[PDF] - Stochastic Systems Lab, Dept. of Computer Science and Automation PDF Document

SLIDE 1

✁

✂✄ ✄ ☎ ✆ ✝ ✞ ✟ ✝ ✄ ✠ ☎✡ ☛ ✡ ☞ ☎✌ ✠ ✝ ☛ ✍✏✎ ☎ ✑ ☛ ✄ ✠ ✂ ✝ ✒✓ ✌ ☛ ☎ ✝ ✄ ✔ ☎ ✂ ✆ ☎✡ ✄ ✔ ☎ ☛ ✕ ✠ ✖✗ ✆ ✘ ✙ ✂ ✡ ✡ ☛✚ ☎ ✆ ✛ ✗ ✆ ✜ ☛ ✝ ✂ ✆ ✟ ✁ ✂✄ ✄ ☎ ✆ ✝✢ ☎ ✌ ✗ ✕ ✝ ☛ ✄ ☛ ✗ ✝ ✣ ✤✥ ✦ ✧ ★ ✩ ★✪ ✫ ✬ ✭ ✮✯ ★ ✰ ★ ✦ ✥ ✱ ✫ ★ ✭ ✲ ✰ ✪ ✳ ★ ✩ ✴ ✵ ✫ ★ ✶ ★✷ ✫ ✸ ✫ ★✪ ✩ ★ ✹ ★ ✰ ✺ ✻✼ ✽ ✾ ✿❀ ✻ ❁ ✽ ✺ ❂❃❀ ✻❄ ❅ ❀ ❆ ✿❇ ✼ ❈ ✿ ✻✼ ❈ ❂ ❉ ❄ ❊ ✻ ❋ ✼

❍

✼ ❅ ❊❏■ ✻ ❄ ❈ ✺ ✽ ❁ ❄ ❑ ✽ ❄ ✿ ❑ ▲ ▼ ■ ✻✼ ❅ ✿ ✻ ❁ ✼ ❑ ◆ ❑ ▲ ❁ ✿ ❑ ◆ ❑ ❀ ✻ ❁ ✻ ■ ✻ ❄ ✼

✺

✽ ❁ ❄ ❑ ✽ ❄ ❖ P ✿ ❑ ◗ ✿ ❘ ✼ ❈ ❄ ❙ ✿ ❈ ✽ ✾ ❚❱❯ ❲ ❲ ❳

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

❨

SLIDE 2

✎

✄ ✙ ☛ ✝ ☎ ✗ ✛ ☞ ✂ ✙ ✁ ✂ ❋ ✄ ❄ ✿ ❈ ❄ ❀ ✻ ✄ ❄ ❁ ◗ ✾ ❇ ✼ ❈ ❍ ❘ ✿ ❀ ❀ ❁ ☎ ❄ ❈ ✆ ✄ ✄ ❍ ✝ ❯ ❋ ✞ ✿ ✻ ✻❄ ❈ ❑ ✺ ❂ ❑ ✻ ✾ ❄ ❀ ❁ ❀ ✟ ❋ ❍ ✼ ❅ ❊ ✿ ✽ ✻ ✠ ❄ ❊ ❈ ❄ ❀ ❄ ❑ ✻ ✿ ✻ ❁ ✼ ❑ ❳ ❋ ▼ ❑✡ ☛ ✽ ❁ ❄ ❑ ✻ ✄ ✄ ❍ ☞ ❋ ❍ ✼ ❑ ✽ ❘ ■ ❀ ❁ ✼ ❑ ❀

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

✌

SLIDE 3 ✔ ☎ ✂ ✆ ☎✡ ✄ ✔ ☎ ☛ ✕ ✠ ✖✗ ✆ ✘ ✙ ✂ ✡ ✡ ☛✚ ☎ ✆

✔

✔ ✘ ✁ ✯ ✂ ★ ✰ ✂ ✦ ✪ ✯ ✂ ✥ ✹ ✫ ✷ ✄ ✰ ☎ ✶ ★ ✦ ✦ ✥ ✆ ✂ ✰ ✝ ✯ ✯ ☎ ✞ ✟ ❍ ❘ ✿ ❀ ❀ ❁ ☎ ❄ ❀ ✻ ✾ ❄ ◗ ❁ ✠ ❄ ❑ ✡ ■ ❄ ❈ ❂ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ✻✼ ✻ ✾ ❄ ✽ ❘ ✿ ❀ ❀ ✼

❁

✻ ❀ ❑ ❄ ✿ ❈ ❄ ❀ ✻ ❑ ❄ ❁ ◗ ✾ ❇ ✼ ❈ ❁ ❑ ✻ ✾ ❄ ✻ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❀ ❄ ✻ ❇ ✿❀ ❄ ▲ ✼ ❑ ✿ ◗ ❁ ✠ ❄ ❑ ▲ ❁ ❀ ✻ ✿ ❑ ✽ ❄ ❅ ❄ ✿❀ ■ ❈ ❄ ❋ ✭ ✂ ✰ ✥ ✪ ✦ ✄ ☛ ✯ ✯ ☎ ✟ ✂ ❋ ☞ ✼ ✼ ▲ ❊ ❄ ❈

