Logistic regression을 이용하면 스팸 메일 감지 등 Binary classification을 실시할 수 있다. 다음 강좌를 공부하고 따라하면서 간단한 Logistic regression 모델을 제작하여 보자.
이러한 Linear regression의 문제를 직접 예시를 보면서 확인해보도록 하자.
먼저 이 문제를 Linear regression으로 학습시키고, 학습된 Hypothesis를 출력시키는 코드는 다음과 같다.
학습의 결과를 그래프로 그려보면, Linear regression의 cost function은 수렴하였지만, Hypothesis가 모든 데이터를 정확하게 추론하지는 못하였음을 발견할 수 있다. 실행 결과와 그래프로 표현된 Hypothesis는 다음과 같다.
Initial State
w: 0.28528583 b: 0.7589016
cost: 1.3864064
accuracy: 0.44444445
step: 0 cost: 1.0683331 accuracy: 0.44444445
step: 500 cost: 0.110783085 accuracy: 0.8888889
step: 1000 cost: 0.11033854 accuracy: 0.8888889
step: 1500 cost: 0.11033752 accuracy: 0.8888889
step: 2000 cost: 0.1103375 accuracy: 0.8888889
step: 2500 cost: 0.11033751 accuracy: 0.8888889
step: 3000 cost: 0.11033751 accuracy: 0.8888889
step: 3500 cost: 0.11033751 accuracy: 0.8888889
step: 4000 cost: 0.11033751 accuracy: 0.8888889
step: 4500 cost: 0.11033751 accuracy: 0.8888889
step: 5000 cost: 0.11033751 accuracy: 0.8888889
step: 5500 cost: 0.11033751 accuracy: 0.8888889
step: 6000 cost: 0.11033751 accuracy: 0.8888889
step: 6500 cost: 0.11033751 accuracy: 0.8888889
step: 7000 cost: 0.11033751 accuracy: 0.8888889
step: 7500 cost: 0.11033751 accuracy: 0.8888889
step: 8000 cost: 0.11033751 accuracy: 0.8888889
step: 8500 cost: 0.11033751 accuracy: 0.8888889
step: 9000 cost: 0.11033751 accuracy: 0.8888889
step: 9500 cost: 0.11033751 accuracy: 0.8888889
step: 10000 cost: 0.11033751 accuracy: 0.8888889
step: 10500 cost: 0.11033751 accuracy: 0.8888889
step: 11000 cost: 0.11033751 accuracy: 0.8888889
step: 11500 cost: 0.11033751 accuracy: 0.8888889
step: 12000 cost: 0.11033751 accuracy: 0.8888889
step: 12500 cost: 0.11033751 accuracy: 0.8888889
step: 13000 cost: 0.11033751 accuracy: 0.8888889
step: 13500 cost: 0.11033751 accuracy: 0.8888889
step: 14000 cost: 0.11033751 accuracy: 0.8888889
step: 14500 cost: 0.11033751 accuracy: 0.8888889
step: 15000 cost: 0.11033751 accuracy: 0.8888889
step: 15500 cost: 0.11033751 accuracy: 0.8888889
step: 16000 cost: 0.11033751 accuracy: 0.8888889
step: 16500 cost: 0.11033751 accuracy: 0.8888889
step: 17000 cost: 0.11033751 accuracy: 0.8888889
step: 17500 cost: 0.11033751 accuracy: 0.8888889
step: 18000 cost: 0.11033751 accuracy: 0.8888889
step: 18500 cost: 0.11033751 accuracy: 0.8888889
step: 19000 cost: 0.11033751 accuracy: 0.8888889
step: 19500 cost: 0.11033751 accuracy: 0.8888889
step: 20000 cost: 0.11033751 accuracy: 0.8888889
Final State
w: 0.1192095 b: 0.15569328
accuracy: 0.8888889
이제 이 문제를 Logistic regression을 이용하여 풀어보자. 데이터를 그대로 학습시키면 학습이 잘 이루어지지 않기 때문에 데이터를 정규화 시켜줄 필요성이 있다.
데이터의 정규화는 일반적으로 ()으로 이루어진다.
이 문제를 풀어본 예시 코드는 다음과 같다.
Initial State
w: -0.08762686 b: -0.83853364
cost: 0.7651719
accuracy: 0.5555556
step: 0 cost: 0.7643202 accuracy: 0.5555556
step: 500 cost: 0.51053536 accuracy: 0.6666667
step: 1000 cost: 0.4196778 accuracy: 0.7777778
step: 1500 cost: 0.37055922 accuracy: 0.7777778
step: 2000 cost: 0.33723614 accuracy: 0.8888889
step: 2500 cost: 0.31211388 accuracy: 0.8888889
step: 3000 cost: 0.29205555 accuracy: 0.8888889
step: 3500 cost: 0.27545375 accuracy: 0.8888889
step: 4000 cost: 0.26136488 accuracy: 0.8888889
step: 4500 cost: 0.24918365 accuracy: 0.8888889
step: 5000 cost: 0.2384975 accuracy: 0.8888889
step: 5500 cost: 0.22901218 accuracy: 0.8888889
step: 6000 cost: 0.22051068 accuracy: 0.8888889
step: 6500 cost: 0.21282858 accuracy: 0.8888889
step: 7000 cost: 0.2058385 accuracy: 0.8888889
step: 7500 cost: 0.19943966 accuracy: 0.8888889
step: 8000 cost: 0.1935512 accuracy: 0.8888889
step: 8500 cost: 0.18810739 accuracy: 0.8888889
step: 9000 cost: 0.1830539 accuracy: 0.8888889
step: 9500 cost: 0.17834553 accuracy: 1.0
step: 10000 cost: 0.17394434 accuracy: 1.0
step: 10500 cost: 0.16981788 accuracy: 1.0
step: 11000 cost: 0.16593865 accuracy: 1.0
step: 11500 cost: 0.16228266 accuracy: 1.0
step: 12000 cost: 0.15882927 accuracy: 1.0
step: 12500 cost: 0.1555604 accuracy: 1.0
step: 13000 cost: 0.15246028 accuracy: 1.0
step: 13500 cost: 0.14951481 accuracy: 1.0
step: 14000 cost: 0.14671165 accuracy: 1.0
step: 14500 cost: 0.1440399 accuracy: 1.0
step: 15000 cost: 0.14148939 accuracy: 1.0
step: 15500 cost: 0.13905148 accuracy: 1.0
step: 16000 cost: 0.13671805 accuracy: 1.0
step: 16500 cost: 0.13448226 accuracy: 1.0
step: 17000 cost: 0.13233723 accuracy: 1.0
step: 17500 cost: 0.13027719 accuracy: 1.0
step: 18000 cost: 0.12829666 accuracy: 1.0
step: 18500 cost: 0.12639087 accuracy: 1.0
step: 19000 cost: 0.12455518 accuracy: 1.0
step: 19500 cost: 0.12278541 accuracy: 1.0
step: 20000 cost: 0.121078014 accuracy: 1.0
Final State
w: 5.549216 b: 1.1411173
accuracy: 1.0
