Slide Presentasi EM Algorithm (Play Tennis & Brain Tissue Segmentation)

Jan 29, 20140 likes1,398 views

Hendri Karisma

Slide Presentasi Machine Learning, EM-Algorithm (Kasus Play Tennis dan Brain tissue Segmentation pada citra MRI)

Referensi
●

Lecture Notes, Andrew Ng

●

Machine Learning, Tom M. Mitchell

●

●

Maximum Likelihood from Incomplete Data via
the EM Algorithm, A. P. Dempster; N. M. Laird;
D. B. Rubin; 1977
Dll

Konsep EM
●

Maximum Likelihood Estimation (MLE)

●

Mixtures of Gaussians

●

Estimation-Maximization (EM)

●

Rate of Convergence

Maximum Likelihood Estimation
(MLE)
●

●

●

Sebuah dataset dengan instans sebanyak m
Parameter dari model p(x, z) akan disesuaikan dengan
data, likelihood diberikan berupa

Dengan Mixture of Gaussian

Maximum yang Digunakan Dalam
EM-Algorithm

Formula Gaussian
●

Gaussian Normal

●

Gaussian Multivariet (extension)
–

Perbedaannya adalah penggunaan matrik covariant
guna memperbaiki model yang dibangun.

Distribusi Gaussian Normal
●

Model distribusi data dengan mean μ dan variansi σ². Contoh:

Visualisasi Gaussian 3D dengan
Mean & Variance yang Berbeda

Contoh Distribusi Gaussian X1 dan
X2
●

Contoh penerapan:

Visualisasi Gaussian 3D
●

Contoh distribusi dan pemodelan dengan Gaussian

Estimation-Maximization (EM)
●

Iterasi yang terdiri dari dua langkah:

●

Step E (Estimation): mendekati z(i)

●

Step M (Maximization): memperbaharui
parameter

Fungsi E-M-Step
●

●

Fungsi E-Step, melakukan estimasi gaussian
awal dan akan di maksimalisasi oleh step M.
Fungsi M-Step, atau Maximization step,
melakukan perubahan parameter pada step
estimasi, sehingga akan merubah posisi
gaussian selanjutnya sehingga mencapai nilai
maksimum.

Slide Presentasi EM Algorithm (Play Tennis & Brain Tissue Segmentation)

Implementasi EM
●

Inisialisasi
–

–
●

Menentukan probabilitas sense P(Sk) dari jumlah cluster yang ditentukan
– total P(Sk) adalah 1
Menentukan probabilitas P(Vj|Sk): angka random

Langkah E
–

●

Langkah M
–

●

Calculate the posterior probability that Sk generated Ci
re-estimate P(Vj|Sk) and P(Sk)

Perhitungan Konvergensi
–

Hitung model likelihood score: l(C|u) = Sum_I[Log_K(P(Ci|Sk)*P(Sk))]

–

Jika | model score baru – model score lama | < threshold, konvergen

Pengujian dengan PlayTennis
●

Pengujian dengan dataset 1 PlayTennis (14 instance)

Cont'd
●

Representasi instance
biner (0 dan 1), akurasi
57%

●

Representasi instance
index (0-2), akurasi 50%

EKSPERIMEN EM
(Partial Volume Segmentation of Brain)
●

Deskripsi Data

●

Hasil Eksperimen

●

Kesimpulan

Partial Volume Segmentation
of Brain
●

●

●

Dibagi menjadi 3 cluster utama + 3 irisan
cluster.
3 Cluster : White Matter, Black Matter, CSF
(Cerebrospinal Fluid)
Data yang diambil adalah histogram dari MRI

Kesimpulan
●

●

●

●

Dalam Algoritma Clustering Expectation Maximization Data harus
didistribusikan dalam bentuk mixture gaussian, dan pada kasus eksplorasi
kedua, mixture dapat memanfaatkan histogram citra MRI.
Dalam Eksplorasi kedua terdapat perbedaan implementasi dengan paper
pertama, dan hasilnya pun berbeda secara signifikan, tidak semua terdistribusi
pada setiap cluster dan penyebab adalah data yang digunakan hanya 1 citra
MRI pada eksplorasi sedangkan pada paper referensi utama 16 MRI.
EM Algorithm untuk kasus segmentasi jaringan otak menghasilkan
kompleksitas yang cukup tinggi.
Belum dapat ditarik kesimpulan mengenai hasil dari eksplorasi karena dataset
yang digunakan belum tepat digunakan dalam proses eksplorasi untuk
mendapatkan akurasi dari implementasi em-algorithm dalam partial volume
segmentation of human brain.