✼

❈ ❅ ✿ ❑ ✽ ❄ ❋ ✌ ✾ ❄ ✼ ❈ ❄ ✻ ❁ ✽ ✿ ❘ ❘ ❂ ✍ ❁ ✻ ✾ ❁ ❑ ☎ ❑ ❁ ✻ ❄ ❑ ■ ❅ ❇ ❄ ❈ ✼

✻

❈ ✿ ❁ ❑ ❁ ❑ ◗ ❊ ✿ ✻ ✻❄ ❈ ❑ ❀ ❚ ✻ ✾ ❄ ❄ ❈ ❈ ✼ ❈ ✼

✄

✄ ❍ ❁ ❀ ❇ ✼ ■ ❑ ▲ ❄ ▲ ❇ ❂ ✻ ✍ ❁ ✽ ❄ ✻ ✾ ❄ P ✿ ❂ ❄ ❀ ❄ ❈ ❈ ✼ ❈ ❋ ❯ ❋ ✄ ✼ ▲ ❄ ❀ ❁ ◗ ❑ ❊ ✾ ✿ ❀ ❄ ❋ ✟ ❋ ✡ ✿❀ ❂ ✻ ✼ ■ ❑ ▲ ❄ ❈ ❀ ✻ ✿ ❑ ▲ ✿ ❑ ▲ ❁ ❅ ❊ ❘ ❄ ❅ ❄ ❑ ✻ ❋ ✵ ✫ ✄ ✰ ✪ ✎ ✄ ✱ ✥ ✩ ✹ ✦ ✄ ☛ ✯ ✯ ☎ ✟ ✂ ❋ ❍ ■ ❈ ❀ ❄ ✼

▲

❁ ❅ ❄ ❑ ❀ ❁ ✼ ❑ ✿ ❘ ❁ ✻ ❂✑✏ ✒ ❁ ✻ ✾ ❘ ❁ ❅ ❁ ✻❄ ▲ ✻ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❀ ❄ ✻ ❚

✼

❈ ✾ ❁ ◗ ✾ ▲ ❁ ❅ ❄ ❑ ❖ ❀ ❁ ✼ ❑ ✿ ❘ ▲ ✿ ✻ ✿ ❚ ✄ ✄ ❍ ✽ ✿ ❑ ❇ ❄ ❀ ❄ ✠ ❄ ❈ ❄ ❘ ❂ ❇ ❁ ✿❀ ❄ ▲ ❋ ❯ ❋ ✓ ■ ◗ ❄ ✽ ❘ ✿❀ ❀ ❁ ☎ ✽ ✿ ✻ ❁ ✼ ❑ ❊ ✾ ✿ ❀ ❄ ❁ ❑ ✻❄ ❈ ❅ ❀ ✼

❇

✼ ✻ ✾ ❀ ✻✼ ❈ ✿ ◗ ❄ ❀ ❊ ✿ ✽ ❄ ✿ ❑ ▲ ✽ ❘ ✿❀ ❀ ❁ ❖ ☎ ✽ ✿ ✻ ❁ ✼ ❑ ✻ ❁ ❅ ❄ ❈ ❄ ✡ ■ ❁ ❈ ❄ ❅ ❄ ❑ ✻ ❀ ❋

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

✔

SLIDE 4

✖
☎

✌ ✄ ☛✁ ☎ ✡ ✗ ✛ ✄ ✠ ☎ ✁ ✂ ✂ ☎ ✆ P ❂ ✿ ▲ ▲ ❁ ❑ ◗ ❀ ✼ ❅ ❄ ▲ ❄ ❀ ❁ ◗ ❑ ❊ ✾ ✿❀ ❄ ✻✼ ✄ ✄ ❍ ❚ ✍ ❄ ❘ ❁ ✄ ❄ ✻✼ ❈ ❄ ▲ ■ ✽ ❄ ❖ ☎ ✮ ☎ ✲ ✰ ✦ ✂ ✄ ☛ ✴ ✥ ✱ ✂ ✩ ✦ ✥ ✄ ✩ ★ ✶ ✥ ✪ ✳ ✂ ✆ ✂ ✎ ✪ ✬ ✝ ✮ ✵ ✪ ✄ ✰ ★ ✹ ✂ ✦ ✞ ★ ✎ ✂ ✰ ✂ ✟ ✲ ✥ ✰ ✂ ✱ ✂ ✩ ✪ ✬ ✠ ✮ ☎ ✶ ★ ✦ ✦ ✥ ✆ ✎ ★✪ ✥ ✄ ✩ ✪ ✥ ✱ ✂ ✰ ✂ ✟ ✲ ✥ ✰ ✂ ✱ ✂ ✩ ✪ ✮

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

✡

SLIDE 5 ✘ ✎ ✆ ✡ ☎ ✗ ✛

☛✁

☎ ✝ ✡ ☛ ✗ ✝ ✂ ✙ ☛ ✄ ✟ ✌ ✍ ✼ ✍ ✿ ❂ ❀ ✻✼ ▲ ❄ ✿ ❘ ✍ ❁ ✻ ✾ ✽ ■ ❈ ❀ ❄ ✼

▲

❁ ❅ ❄ ❑ ❀ ❁ ✼ ❑ ✿ ❘ ❁ ✻ ❂ ❊ ❈ ✼ ❇ ❘ ❄ ❅ ✿ ❈ ❄ ✏ ✂ ❋ ✠ ❄ ▲ ■ ✽ ❄ ✻ ✾ ❄ ▲ ❁ ❅ ❄ ❑ ❀ ❁ ✼ ❑ ✿ ❘ ❁ ✻ ❂ ❇ ❂

❄

✿ ✻ ■ ❈ ❄ ❀ ❄ ❘ ❄ ✽ ✻ ❁ ✼ ❑ ❅ ❄ ✻ ✾ ✼ ▲ ❀ ❋ ❯ ❋ ◆ ❑ ✽ ❈ ❄ ✿❀ ❄ ✻ ✾ ❄ ✻ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❀ ❄ ✻ ❀ ❁ ✂ ❄ ❋ ✄ ☎ ❄ ✿ ✻ ■ ❈ ❄ ❀ ❄ ❘ ❄ ✽ ✻ ❁ ✼ ❑ ❁ ❀ ✿ ✍ ❄ ❘ ❘ ❀ ✻ ■ ▲ ❁ ❄ ▲ ✿ ❈ ❄ ✿ ❋ P ✿❀ ❁ ✽ ✿ ❘ ❘ ❂ ❈ ❄ ❅ ✼ ✠ ❄ ❀ ❈ ❄ ▲ ■ ❑ ▲ ✿ ❑ ✻ ✿ ❑ ▲ ❁ ❈ ❈ ❄ ❘ ❄ ✠ ✿ ❑ ✻

