scholarly journals Penerapan Sparse Principal Component Analysis dalam Menghasilkan Matriks Loading yang Sparse

2018 ◽  
Vol 15 (2) ◽  
pp. 44
Author(s):  
Georgina M. Tinungki ◽  
Nurtiti Sunusi
Keyword(s):  
Principal Component Analysis ◽  
Sparse Matrix ◽  
Principal Component ◽  
Component Analysis ◽  
Sparse Principal Component Analysis ◽  
Sparse Pca ◽  
Variable Reduction ◽  
Zero Entry ◽  
Pca Method ◽  
New Variables

Abstract Sparse Principal Component Analysis (Sparse PCA) is one of the development of  PCA. Sparse PCA modifies new variables as a linier combination of  p old variables (original variable) which  is yielded by PCA method. Modifying new variables is conducted by producing a loading yang sparse matrix, such that old variable which is not effective (value of loading is zero) able be exit from PCA.  In this study, Sparse PCA method was applied on data of Indonesia Poverty population in 2015, that contains 13 variables and 34 observation with variable reduction such that yields 4 (four) new variables, which can explain 80.1% of total variance data. This study show, the loading matrix that has been yielded by using Sparse PCA method to become sparse with there exist 11 elements (loading value) zero entry of matrix, such that the model that has been produced to be simpler and easy to be interpreted. Keywords:  Principal Component Analysis, Sparse Principal Component Analysis, reduksi dimensi, matriks loading yang sparse Abstrak Sparse Principal Component Analysis (Sparse PCA) merupakan salah satu pengembangan dari metode PCA. Sparse PCA memodifikasi variabel-variabel baru yang merupakan kombinasi linear dari  variabel lama (variabel asli) yang dihasilkan oleh metode PCA. Pemodifikasian variabel baru ini dilakukan dengan dengan menghasilkan matriks loading yang sparse sehingga variabel lama yang tidak efektif (memiliki nilai loading sama dengan nol) dapat dikeluarkan dari model PCA. Pada penelitian ini, metode Sparse PCA diterapkan pada data Indikator Kemiskinan Penduduk Indonesia Tahun 2015 yang memuat 13 variabel dan 34 observasi dengan reduksi variabel menghasilkan 4 (empat) variabel baru yang telah mampu menjelaskan 80,1% dari total variansi data. Hasil penelitian menunjukkan, matriks loading yang dihasilkan menggunakan metode Sparse PCA menjadi sparse dengan terdapat 11 elemen (nilai loading) matriks bernilai nol sehingga model yang dihasilkan menjadi lebih sederhana dan mudah untuk diinterpretasikan. Kata Kunci: Principal Component Analysis, Sparse Principal Component Analysis, reduksi dimensi, matriks loading yang sparse

Penerapan Sparse Principal Component Analysis dalam Menghasilkan Matriks Loading yang Sparse

2018 ◽  
Vol 15 (2) ◽  
pp. 42
Author(s):  
Georgina M. Tinungki ◽  
Nurtiti i Sunusi
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Sparse Principal Component Analysis ◽  
Sparse Pca

Sparse Principal Component Analysis (Sparse PCA) merupakan salah satu pengembangan dari metode PCA. Sparse PCA memodifikasi variabel-variabel baru yang merupakan kombinasi linear dari  variabel lama (variabel asli) yang dihasilkan oleh metode PCA. Pemodifikasian variabel baru ini dilakukan dengan dengan menghasilkan matriks loading yang sparse sehingga variabel lama yang tidak efektif (memiliki nilai loading sama dengan nol) dapat dikeluarkan dari model PCA. Pada penelitian ini, metode Sparse PCA diterapkan pada data Indikator Kemiskinan Penduduk Indonesia Tahun 2015 yang memuat 13 variabel dan 34 observasi dengan reduksi variabel menghasilkan 4 (empat) variabel baru yang telah mampu menjelaskan 80,1% dari total variansi data. Hasil penelitian menunjukkan, matriks loading yang dihasilkan menggunakan metode Sparse PCA menjadi sparse dengan terdapat 11 elemen (nilai loading) matriks bernilai nol sehingga model yang dihasilkan menjadi lebih sederhana dan mudah untuk diinterpretasikan.

