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@gihyunkim
Created October 11, 2019 05:18
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# PCA/LDA\n",
"\n",
"## 1. 차원의 저주\n",
"다변량 자료분석 시, 차원이 증가함에 따라 생기는 문제들을 말한다.\n",
"\n",
"예제) 3클래스 패턴인식 문제.\n",
"1. 특징공간은 일정한 구역으로 나누고\n",
"\n",
"\n",
"2. 각 구역에 속한 각 클래스 표본들의 비를 구하고\n",
"\n",
"\n",
"3. 새로운 표본의 경우 해당하는 구역을 찾아 그 구역에서 우세한 클래스로 선택.\n",
"\n",
"단일 특징의 경우, 아래와 같이 1차원 축을 세 부분으로 나누게 될 때, 너무 많은 부분에서 클래스들이 겹치게 된다."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image('./image/dim_curse01.PNG')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"두 개의 특징을 사용하개 되면 구역의 개수는 9개로 증가\n",
"\n",
"1. 각 구역마다 포함되는 표본의 개수를 일정하게 하던가\n",
"=> 너무 많은 수의 표본이 필요\n",
"\n",
"\n",
"2. 1차원의 경우와 같은 수의 표본을 유지 하던가.\n",
"=> 구역의 수가 너무 많아 빈공간이 생기게 된다.\n",
"\n",
"**이것은 고차원으로 갈수록 더욱 심해진다**\n",
"\n",
"### 1.1 차원이 높아짐에 따라 생길 수 있는 문제점\n",
"1. 특징이 많으면 잡음 특성들까지 포함되어 분류도에 정확도를 낮춘다.\n",
"\n",
"\n",
"2. 패턴 분류기에 의한 학습과 인식 속도가 느려진다.\n",
"\n",
"\n",
"3. 모델링에 필요한 학습 집합 크기가 커진다.\n",
"\n",
"\n",
"\\* 실제로 \"**차원의 저주**\"는 주어진 표본의 크기에서 분류기의 성능을 개선하기 보다는 감소시키는 최대 특징 수가 존재함을 의미.\n",
"\n",
"\n",
"### 1.2 이 문제를 극복하기 위해서는\n",
"1. 사전지식을 활용\n",
"\n",
"\n",
"2. 타겟 함수의 smoothness를 증가\n",
"\n",
"\n",
"3. **차원을 줄인다.**"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image('./image/dim_curse02.PNG')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2. 차원 축소\n",
"\n",
"### 2.1 차원을 축소시킬 두 가지 방법\n",
"\n",
"1. 특징선택(feature selection) : 전체 특징들로부터 부분집합을 선택.\n",
"\n",
"\n",
"2. 특징추출(feature extraction) : 기존의 특징들의 조합으로 구성된 **새로운 특징**들의 부분집합.\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image('./image/dim_reduce.PNG')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"특징 추출 매핑 함수의 선택은 우리가 최적화 시키고자 하는 목적에 의해 결정.\n",
"\n",
"1. 신호표현(Signal Representation) : 특징 추출 매핑의 목적이, 낮은 차원공간에서 **정확하게** 표현하고자 할 때 -> **주성분분석법(PCA: Principal Components Analysis)**\n",