❄

✿ ✻ ■ ❈ ❄ ❀ ❋ ✄ ◆ ❑ ✽ ❈ ❄ ✿❀ ❁ ❑ ◗ ✻ ✾ ❄ ✻ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❀ ❄ ✻ ❀ ❁ ✂ ❄ ❇ ❂ ✿ ▲ ▲ ❁ ❑ ◗ ✿ ❈ ✻ ❁ ☎ ✽ ❁ ✿ ❘ ❊ ✿ ✻ ✻❄ ❈ ❑ ❀ ✻✼ ✻ ✾ ❄ ✻ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❀ ❄ ✻ ❁ ❀ ✿ ❑ ❄ ✍ ✿ ❊ ❊ ❈ ✼ ✿ ✽ ✾ ❋ ✆ ✂ ✎ ✄ ✩ ✎ ✂ ✩ ✪ ✰ ★✪ ✂ ✄ ✩ ✪ ✫ ✂ ✦ ✂ ✎ ✄ ✩ ✴ ★ ✞ ✞ ✰ ✄ ★ ✎ ✫ ✥ ✮ ✂ ✮ ✬ ★ ✴ ✴ ✥ ✩ ✹ ★ ✰ ✪ ✥ ✆ ✎ ✥ ★ ✶ ✞ ★✪ ✪ ✂ ✰ ✩ ✦ ✪ ✄ ✪ ✫ ✂ ✪ ✰ ★ ✥ ✩ ✥ ✩ ✹ ✦ ✂ ✪ ★ ✩ ✴ ✥ ✦ ✎ ★ ✶ ✶ ✂ ✴ ✞ ★✪ ✪ ✂ ✰ ✩ ✦ ✳ ✩ ✪ ✫ ✂ ✦ ✥ ✦ ✮

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

✝

SLIDE 6 ✁ ✂✄ ✄ ☎ ✆ ✝ ✞ ✟ ✝ ✄ ✠ ☎✡ ☛ ✡ ✌ ✂ ✝ ✖ ☎ ✌ ✂✄ ☎ ✕ ✗ ✆ ☛ ☎

✂

✡ ✁ ✂ ❋ ❙ ✼ ▲ ❄ ❘ ❇ ✿❀ ❄ ▲ ❊ ✿ ✻ ✻❄ ❈ ❑ ❀ ❂ ❑ ✻ ✾ ❄ ❀ ❁ ❀ ❋ ✄ ▼ ❅ ✼ ▲ ❄ ❘ ✆ ✼ ❈ ▲ ❄ ❀ ✽ ❈ ❁ ❊ ✻ ❁ ✼ ❑ ✝ ✿❇ ✼ ■ ✻ ✻ ✾ ❄ ▲ ✿ ✻ ✿ ❁ ❀

✼

■ ❑ ▲ ☎ ❈ ❀ ✻ ❋ ✄ ✌ ✾ ❄ ❅ ✼ ▲ ❄ ❘ ❁ ❀ ■ ❀ ❄ ▲ ✻✼ ◗ ❄ ❑ ❄ ❈ ✿ ✻ ❄ ❀ ❂ ❑ ✻ ✾ ❄ ✻ ❁ ✽ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ❋ ✄ ❍ ✿ ❑ ❇ ❄ ■ ❀ ❄ ▲ ✻ ✼ ◗ ❄ ❑ ❄ ❈ ✿ ✻❄ ❁ ❑ ☎ ❑ ❁ ✻ ❄ ❘ ❂ ❅ ✿ ❑ ❂ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ❋ ✄ ❍ ✼ ❅ ❊ ■ ✻ ✿ ✻ ❁ ✼ ❑ ✿ ❘ ❈ ❄ ✡ ■ ❁ ❈ ❄ ❅ ❄ ❑ ✻ ❀ ✂ ✄ ◆

❊

✿ ✻ ✻ ❄ ❈ ❑ ✽ ❘ ✿ ❀ ❀ ❁ ☎ ✽ ✿ ✻ ❁ ✼ ❑ ❁ ❀ ✻ ✾ ❄ ❊ ■ ❈ ❊ ✼ ❀ ❄ ❚ ✻ ✾ ❄ ❑ ✻ ✾ ❄ ❅ ✼ ▲ ❄ ❘ ❁ ✻ ❀ ❄ ❘

✽

✿ ❑ ❇ ❄ ■ ❀ ❄ ▲ ✍ ❁ ✻ ✾ ✼ ■ ✻ ◗ ❄ ❑ ❄ ❈ ✿ ✻ ❁ ❑ ◗ ✿ ❑ ❂ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ✄ ❯ ❋ ◆ ❑ ❀ ✻ ✿ ❑ ✽ ❄ ❇ ✿ ❀ ❄ ▲ ❊ ✿ ✻ ✻❄ ❈ ❑ ❀ ❂ ❑ ✻ ✾ ❄ ❀ ❁ ❀ ❋ ✄ ✌ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❀ ❄ ✻ ✿ ❑ ▲ ❀ ✼ ❅ ❄ ❊ ❈ ✼ ❊ ❄ ❈ ✻ ❁ ❄ ❀ ✿❇ ✼ ■ ✻ ✻ ✾ ❄ ▲ ✿ ✻ ✿ ✿ ❈ ❄ ■ ❀ ❄ ▲ ✻ ✼ ◗ ❄ ❑ ❖ ❄ ❈ ✿ ✻ ❄ ❑ ❄ ✍ ❊ ✿ ✻ ✻❄ ❈ ❑ ❀ ❋ ✄ ☞ ❁ ✠ ❄ ❑ ✿ ☎ ❑ ❁ ✻ ❄ ✻ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❀ ❄ ✻ ❚ ✼ ❑ ❘ ❂ ✿ ☎ ❑ ❁ ✻ ❄ ❑ ■ ❅ ❇ ❄ ❈ ✼

