminant analysis small sample size singular value decomposition (svd) cholesky decomposition qr decomposition |
| url | https://jurnal.iaii.or.id/index.php/RESTI/article/view/5637 |
| work_keys_str_mv | AT carissadevinausman comparisonofmatrixdecompositioninnullspacebasedldamethod AT farikhin comparisonofmatrixdecompositioninnullspacebasedldamethod AT titiudjiani comparisonofmatrixdecompositioninnullspacebasedldamethod |