"\n",
"2. 분류(Classification) : 특징 추출매핑의 목적이, 낮은 차원에서 클래스를 **더 정확하게 분류**하게 하기 위한 경우 -> **선형판별분석법(LDA: Linear Discriminant Analysis)**"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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pB4w9qgkhAchJEQYMTUegCOcgEGB3hjQhhAQgZ0UYwCN+YuRUee2zfVJRdUJqz5yz1xQPmRDhRL2jOy/YYZbn7RzEYYPzVz3gSy+NhZrD7B2NY6KeGQleOBb+4rn1GyKEFBY5LcJgzvJKafzmMvnG8BXGFm8vrrrLdItwot7RmuwFowjbYGIIFVrnWG+YvaP1NXTMWvtiQ4gJIQWF9cvODEFFGHxa8Zm0GfSuNB6yRM63BOG+D7bIhHUH5csi8IzTKcLxekdP33FMmk5aa543HhNZThG2mDEjJqwtWsR6VKM3NZYNGWJvaJFK72gcB8fVoRiEv3GcH/0o8pwQUjBYv+zMkIoIK68NHmaEWL3i28s2Su3ZwhbidIpwvN7R3W0PePKqfdJu7naKsIKmHCqsXgaxVMLsHY0e1zgOapEJIQWF9cvODGGIMGj7RmlUhGFXjl0lSyzPjfhnkiWyilOEZ248LJsORvpKU4QDoj2qYan0qMa+ehyGowkpOPJOhPdWH5cPPzolj721Xm56e5NcMHKlEeN7PthStMlbyXL23NcyYNV+2XL4lL0kRrw6YYqwT9C6UltkIqFq5kx7RQAgwL/6VUyE2YWLkMIBHff69s0/EVYQmp5jifGN49ZLj7LdUjJmbdQ7nreFk6h70W/xzriCShEOgTB7R2NfZ/hbE74IIYUB8j6s33beijAYVzZfSgZ9LC+UH5B2U3bK0DlH5e73dhoh/vFba2TyuoPG+yt2Vu8/acZ/IaYU4TSB8eCwekcjkUvLk5o0iYg7IaSwQIOf227LbxEG8Ih/2X+OEd7eM6ql07s7ZMTco/Lw5K1m2avL9thbFidHvzgTFV9N2KIIp4Ewe1Q7x5Ot3w0hpHDJexEGEGJ4xBqOhgjfNXGjDJ19WJ4qq5Ily7fZWxYfKsLIdF687ShFOB1AdFU0vcxv72j1gt1WUmJvQAgpFKxfdmZIpwiDkVPm1BFiWMtJW+T6SZvljx8ekTmLTsqf3loke9YeF+nVS05u3G+6H509UiN/KeDWmKilXn8gkumcSISHrDkgz6+IZUsr07YfM8u9krmIDbxVrRn2MtQMJwuSsbyOAXPWIRNCCoKCEWHgDE17WdOxa2XVGx+K9UZk46y95u/6hcdkz8DpUjtzkcixwi51SiTChBBCMk9BiTBAd61Wb3zgKcJqN/abK7NaPmhE+EyT6+Sra2+V7eMrZO/gD+Xo6JlyfMkWOTv9Qzm19YB8vWmLnDl8Ur6uiXiT+UyYIpyo33RB069f3dmT0K5y0KC6jTqcYDm8WA0xN2oUGfMNUrp09KhIhw6Rbl36+njcqZPI5/l/fhJSjFi/4syQKREGEOJEHrHa7QMXy5I2PYwYq9Xe8ZCceri71N71G9kxcaV5jCG9451fld3vrZVTU+eL7LW86DwkLBFO1G+6oEGZEIQPMyhBXJ0lSUjM8kL7PmsfaJxMug/C2H7Q9pgoXULY2lnGNGyYvREhJJ+wfr2ZIZMiDCDEXV5/R74zNDb5Qzxr/oc50qP9y1J15fV1BBn29QUXGW/5zOVXy4FHe8oXN90lx7sOkL2jF8rJd+bJgR21cna19ZnyYO7jVEV438nTcnf