scholarly journals Using ℓ1-Relaxation and Integer Programming to Obtain Dual Bounds for Sparse PCA

2021 ◽  
Author(s):  
Santanu S. Dey ◽  
Rahul Mazumder ◽  
Guanyi Wang
Keyword(s):  
Principal Component Analysis ◽  
Integer Programming ◽  
Principal Component ◽  
Component Analysis ◽  
Sparse Principal Component Analysis ◽  
Worst Case ◽  
Sparse Pca ◽  
Feasible Solutions ◽  
Dual Bounds

Dual Bounds of Sparse Principal Component Analysis Sparse principal component analysis (PCA) is a widely used dimensionality reduction tool in machine learning and statistics. Compared with PCA, sparse PCA enhances the interpretability by incorporating a sparsity constraint. However, unlike PCA, conventional heuristics for sparse PCA cannot guarantee the qualities of obtained primal feasible solutions via associated dual bounds in a tractable fashion without underlying statistical assumptions. In “Using L1-Relaxation and Integer Programming to Obtain Dual Bounds for Sparse PCA,” Santanu S. Dey, Rahul Mazumder, and Guanyi Wang present a convex integer programming (IP) framework of sparse PCA to derive dual bounds. They show the worst-case results on the quality of the dual bounds provided by the convex IP. Moreover, the authors empirically illustrate that the proposed convex IP framework outperforms existing sparse PCA methods of finding dual bounds.

The Design of Index about Corporate Governance Based on PCA Method

2014 ◽  
Vol 926-930 ◽  
pp. 4085-4088
Author(s):  
Chuan Jun Li
Keyword(s):  
Principal Component Analysis ◽  
Corporate Governance ◽  
Principal Components ◽  
Principal Component ◽  
Component Analysis ◽  
Contribution Rate ◽  
Variance Contribution ◽  
Pca Method

This article uses the PCA method (Principal component analysis) to evaluate the level of corporate governance. PCA is used to analyze the correlation among 10 original indicators, and extract some principal components so that most of the information of the original indicators is extracted. The formulation of the index of corporate governance can be got by calculating the weight based on the variance contribution rate of the principal component, which can comprehensively evaluate corporate governance.

scholarly journals Patch-Based Principal Component Analysis for Face Recognition

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Tai-Xiang Jiang ◽  
Ting-Zhu Huang ◽  
Xi-Le Zhao ◽  
Tian-Hui Ma
Keyword(s):  
Principal Component Analysis ◽  
Face Recognition ◽  
Nearest Neighbor ◽  
Spatial Information ◽  
Principal Component ◽  
Component Analysis ◽  
Two Dimensional ◽  
Face Images ◽  
Pca Method ◽  
Local Spatial Information

We have proposed a patch-based principal component analysis (PCA) method to deal with face recognition. Many PCA-based methods for face recognition utilize the correlation between pixels, columns, or rows. But the local spatial information is not utilized or not fully utilized in these methods. We believe that patches are more meaningful basic units for face recognition than pixels, columns, or rows, since faces are discerned by patches containing eyes and noses. To calculate the correlation between patches, face images are divided into patches and then these patches are converted to column vectors which would be combined into a new “image matrix.” By replacing the images with the new “image matrix” in the two-dimensional PCA framework, we directly calculate the correlation of the divided patches by computing the total scatter. By optimizing the total scatter of the projected samples, we obtain the projection matrix for feature extraction. Finally, we use the nearest neighbor classifier. Extensive experiments on the ORL and FERET face database are reported to illustrate the performance of the patch-based PCA. Our method promotes the accuracy compared to one-dimensional PCA, two-dimensional PCA, and two-directional two-dimensional PCA.