✿

▲ ▲ ❁ ✻ ❁ ✼ ❑ ✿ ❘ ❊ ✿ ✻ ❖ ✻ ❄ ❈ ❑ ❀ ✿ ❈ ❄ ✿ ▲ ▲ ❄ ▲ ❋ ✄ ☎ ❄ ❈ ❂ ■ ❀ ❄

■

❘

✼

❈ ❑ ✼ ❑ ❖ ❊ ✿ ❈ ✿ ❅ ❄ ✻ ❈ ❁ ✽ ❅ ❄ ✻ ✾ ✼ ▲ ❀ ✆ ❄ ❋ ◗ ✏ ✄ ✄ ❍ ❚ ✞ ✿ ❈ ✂ ❄ ❑ ✍ ❁ ❑ ❖ ▲ ✼ ✍ ❀ ❅ ❄ ✻ ✾ ✼ ▲ ✝ ✍ ✾ ❁ ✽ ✾ ▲ ❄ ❊ ❄ ❑ ▲ ❀ ▲ ❁ ❈ ❄ ✽ ✻ ❘ ❂ ✼ ❑ ✻ ✾ ❄ ✻ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ❋ ✄ ❍ ✼ ❅ ❊ ■ ✻ ✿ ✻ ❁ ✼ ❑ ✿ ❘ ❘ ❂ ✽ ✿ ❑ ❇ ❄ ✽ ✾ ❄ ✿ ❊ ❄ ❈ ❋

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

✆

SLIDE 7

✝

☛ ✝ ✡ ✄ ✂ ✝ ✌ ☎ ✖ ✂ ✡ ☎

✂

✂✄ ✄ ☎ ✆ ✝ ✡ ✟ ✝ ✄ ✠ ☎ ✡ ☛ ✡

✁

✂ ✰ ✶ ★ ✞ ✷ ★ ✦ ✂ ✴ ✞ ★✪ ✪ ✂ ✰ ✩ ✦ ✳ ✩ ✪ ✫ ✂ ✦ ✥ ✦ ✏ ✂ ❄ ❂ ❁ ▲ ❄ ✿ ❄ ✄ ❊ ❘ ✿ ❁ ❑ ❄ ▲ ✍ ❁ ✻ ✾ ✿ ❑ ❄ ✄ ✿ ❅ ❊ ❘ ❄ ✏ ❆ ❄ ✻ ☎ ✆ ✝ ✞ ✟ ✠ ✞ ✡ ✠ ✞ ☛ ✠ ✞ ☞ ✠ ✞ ✌ ✍ ❇ ❄ ✻ ✾ ❄ ❀ ❄ ✻ ✼

❄

✿ ✻ ■ ❈ ❄ ❀ ❋ ❆ ❄ ✻ ✎ ✆ ✝✑✏ ✠✓✒ ✠✕✔ ✍ ❇ ❄ ✿ ✻ ✾ ❈ ❄ ❄ ❇ ❘ ✼ ✽ ✄ ❊ ✿ ❈ ✻ ❁ ✻ ❁ ✼ ❑ ✼

☎

✍ ❁ ✻ ✾ ✏ ✆ ✝ ✞ ✟ ✍ ✠ ✒ ✆ ✝ ✞ ✡ ✠ ✞ ☛ ✍ ✿ ❑ ▲ ✔ ✆ ✝ ✞ ☞ ✠ ✞ ✌ ✍ ❋ ❆ ❄ ✻ ✏ ❁ ❀ ✽ ✼ ❑ ▲ ❁ ✻ ❁ ✼ ❑ ✿ ❘ ❘ ❂ ❁ ❑ ▲ ❄ ❊ ❄ ❑ ▲ ❄ ❑ ✻ ✼

✔

❚ ◗ ❁ ✠ ❄ ❑ ✒ ❋ ❆ ❄ ✻ ✖ ✆ ✗✙✘ ✠✛✚ ✠✛✜ ✠✛✢ ✠✛✣ ✤✦✥ ✿ ❑ ▲ ✧ ✆ ✗ ★ ✠ ✚ ✠✛✜ ✠✩ ✠✛✪ ✤✦✥ ❇ ❄ ✻ ✍ ✼ ❊ ✿ ✻ ✻❄ ❈ ❑ ❀ ◗ ❁ ✠ ❄ ❑ ❋ ✌ ✾ ❄ ❑ ❚ ✻ ✍ ✼ ✿ ▲ ▲ ❁ ✻ ❁ ✼ ❑ ✿ ❘ ❊ ✿ ✻ ✻❄ ❈ ❑ ❀ ✗ ✘ ✠ ✚ ✠ ✜ ✠ ✩ ✠✛✪ ✤✦✥ ✿ ❑ ▲ ✗ ★ ✠ ✚ ✠ ✜ ✠ ✢ ✠✛✣ ✤ ✥ ✿ ❈ ❄ ✿ ❘ ❀ ✼

❈

✼ ❅ ✻ ✾ ❄ ❀ ✿ ❅ ❄ ▲ ❁ ❀ ✻ ❈ ❁ ❇ ■ ✻ ❁ ✼ ❑ ✿ ❀ ✻ ✾ ✿ ✻ ✼

✖

✿ ❑ ▲ ✧ ❋ ✗ ✚ ✠ ✜ ✤ ✥ ❁ ❀ ✽ ✼ ❅ ❅ ✼ ❑ ❇ ❄ ✻ ✍ ❄ ❄ ❑ ✖ ✿ ❑ ▲ ✧ ✿ ❑ ▲ ❁ ❀ ✽ ✿ ❘ ❘ ❄ ▲ ✻ ✾ ❄ ✫ ✬ ✭ ✮✯ ✰ ✱ ❋