5ZnMMd7/pogACCq/WOcbrnNLw9Gl7oYPS0sg+mneAv7o9Jnnww7RpkWM5Z2bCNIo41qOP2gsIIfmE9evNDJkWYQVC7CW88WzTTffWE+J4VtPpZdkxaY0c+f1AWb30tJx6cZic3Zm7XnKqIrxib43Z36vfdFGC2ZFUUGHJAO9Xt0d/6VSAN66eMELShJC8I8krR+pkS4STDU2rfWfYchn/26FS+3+v8BReL4OnrIJc9dr7cub14Xkbsk4ERNgp4EUvwhMnxgQVY8XJ0KVLbB8IcirgNfVYo0bZCwkh+YT1680M2RJh4Cc0rfbdYRUyuO2TcvbbF3gKr5edu7jEhK23vbNOdo5fLn+e+F4sDJnjTLG8ZK8SpUSEJcLnvv6LjLJLpFDXnPPgO0UoGRP3QwCRnNXQnMEYwx0wIJKYhX1eeMH64Cn0Oe/fPybASBRD0hYhJO8oChFW/IamYSVv/kkGdx8tJ/+pxFN4E1nlnANy7FXLW8rx8WKEliGmfgU1LBFeuut49PVzvh4ZAuwcB9aEq0RAgMPsA63JXjBNEiOE5CXWrzgz5III76neJ48MmiYXWF6ul+AmsvP/uFxu7jdHHnx2kjzRZag8e09XmdHiAZn7H/fJxqYt5cBlV8vRf2kiX33rO1ER/upH18qJ1o9K9VsfyV+OHbffRe5w6POvpMuS3SbJKhsifOTUVzJz8xG59O21+SPCvXrFBBDeaDI89FBsn7Fj7YUBwKwr8LpxHHjh8MbzJNJCCPHG+jVnhlwQYaXPkLGBhNiPtX91lrzRbZR80LdMln9QLZsnfGC/eu6gkzqg3EiF2A+piDA6eanw6nFgOS3CaLiuYprsGLBOyA/D41RAGZIeC+PRhJC8x/o1Z4ZcEmFw35D3PcUzXdZt6u7o4/9+f7NMXXtAthw6JXuPZy9UDRFOJdM5LBGeWXkw+jinRdiZCOVlXmFhZxjabShf8oNzYge3YQ5jQkjeYf16M0OuifDu6gNGiNPtEcMuGLlSXio/4LlO7bujVsotUyql48Kd8ubq/XLw86/sd5o+1u2PdVkKIqjx+k0nA6aYnL/9mAlJ7zoWG5POaRFGBjLqdOOZOzScqA80rLLS3jBJJkzwPg4MNcSEkLyjaEVYyURoGta6dLv0KIt5w8nY4CW75ViGsoVT8WpTJW9EmBBCQqboRRj0n7Y47UL8H5O2yH1TdnmuS2Tfsbzo9vN3yKIdx+Tk6fQl4WRChN/edDgqtk7iiTDKlZqXRvpTw2smhJBCgyJsA4/48qGfegphGHbxqNVStviUb29Y7XzLfjx2ddqEON0ijHHneFnY8URY5zKGUYQJIYUIRdhBukPTSyvOydDZhz3XJWMQ4jGr99vvNlzSKcKTV+2LiqmaE7cIwwPut3hnne0pwoSQQoQi7CKdoemrx6yVR2dUS5PxlZ7rk7GLx6+RAyc9JgpIkXSJsPabxvEfm701KqpO3CKMjG087jR3W3Q5RZiEwbRp02S9cwIMQrIMRdiDdIamEZK+451tnuuStdsnrbPfae7j7DddWnkoKqqJeHrONjPZhLOMiSJMUmXJkiXSP9kGK4RkCIpwHD6qWC1XD13gKYKp2nPv75N7J1v/D491ydqEFdX2O80fkhVhpWBE+NChWHkT+kdbvwWSOWpqaqRnz55GgL/6Kv2lf4T4gSKcAAhxOjzi69/aKFeMXh04SUstU+VLYVGUIoyJFUpKrF+a9VNzGno+k4wAAd5bgLOakcKAItwA6QpNQ4AxR3zLScE94iU78kuYilKEdbIFnegBX7oKMT3itMMQNMl1KMJJkK7QNMaGfzt1tzxRVuW5viG7Z8oG+x3mB0UpwmhNiTC0dtPCXxVhTMBA