scholarly journals Deteksi Formalin Pada Buah Tomat (Lycopersicum esculentum Mill) Dengan Teknologi Hidung Elektronik (Electronic Nose)

2019 ◽  
Vol 4 (2) ◽  
pp. 359-366
Author(s):  
Irfan Maibriadi ◽  
Ratna Ratna ◽  
Agus Arip Munawar
Keyword(s):  
Principal Component Analysis ◽  
Electronic Nose ◽  
Principal Component ◽  
Component Analysis ◽  
Lycopersicum Esculentum ◽  
Olfactory Ability ◽  
Pca Method ◽  
The Difference ◽  
Electronic Nose Technology

Abstrak,  Tujuan dari penelitian ini adalah mendeteksi kandungan dan kadar formalin pada buah tomat dengan menggunakan instrument berbasis teknologi Electronic nose. Penelitian ini menggunakan buah tomat yang telah direndam dengan formalin dengan kadar 0.5%, 1%, 2%, 3%, 4%, dan buah tomat tanpa perendaman dengan formalin (0%). Jumlah sampel yang digunakan pada penelitian ini adalah sebanyak 18 sampel. Pengukuran spektrum beras menggunakan sensor Piezoelectric Tranducer. Klasifikasi data spektrum buah tomat menggunakan metode Principal Component Analysis (PCA) dengan pretreatment nya adalah Gap Reduction. Hasil penelitian ini diperoleh yaitu: Hidung elektronik mulai merespon aroma formalin pada buah tomat pada detik ke-8.14, dan dapat mengklasifikasikan kandungan dan kadar formalin pada buah tomat pada detik ke 25.77. Hidung elektronik yang dikombinasikan dengan metode principal component analysis (PCA) telah berhasil mendeteksikandungan dan kadar formalin pada buah tomat dengan tingkat keberhasilan sebesar 99% (PC-1 sebesar 93% dan PC-2 sebesar 6%). Perbedaan kadar formalin menjadi faktor utama yang menyebabkan Elektronik nose mampu membedakan sampel buah tomat yang diuji, karena semakin tinggi kadar formalin pada buah tomat maka aroma khas dari buah tomat pun semakin menghilang, sehingga Electronic nose yang berbasis kemampuan penciuman dapat membedakannya.Detect Formaldehyde on Tomato (Lycopersicum esculentum Mill) With Electronic Nose TechnologyAbstract, The purpose of this study is to detect the contents and levels of formalin in tomatoes by using instruments based on Electronic nose technology. This study used tomatoes that have been soaked in formalin with a concentration of 0.5%, 1%, 2%, 3%, 4%, 5% and tomatoes without soaking with formalin (0%). The samples in this study were 18 samples. The measurements of the intensity on tomatoes aroma were using Piezoelectric Transducer sensors. The classification of tomato spectrum data was using the Principal Component Analysis (PCA) method with Gap Reduction pretreatment. The results of this study were obtained: the Electronic nose began to respond the smell of formalin on tomatoes at 8.14 seconds, and it could classify the content and formalin levels in tomatoes at 25.77 seconds. Electronic nose combined with the principal component analysis (PCA) method have successfully detected the content and levels of formalin in tomatoes with a success rate at 99% (PC-1 of 93% and PC-2 of 6%). The difference of grade formalin levels is the main factor that causes Electronic nose to be able to distinguish the tomato samples tested, because the higher of formalin content in tomatoes, the distinctive of tomatoes aroma is increasingly disappearing. Thereby, the Electronic nose based on  the olfactory ability can distinguish them. 

Integrative sparse principal component analysis

2018 ◽  
Vol 166 ◽  
pp. 1-16 ◽  
Author(s):  
Kuangnan Fang ◽  
Xinyan Fan ◽  
Qingzhao Zhang ◽  
Shuangge Ma
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Sparse Principal Component Analysis
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