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Slide Presentasi EM Algorithm (Play Tennis & Brain Tissue Segmentation)

1. Expectation-Maximalization (EM) Algorithm Hendri Karisma 23512060 Luqman Abdul Mushawwir 23512146

2. Referensi ● Lecture Notes, Andrew Ng ● Machine Learning, Tom M. Mitchell ● ● Maximum Likelihood from Incomplete Data via the EM Algorithm, A. P. Dempster; N. M. Laird; D. B. Rubin; 1977 Dll

3. Konsep EM ● Maximum Likelihood Estimation (MLE) ● Mixtures of Gaussians ● Estimation-Maximization (EM) ● Rate of Convergence

4. Maximum Likelihood Estimation (MLE) ● ● ● Sebuah dataset dengan instans sebanyak m Parameter dari model p(x, z) akan disesuaikan dengan data, likelihood diberikan berupa Dengan Mixture of Gaussian

5. Maximum yang Digunakan Dalam EM-Algorithm

6. Formula Gaussian ● Gaussian Normal ● Gaussian Multivariet (extension) – Perbedaannya adalah penggunaan matrik covariant guna memperbaiki model yang dibangun.

7. Distribusi Gaussian Normal ● Model distribusi data dengan mean μ dan variansi σ². Contoh:

8. Visualisasi Gaussian 3D dengan Mean & Variance yang Berbeda

9. Contoh Gaussian pada histogram

10. Contoh Distribusi Gaussian X1 dan X2 ● Contoh penerapan:

11. Visualisasi Gaussian 3D ● Contoh distribusi dan pemodelan dengan Gaussian

12. Gaussian Multivariate

13. Gaussian Multivariate

14. Mixture Gaussian

15. Estimation-Maximization (EM) ● Iterasi yang terdiri dari dua langkah: ● Step E (Estimation): mendekati z(i) ● Step M (Maximization): memperbaharui parameter

16. Fungsi E-M-Step ● ● Fungsi E-Step, melakukan estimasi gaussian awal dan akan di maksimalisasi oleh step M. Fungsi M-Step, atau Maximization step, melakukan perubahan parameter pada step estimasi, sehingga akan merubah posisi gaussian selanjutnya sehingga mencapai nilai maksimum.

18. Implementasi EM ● Inisialisasi – – ● Menentukan probabilitas sense P(Sk) dari jumlah cluster yang ditentukan – total P(Sk) adalah 1 Menentukan probabilitas P(Vj|Sk): angka random Langkah E – ● Langkah M – ● Calculate the posterior probability that Sk generated Ci re-estimate P(Vj|Sk) and P(Sk) Perhitungan Konvergensi – Hitung model likelihood score: l(C|u) = Sum_I[Log_K(P(Ci|Sk)*P(Sk))] – Jika | model score baru – model score lama | < threshold, konvergen

19. Pengujian dengan PlayTennis ● Pengujian dengan dataset 1 PlayTennis (14 instance)

20. Cont'd ● Representasi instance biner (0 dan 1), akurasi 57% ● Representasi instance index (0-2), akurasi 50%

21. EKSPERIMEN EM (Partial Volume Segmentation of Brain) ● Deskripsi Data ● Hasil Eksperimen ● Kesimpulan

22. Partial Volume Segmentation of Brain ● ● ● Dibagi menjadi 3 cluster utama + 3 irisan cluster. 3 Cluster : White Matter, Black Matter, CSF (Cerebrospinal Fluid) Data yang diambil adalah histogram dari MRI

23. Input Data

24. Hasil Eksperimen

25. Hasil dalam Histogram

26. Kesimpulan ● ● ● ● Dalam Algoritma Clustering Expectation Maximization Data harus didistribusikan dalam bentuk mixture gaussian, dan pada kasus eksplorasi kedua, mixture dapat memanfaatkan histogram citra MRI. Dalam Eksplorasi kedua terdapat perbedaan implementasi dengan paper pertama, dan hasilnya pun berbeda secara signifikan, tidak semua terdistribusi pada setiap cluster dan penyebab adalah data yang digunakan hanya 1 citra MRI pada eksplorasi sedangkan pada paper referensi utama 16 MRI. EM Algorithm untuk kasus segmentasi jaringan otak menghasilkan kompleksitas yang cukup tinggi. Belum dapat ditarik kesimpulan mengenai hasil dari eksplorasi karena dataset yang digunakan belum tepat digunakan dalam proses eksplorasi untuk mendapatkan akurasi dari implementasi em-algorithm dalam partial volume segmentation of human brain.

Slide Presentasi EM Algorithm (Play Tennis & Brain Tissue Segmentation)

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