0gJD0CRfKFoR3oRm/D5IZ2i607s75K6JG+XqAFnT+UTRjgk7gferIjx/vr2QhA1D0CRfKCoRPnfunAwYMEBKSkqkVatWcvfdd0u7du1k377k+h9DiNPVb7rr9D3SyfKK4R2j17TXNl6WT1Qe+sL0mk623zT6S+v2O47l9pzMSYFe0i1bRgT4oosiCVu5xNSpIj//eWS8euhQkYORrPZ8oqqqygjwwoUL7SWE5DZFJcIQ2/OsC2A/xzR0w4cPl7aYncYH6WrqAa8YQ4a9Z1SbDlte2zit/bT8C+0XLZY41JlRCV90rgHP0fqNRu3CC0VWr7ZX5j4Y/23WrBk9YJJXFLwIn3XMbKMiPHnyZHtJhDvvvFO+9JqGLgHpmgoRoWlkTn/wSa0JUXtto5arIjxs5X4TQtb64KIHHrBTgBcvtlfkIE4RVhs8uP4MUTkGPGAKMMlHClqEkZzxy1/+0vxAAYQWoejmzZvXEWeEpKciFOeDdE+F+LOJm6L9pttYwowwdZNx6+ts88Ynu+13kzugOcclb62hCDt56KGYAI8day/MUa6+2luIH35YZPt2e6PcAr/vF198UU6ePGkvISR/KGgRLi8vrxdqxjJ4w3g/SosWLczyIKS73zQM4ovoZb/yA/KHDw4abxnLtxzKnWn/MC9wx/c3RROpKMI2OK9UgAOeYxnFLb5u69ZNLLWzN84+GoKmAJN8paBFePny5XLHHXfYzyLAO27atKkMGjTIXiLyySef2I9E9uzZI126dKkj0g2RiakQYfCMW0zeasaOe8/YK5Uf7pM/T59lv4vs0n3ZHiO8d5dvllvKNlCEAcLQSMBSEXYbypdyiY8/9hZet6H5SEWFvVP2QB9olCBRgEk+Y10JMkM2RBggC9rt5T799NPSoUMH+1mMo0ePmveJxC2/Y8Tp7DftZfcMmC9nbrxLqvuWSs3kuSK12c0enrnxsGw6+Ll5rFMQ0hPOEn5/Yzh3Wrf2FtxEhrHiLMEmHKRQKHgRxush3IxyJCRkderUyXJOLpIxY8bYW4jMmjXLjBM/8sgjvsXXSTr7Tbut64vTzYXwZOtH5FTL++TwgElyalNu9JP2K8Lnvv6LjFpzwJQiYRrDZED4W8uXvjzzZ3tpcFCHPKYyx0qGgvLoo5ESI7TMTIZq67xxiqsfGz/ePkhmYBMOUmgUvAgr8Ia7du0qHTt2jHrG8HzhFSNZa3FIGavpaurhtqkd+9W5GB7uPV6Ot38uUmaSZfyK8NJdx832MOek/vFA/bBOdwiDIKcC3ieO07y0AKa4c5cZffaZvaIBmjWru1+ydtll9gEyA5twkEKjaETYDd7PtddeK0jSWrZsmb00HDIRmnaLMOxE60dl94QKkWPZ7S7lV4RbTY8ldCUjwmUbYp23YKmIsHMu47wXYa+w8k9+ktyNGULLzv38WIa8YYagSSFSdCKM0qRXXnlFbrnlFpk4caKpHUYnLUz0PWrUKOMpI2RdWloqJ06csPfyT7pD014iXPuTn8mhrgPki9/1kbNV2RuPTUaE4c12+miXNJ20VhqPWRkVwkQiDMHEsRuNWiklE1ZH9wkqwmNX7zflVHqsvBZhJIFBcF3nRNTuu09k7Vp7Yw+Q3ASv1mvfZOzmm0V69BCZPl1k7txIkpf1mw+jvpghaFLIFKUnjLpCZ6vKsrIy4xFj3BhhaRiSs7ySt/yQztC0lwirbZxVLfvKspe9mowIO/tCz6yMhINhiUQYE/1jmw4LdshwOxsbFlSEEdKG8FYdj3jDeS3C+F15nAv1LFE9fCrecDxDmBvHDZI4CA/eum70fOIJhqBJwVK04Whl165dctNNN8mKFSvqNPAAvXr1kiNHjpg78aBAiB