Adaptive Sparse Group Lasso untuk Estimasi Fungsi Intensitas Multitype Poisson Point Process (Studi Kasus: Pemodelan Sebaran Pohon di Pulau Barro Colorado)

Assadiky, Refki (2026) Adaptive Sparse Group Lasso untuk Estimasi Fungsi Intensitas Multitype Poisson Point Process (Studi Kasus: Pemodelan Sebaran Pohon di Pulau Barro Colorado). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Spatial point pattern merupakan sekumpulan lokasi kejadian atau objek dalam suatu wilayah tertentu dan analisis data point pattern yang melibatkan covariate sudah berkembang seiring kemajuan teknologi pengambilan dan pemrosesan data. Penelitian ini terinspirasi dari data spesies pohon di Barro Colorado Island (BCI) yang telah banyak digunakan dalam penelitian spatial point process. Pada data tersebut, digunakan 6 spesies pohon dan 13 faktor lingkungan. Pada penelitian ini dikonstruksi model inhomogeneous multitype Poisson point process (IMPP) yang dapat melakukan analisis data secara simultan. Metode estimasi parameter pada model IMPP menggunakan pendekatan Berman-Turner (BT) dan Random Quadrature (RQ). Model selanjutnya ditambahkan metode regularisasi adaptive sparse group lasso (ASGL) yang memungkinkan seleksi variabel di tingkat group dan individu, kemudian dalam memilih pendekatan terbaik dilakukan studi simulasi, pemilihan pendekatan terbaik dilihat dari metriks evaluasi, rata-rata jumlah dummy point dan rata-rata waktu komputasi serta dalam menentukan hasil estimasi parameter terbaik dipilih berdasarkan nilai bayesian information criteria (BIC) yang paling optimal. Berdasarkan hasil analisis studi simulasi, model IMPP-ASGL RQ manjadi model terbaik dengan nilai rata-rata jumlah dummy point 4 kali lebih sedikit dibandingkan model IMPP-ASGL BT mengakibatkan waktu komputasi lebih cepat 98%, sedangkan untuk metriks evaluasi lainnya perbedaan kedua model tidak terlalu berbeda. Selanjutnya pemodelan dilakukan pada studi terapan, terlebih dahulu menggunakan IMPP RQ tanpa regularisasi selain untuk mendapatkan bobot untuk ASGL juga bisa mengetahui variabel yang berpengaruh, diperoleh bahwa kovergensi dan deviasi rata-rata dalam radius pencarian 15 pixel mayoritas tidak berpengaruh terhadap keberadaan enam species pohon. Sejalan dengan panambahan metode ASGL, untuk tunning paramater kedua α=0.9 diperoleh bahwa konvergensi tereliminasi secara group dan indeks multi-resolusi kedataran dasar lembah tereliminasi mayoritas secara individu, sehingga kedua variabel lingkungan tersebut tidak berpengaruh terhadap keberadaan enam spesies pohon di BCI dan dapat dihilangkan dalam model.
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Spatial point pattern refers to a set of event or object locations within a specific area, and the analysis of point pattern data involving covariates has advanced alongside the progress in data collection and processing technologies. This study is inspired by tree species data from Barro Colorado Island (BCI), which has been widely used in spatial point process research. In this dataset, six tree species and thirteen environmental factors are considered. In this study, an inhomogeneous multitype Poisson point process (IMPP) model is constructed, which enables simultaneous data analysis. The parameter estimation method for the IMPP model utilizes the Berman-Turner (BT) and Random Quadrature (RQ) approaches. The model is subsequently augmented with the adaptive sparse group lasso (ASGL) regularization method, which allows for variable selection at both the group and individual levels. A simulation study is then conducted to select the best approach, with the choice of the best method determined by evaluation metrics, including the average number of dummy points, average computation time, and the selection of the best parameter estimation results based on the optimal Bayesian Information Criteria (BIC) value. Based on the simulation study analysis, the IMPP-ASGL RQ model emerges as the best model, with an average number of dummy points four times fewer than the IMPP-ASGL BT model, resulting in 98% faster computation time. For other evaluation metrics, the difference between the two models is minimal. The modeling is then applied to a case study, starting with the IMPP RQ model without regularization. This approach not only helps obtain weights for ASGL but also identifies the influential variables. The results show that convergence and mean deviation within a 15-pixel search radius largely have no effect on the presence of the six tree species. With the addition of the ASGL method and parameter tuning at α=0.9, convergence is eliminated at the group level, and multi-resolution indices of valley flatness are mostly eliminated at the individual level. Therefore, these two environmental variables have no effect on the presence of the six tree species on BCI and can be removed from the model.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	adaptive sparse grooup lasso, Berman-Turner, inhomogenous multitype Poisson point process, metode regularisai, Random Quadrature, adaptive sparse grooup lasso, Berman-Turner, inhomogenous multitype Poisson point process, Random Quadrature, regularization method
Subjects:	Q Science > QA Mathematics > QA278 Cluster Analysis. Multivariate analysis. Correspondence analysis (Statistics)
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Refki Assadiky Assadiky
Date Deposited:	21 Jan 2026 06:13
Last Modified:	21 Jan 2026 06:13
URI:	http://repository.its.ac.id/id/eprint/129958

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