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

✲

SLIDE 8

✝

✒ ✂ ✁ ✂ ✙ ☎ ✑ ☛ ✄ ✠

✘

✢

☛

✕ ☛ ✄ ✁ ✂ ✁

Synthetic Patterns generated portions by swapping the non−overlapping

Two patterns length minimum specified

Original Patterns Original Patterns one over the other

are over−lapping here for atleast the

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

✄

SLIDE 9

✝

☛ ✝ ✡ ✄ ✂ ✝ ✌ ☎ ✖ ✂ ✡ ☎

✂

✂✄ ✄ ☎ ✆ ✝ ✡ ✟ ✝ ✄ ✠ ☎ ✡ ☛ ✡

✁

✂ ✰ ✶ ★ ✞ ✷ ★ ✦ ✂ ✴ ✞ ★✪ ✪ ✂ ✰ ✩ ✦ ✳ ✩ ✪ ✫ ✂ ✦ ✥ ✦ ✏ ◆ ❑ ✻ ■ ❁ ✻ ❁ ✼ ❑ ✏ ✿ ❑ ❄ ✄ ✿ ❅ ❊ ❘ ❄ ■ ❀ ❁ ❑ ◗

❍

✠ ▲ ❁ ◗ ❁ ✻ ✁ ✟ ✁

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Digit C 1 1 1 1 1 1 1 Digit D 1 1 .

s

0’

have

Original Patterns

Digit A Digit B

Synthetic Patterns

Note: The empty cells are assumed to

Shaded portion is the overlap.

1

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

✂

SLIDE 10

✗

✑ ✄ ✗ ✚ ✝

✄

✠ ☎

✁

☎ ✆ ✙ ✂ ✂ ✡ ✂ ❋ ❉ ✼ ❅ ✿ ❁ ❑ ✂ ❑ ✼ ✍ ❘ ❄ ▲ ◗ ❄ ❋ ❯ ❋ ▼ ❊ ❊ ❈ ✼ ✄ ❁ ❅ ✿ ✻❄ ❅ ❄ ✻ ✾ ✼ ▲ ❀ ■ ❀ ❁ ❑ ◗ ✽ ✼ ❈ ❈ ❄ ❘ ✿ ✻ ❁ ✼ ❑ ❀ ❇ ❄ ✻ ✍ ❄ ❄ ❑

❄

✿ ✻ ■ ❈ ❄ ❀ ❋ ✟ ❋ ☎ ✼ ❈

❍

✠ ▲ ✿ ✻ ✿ ✻ ✾ ❄ ❊ ❈ ✼ ❊ ❄ ❈ ✻ ❂ ✼ ❇ ❀ ❄ ❈ ✠ ❄ ▲ ❁ ❀ ✏ ✻ ✾ ❄

❄

✿ ✻ ■ ❈ ❄ ❀ ✾ ✿ ✠ ❄ ✿ ❑ ✿ ✻ ■ ❈ ✿ ❘ ✼ ❈ ▲ ❄ ❈ ❁ ❑ ◗ ❀ ■ ✽ ✾ ✻ ✾ ✿ ✻ ❑ ❄ ✿ ❈ ❇ ❂

❄

✿ ✻ ■ ❈ ❄ ❀ ✿ ❈ ❄ ✾ ❁ ◗ ✾ ❘ ❂ ✽ ✼ ❈ ❈ ❄ ❘ ✿ ✻❄ ▲ ✻ ✾ ✿ ❑

✼

❈

✿

❈ ✿ ❊ ✿ ❈ ✻ ✼ ❑ ❄ ❀ ❋ ✺ ✼ ❚

✼

❈ ✿ ◗ ❁ ✠ ❄ ❑ ❑ ✼ ❑ ❖ ❑ ❄ ◗ ✿ ✻ ❁ ✠ ❄ ❑ ■ ❅ ❇ ❄ ❈ ✁ ❚ ❁

✻

✍ ✼ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ✾ ✿ ✠ ❄ ✽ ✼ ❅ ❖ ❅ ✼ ❑

❄

✿ ✻ ■ ❈ ❄ ❖ ✠ ✿ ❘ ■ ❄ ❀

✼

❈ ✽ ✼ ❑ ❀ ❄ ✽ ■ ✻ ❁ ✠ ❄ ✁

❄

✿ ✻ ■ ❈ ❄ ❀ ✻ ✾ ❄ ❑ ✻ ✾ ❁ ❀ ❁ ❀ ✻ ✿ ✄ ❄ ❑

✼

❈ ✿ ❑ ✼ ✠ ❄ ❈ ❘ ✿ ❊ ❇ ❄ ✻ ✍ ❄ ❄ ❑ ✻ ✾ ❄ ❅ ❋ ✁ ❁ ❀ ✽ ✿ ❘ ❘ ❄ ▲ ✻ ✾ ❄ ✫ ✬ ✭ ✮✯ ✰ ✱ ✯ ✭ ✂ ✄✆☎ ✝ ❋

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

❨ ✞

SLIDE 11

✘

✗ ✁ ✂ ✂ ✌ ✄ ✢ ☎ ✂ ✆ ☎✡ ☎ ✝ ✄ ✂ ✄ ☛ ✗ ✝ ✌ ✂ ✙ ✙ ☎

✁

✂☎✄ ✆✞✝ ✟ ✠☛✡ ✄ ▼ ❊ ✿ ✻ ✾

❈

✼ ❅ ❘ ❄

✻

❄ ❑ ▲ ✻✼ ❈ ❁ ◗ ✾ ✻ ❄ ❑ ▲ ▲ ❄ ❑ ✼ ✻ ❄ ❀ ✿ ❊ ✿ ✻ ✻❄ ❈ ❑ ❋ ✄ ▼ ❘ ❘ ✼

✻

✾ ❄ ❊ ✿ ✻ ✻❄ ❈ ❑ ❀ ✻ ✾ ✿ ✻ ✽ ✿ ❑ ❇ ❄ ❄ ✄ ✻ ❈ ✿ ✽ ✻ ❄ ▲

❈

✼ ❅ ✻ ✾ ❄ ◗ ❈ ✿ ❊ ✾

✼

❈ ❅ ❀ ✻ ✾ ❄ ❀ ❂ ❑ ✻ ✾ ❄ ✻ ❁ ✽ ❀ ❄ ✻ ❋ ✡ ✄ ✿ ❅ ❊ ❘ ❄ ✏ ❆ ❄ ✻ ✻ ✾ ❄ ✼ ✠ ❄ ❈ ❘ ✿ ❊ ❘ ❄ ❑ ◗ ✻ ✾ ❈ ❄ ✡ ■ ❁ ❈ ❄ ▲ ❁ ❀ ❯

❄

✿ ✻ ■ ❈ ❄ ❀ ❋

Original Patterns Original Patterns

(a, b, c, d, e ) (p, b, c, q, r ) (u, v, c, q, w )

T T T

(a, b, c, d, e ) (p, b, c, q, r ) (u, v, c, q, w )

T T T

a b c d e p c q r u v q w a b c d e p c q r u v q w

Graph

a b c d e p c q r u v q w a b c d e p c q r u v q w a b c d e p c q r u v q w a b c d e p c q r u v q w

Graph

a b c d e p c q r u v q w a b c d e p c q r u v q w

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

❨ ❨

SLIDE 12

✁

✁ ✕ ✆ ✂ ✂ ✠ ✄

❆

✞ ❖ ◗ ❈ ✿ ❊ ✾ ✽ ✿ ❑ ❇ ❄ ✽ ✼ ❑ ❀ ✻ ❈ ■ ✽ ✻ ❄ ▲ ❇ ❂ ❀ ✽ ✿ ❑ ❑ ❁ ❑ ◗ ✻ ✾ ❄ ✻ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ✼ ❑ ❘ ❂ ✼ ❑ ✽ ❄ ❋ ✄ ◆ ❑ ❅ ❄ ❅ ✼ ❈ ❂ ✻ ❁ ❅ ❄ ❖ ✽ ✼ ❅ ❊ ❘ ❄ ✄ ❁ ✻ ❂ ✻ ✼ ❇ ■ ❁ ❘ ▲ ✻ ✾ ❄

❆

✞ ❖ ◗ ❈ ✿ ❊ ✾ ❁ ❀ ✂ ✗☎✄ ✡ ✢ ✁ ✤ ✆ ✂ ✗ ✄ ✡ ✤ ❚ ✍ ✾ ❄ ❈ ❄ ✄ ❁ ❀ ✻ ✾ ❄ ❑ ■ ❅ ❇ ❄ ❈ ✼

❊

✿ ✻ ✻❄ ❈ ❑ ❀ ❚ ✢ ❁ ❀ ✻ ✾ ❄ ▲ ❁ ❅ ❄ ❑ ❀ ❁ ✼ ❑ ✿ ❘ ❁ ✻ ❂ ❚ ✁ ❁ ❀ ✻ ✾ ❄ ✼ ✠ ❄ ❈ ❘ ✿ ❊ ❘ ❄ ❑ ◗ ✻ ✾ ✽ ✼ ❑ ❀ ❁ ▲ ❄ ❈ ❄ ▲ ❋ ✄ ✺ ❊ ✿ ✽ ❄ ✽ ✼ ❅ ❊ ❘ ❄ ✄ ❁ ✻ ❂ ❁ ❀ ✂ ✗☎✄ ✢ ✤ ✆ ✂ ✗ ✄ ✤ ❋ P ■ ✻ ✻ ✾ ❄ ✿ ✽ ✻ ■ ✿ ❘ ❀ ❊ ✿ ✽ ❄ ❈ ❄ ✡ ■ ❁ ❈ ❄ ❖ ❅ ❄ ❑ ✻ ✆

✼

❈

❍

✠ ▲ ✿ ✻ ✿ ✝ ❁ ❀ ❅ ■ ✽ ✾ ❀ ❅ ✿ ❘ ❘ ❄ ❈ ✻ ✾ ✿ ❑ ✻ ✾ ❄ ✼ ❈ ❁ ◗ ❁ ❑ ✿ ❘ ✻ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❀ ❄ ✻ ❀ ❁ ✂ ❄ ❋ ✄ ▼ ❑

❆

✞ ❖ ◗ ❈ ✿ ❊ ✾ ❁ ❀ ❇ ■ ❁ ❘ ✻

✼

❈ ❄ ✿ ✽ ✾ ✽ ❘ ✿❀ ❀ ✼

❊

✿ ✻ ✻ ❄ ❈ ❑ ❀ ❋

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

❨ ✌

SLIDE 13 ✔ ✔ ✘ ✎ ✡ ☛ ✝ ✕ ✄ ✠ ☎ ✡ ✟ ✝ ✄ ✠ ☎ ✄ ☛ ✌ ✂ ✂✄ ✄ ☎ ✆ ✝ ✡ ✄ ✌ ✾ ❄ ❑ ■ ❅ ❇ ❄ ❈ ✼

❀

❂ ❑ ✻ ✾ ❄ ✻ ❁ ✽ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ✻ ✾ ✿ ✻ ✽ ✿ ❑ ❇ ❄ ◗ ❄ ❑ ❄ ❈ ✿ ✻ ❄ ▲ ✽ ✿ ❑ ❇ ❄ ✠ ❄ ❈ ❂ ❘ ✿ ❈ ◗ ❄ ❋ ✺ ✼ ✽ ✼ ❑ ✠ ❄ ❑ ✻ ❁ ✼ ❑ ✿ ❘ ✄ ✄ ❍ ❈ ❄ ✡ ■ ❁ ❈ ❄ ❀ ✠ ❄ ❈ ❂ ✾ ❁ ◗ ✾ ❀ ❊ ✿ ✽ ❄ ✿ ❑ ▲ ✻ ❁ ❅ ❄ ❈ ❄ ❖ ✡ ■ ❁ ❈ ❄ ❅ ❄ ❑ ✻ ❀ ❋ ✄

❆

✞ ❖ ✄ ✄ ❍ ❁ ❀ ✿ ❑ ❄ ✿ ❈ ❄ ❀ ✻ ❑ ❄ ❁ ◗ ✾ ❇ ✼ ❈ ✽ ❘ ✿ ❀ ❀ ❁ ☎ ❄ ❈ ✍ ✾ ❁ ✽ ✾ ▲ ❁ ❈ ❄ ✽ ✻ ❘ ❂ ✍ ✼ ❈ ✄ ❀ ✍ ❁ ✻ ✾ ✻ ✾ ❄

❆

✞ ❖ ◗ ❈ ✿ ❊ ✾ ❈ ❄ ❊ ❈ ❄ ❀ ❄ ❑ ✻ ✿ ✻ ❁ ✼ ❑ ❀ ❋ ✄ ✌ ✾ ❄ ▲ ❁ ❀ ✻ ✿ ❑ ✽ ❄ ❅ ❄ ✿❀ ■ ❈ ❄ ■ ❀ ❄ ▲ ❇ ❂

❆

✞ ❖ ✄ ✄ ❍ ❁ ❀

✁✄✂

✰ ✮ ✭☎ ✆ ✂ ✝ ✯ ✞ ☎ ✭ ✰ ✂ ☎ ✞ ✠✟ ☎ ✰ ✂ ✝ ✭ ❋ ✄

❆

✞ ❖ ✄ ✄ ❍ ■ ❀ ❄ ❀ ✿ ▲ ❂ ❑ ✿ ❅ ❁ ✽ ❊ ❈ ✼ ◗ ❈ ✿ ❅ ❅ ❁ ❑ ◗ ✻ ❄ ✽ ✾ ❑ ❁ ✡ ■ ❄ ✻ ✼ ❈ ❄ ▲ ■ ✽ ❄ ✻ ✾ ❄ ✻ ❁ ❅ ❄ ❈ ❄ ✡ ■ ❁ ❈ ❄ ❅ ❄ ❑ ✻ ✏ ✞ ✿ ❈ ✻ ❁ ✿ ❘ ▲ ❁ ❀ ✻ ✿ ❑ ✽ ❄ ✽ ✼ ❅ ❊❏■ ✻ ✿ ✻ ❁ ✼ ❑ ❀ ✿ ❈ ❄ ❀ ✻ ✼ ❈ ❄ ▲ ❁ ❑ ✻ ✾ ❄ ❑ ✼ ▲ ❄ ❀ ✼

✻

✾ ❄

❆

✞ ❖ ◗ ❈ ✿ ❊ ✾ ❚ ✍ ✾ ❁ ✽ ✾ ✿ ✠ ✼ ❁ ▲ ❀ ❈ ❄ ✽ ✼ ❅ ❊ ■ ✻ ✿ ✻ ❁ ✼ ❑ ❀ ❋ ✄ ✌ ❁ ❅ ❄ ✽ ✼ ❅ ❊ ❘ ❄ ✄ ❁ ✻ ❂ ✼

❆

✞ ❖ ✄ ✄ ❍ ✡ ✂ ✗ ✄ ✤ ✍ ✾ ❄ ❈ ❄ ✄ ❁ ❀ ✻ ✾ ❄ ❑ ■ ❅ ❇ ❄ ❈ ✼

✼

❈ ❁ ◗ ❁ ❑ ✿ ❘ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ✼ ❑ ❘ ❂ ❋ ▼ ✽ ✻ ■ ✿ ❘ ✻ ❁ ❅ ❄ ❅ ❄ ✿❀ ■ ❈ ❄ ❅ ❄ ❑ ✻ ❀ ✆ ✍ ❁ ✻ ✾

❍

✠ ▲ ✿ ✻ ✿ ✝ ✿ ❈ ❄ ❀ ❅ ✿ ❘ ❘ ❄ ❈ ✻ ✾ ✿ ❑ ✻ ✾ ❄ ✽ ✼ ❑ ✠ ❄ ❑ ✻ ❁ ✼ ❑ ✿ ❘ ✄ ✄ ❍ ✍ ❁ ✻ ✾ ✼ ❈ ❁ ◗ ❁ ❑ ✿ ❘ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ❋

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

❨ ✔

SLIDE 14 ✒ ✂ ☎ ✆ ☛✁ ☎ ✝ ✄ ✂ ✙ ✡ ✄ ✎

✟

✑ ☛ ✄ ✠

✘

✢

✂✄

✂ ✄ ❉ ❁ ❅ ❄ ❑ ❀ ❁ ✼ ❑ ✿ ❘ ❁ ✻ ❂ ✡ ✂

❯

✄ ✄ ■ ❅ ❇ ❄ ❈ ✼

✽

❘ ✿ ❀ ❀ ❄ ❀ ✡ ✂ ❲ ✄ ✌ ✼ ✻ ✿ ❘ ❑ ■ ❅ ❇ ❄ ❈ ✼

✻

❈ ✿ ❁ ❑ ❁ ❑ ◗ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ✡ ✁ ✁ ✂ ❲ ✄ ✡ ✄ ❊ ❄ ❈ ❁ ❅ ❄ ❑ ✻ ❀ ✿ ❈ ❄ ✽ ✼ ❑ ▲ ■ ✽ ✻❄ ▲ ❇ ❂ ■ ❀ ❁ ❑ ◗ ❈ ✿ ❑ ▲ ✼ ❅ ❘ ❂ ✽ ✾ ✼ ❀ ❄ ❑ ✻ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❊ ✿ ✻ ❖ ✻❄ ❈ ❑ ❀ ✽ ✼ ❑ ❀ ❁ ❀ ✻ ❁ ❑ ◗ ✼

❯

❲ ❲ ❲ ❚ ❳ ❲ ❲ ❲ ✿ ❑ ▲ ✁ ✁ ✂ ❲ ❊ ✿ ✻ ✻❄ ❈ ❑ ❀ ❚ ❈ ❄ ❀ ❊ ❄ ✽ ✻ ❁ ✠ ❄ ❘ ❂ ❋ ✄ ✄ ■ ❅ ❇ ❄ ❈ ✼

✻❄

❀ ✻ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ✡ ✟ ✟ ✟ ✟ ❍ ❘ ✿❀ ❀ ❁ ☎ ❄ ❈ ❀ ✽ ✼ ❅ ❊ ✿ ❈ ❄ ▲ ✂ ❋ ✄ ✄ ❍ ❯ ❋ ✄ ❖ ✄ ✄ ❍ ✟ ❋ ✄ ✄ ❍ ■ ❀ ❁ ❑ ◗ ✓ ✿ ❅ ✿ ❅ ✼ ✻ ✼ ✁ ❀ ❇ ✼ ✼ ✻ ❀ ✻ ❈ ✿ ❊ ❅ ❄ ✻ ✾ ✼ ▲ ❳ ❋

❆

✞ ❖ ✄ ✄ ❍

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

❨ ✡

SLIDE 15 ✒

✂

☎ ✆ ☛✁ ☎ ✝ ✄ ✂ ✙ ✢ ☎✡ ✎ ✙ ✄ ✡ ✑ ☛ ✄ ✠

✘

✢

✂

✄ ✂

Number of Training Patterns Space Required (KB) Design Time (Sec) Classification Time (Sec) Classification Accuracy (%)

311 473 2000 4000 6670 2000 4000 6670 2000 4000 6670 2000 4000 6670 16 34 55 6 22 10 772 1544 2575 772 1544 2575 772 1544 2575 629 98 175 306 106 200 329 99 172 310 91 205 145 87.67 90.16 91.11 87.79 90.22 92.68 88.86 90.84 92.88 92.44 92.89 NNC OLP−NNC k−NNC NNC (Based on Method)

Hamamoto’s

93.85

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

❨ ✝

SLIDE 16 ✒

✂

☎ ✆ ☛✁ ☎ ✝ ✄ ✂ ✙ ✢ ☎✡ ✎ ✙ ✄ ✡ ✁ ✢ ☎ ✁ ✂ ✆ ✁ ✡ ✄

❆

✞ ❖ ✄ ✄ ❍ ✍ ❁ ✻ ✾ ❀ ✿ ❅ ❄ ❑ ■ ❅ ❇ ❄ ❈ ✼

✻

❈ ✿ ❁ ❑ ❁ ❑ ◗ ❊ ✿ ✻ ✻❄ ❈ ❑ ❀ ✼ ■ ✻ ❊ ❄ ❈

✼

❈ ❅ ❀ ✻ ✾ ❄ ✼ ✻ ✾ ❄ ❈ ✽ ❘ ✿ ❀ ❀ ❁ ☎ ❄ ❈ ❀ ❋ ✄

❆

✞ ❖ ✄ ✄ ❍ ✍ ❁ ✻ ✾

■

❀ ✻ ❯ ❲ ❲ ❲ ✻ ❈ ✿ ❁ ❑ ❁ ❑ ◗ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ❀ ✾ ✼ ✍ ❀ ✼ ❑ ❊ ✿ ❈ ❊ ❄ ❈

✼

❈ ❅ ✿ ❑ ✽ ❄ ✿ ❀ ✻ ✾ ✿ ✻ ✼

✻

✾ ❄ ✼ ✻ ✾ ❄ ❈ ✽ ❘ ✿❀ ❀ ❁ ☎ ❄ ❈ ❀ ✍ ❁ ✻ ✾ ✁ ✁ ✂ ❲ ❊ ✿ ✻ ✻ ❄ ❈ ❑ ❀ ❋ ✄ ✌ ✾ ❄ ✽ ✼ ❅ ❊❏■ ✻ ✿ ✻ ❁ ✼ ❑ ✿ ❘ ❈ ❄ ✡ ■ ❁ ❈ ❄ ❅ ❄ ❑ ✻ ❀ ✼

❆

✞ ❖ ✄ ✄ ❍ ✆ ❄ ✄ ✽ ❄ ❊ ✻

✼

❈ ❀ ❅ ✿ ❘ ❘ ▲ ❄ ❖ ❀ ❁ ◗ ❑ ✼ ✠ ❄ ❈ ✾ ❄ ✿ ▲ ✝ ❁ ❀ ❘ ✼ ✍ ❄ ❈ ✻ ✾ ✿ ❑ ✻ ✾ ❄ ✼ ✻ ✾ ❄ ❈ ❅ ❄ ✻ ✾ ✼ ▲ ❀ ❋

Stochastic Systems Lab, Dept. of Computer Science and Automation Indian Institute of Science - Bangalore

❨ ✆