8cNF3+bthyTzENam90G+V90bPs3MUlcuzh7nJmRXZEZdr2YyZhKpGgwhNGMhQE1BkSbsgTRjMQ7BuGCOP1T9SeNclgeS/COHcTecJOw3YjR9b3UlF25LV9GHbJJSKWmBovGYlguA6sWSPy7ruRZXj81FMRj/q660QaN5Yqa7+ef//3svDDD+03SEjhUfQijIzpeB4vsqXVQ3YLtF8gxF5iGtS69SnzvtjZduCZEXLsrXn2q+c22458ERXURUnOkRyGCCsFIcJgyRLPcyGuwUudM8fe2QJestd2WTAIcLPvf58eMCl4ilaEtU2lli250c5ayJ5GFjVIpXxpybKV0mRIeKHpjn3LPS9edax9e/vVc5vyzUcowmGAkG+QLOdXXzVh38AZ0mkweMAUYFIMFKUIQ0yvQ8jLfvzUU0/JsGHDZObMmaaTFuqKYfPmRTxJJG099NBD8tprr6UsxGGFpm97faHnxUutptXDsqVsa9abeCQC4jnTEuBL315LEQ4LJF81auR5TuSDMQRNio2i9YQRataJHQA8X5QsoZGH1gxjPBjZ0vCI0eoSYWn1jlMR47BC0+4LmKfBw8lBnIlZ/zR2VfQxRTgErHPb81zIcWMImhQjRSvClZWV0qZNGzPBA/6iYQfGhpGohcxplCjdfPPNJlSNpK3Tp0+b/SDMY8eOld///vfmeRCq9u43Qvy9N1PrN3322xd4XsxgZ674qaxbcFS+KMvNcWGIMEQPZUrvV8bqfinCIbB5c2QuYI/zIlcNAvzibbexDzQpOoo+MWvTpk2y1lE/CZGFtwtDGNoLeM3wilPlDwNHpiTEW2592POC5rQz3XrZr5a7JJsdTXyAhCuP8yEXbYllzaybYAowKUaKXoS9QDga4uwGIWjUD0OgMYYcBqmEpgd3H+15UVPDmDBqhsNomJBOKMJp4qWXPM+LXDITgrYEmCFoUqxQhJMA5UlI2MKYcbt27WTp0qWmyxZA6Prw4cPmcRBSDU0v/dmvPC9usNrrb5ejnfvJubW5/T/3K8KY8GFoRXjh6IIFN1+YT9vj3MgFMyHo//xPesCkqKEIN4AmbCFb2p2MNXz48GjoGo9TSdYKGpq+aFhFwrA0vOF9y3NjdqV4+BXhMHtHFzxIPvQ4L7JtDEETEoEi3AB43+gprX2kMU7cvXt36d27t1kH2759u+lHjQzqVMJqA6csDOwR39hvrrz5q99K1ZXXS+33Lo5e7M40uU6Od3xeTqzYlbPlSsmKMLYLs3d00YBuVOhEZZ8T2bZp558v/V9+mQJMiAVF2AcYK4bXi7KlSZMmRT1gBePFEOxUgEccRlOP7r3fkyVtehgvGbMrmZphNGPIwQtfsiIcdu/oogI3YMm2tUyjwQOGABNCIlCEfYDuWhBerS9G8hZC1bNnzzbPUT8Mc+OV5JWIVLOmveyJ1+bJO9N3S+mCXTJ17QFPG//ZXuk2a4s8/v4maT9to9nvkjGr5CVL9OZsOiy1ZyLj4NkCIgzxRXkTRTgAmAbQIYiZNoagCakPRdgHqC1GMw9MgaiJWZjc4cEHHzSh6FatWtWZnWnWrFnSvHlzs1xbXyZLKqHpePZEWZXcU7pdSsas9VzfkJW8vVbGrN4vJ09nP9s6iAhjO0ws8cHu4FNU5jWYZzqV6QpTMIagCfGGIuwTeMHwdu+8804TloYnjEYfaOihwPPFOvdyv4QVmnbakzP3ycJPz3iuS9Yut7zjvSeyO77sV4Qx8xKmLsT2aBBStPid5CEEYwiakPhQhAPypz/9yYSm0WXr0KFDZhkaffTp08d4xVgeRu0j+k3/+5D5nmIYxL43arXxhPvNOiTXvb3Zc5uG7G8s++6olTJv53H7XWYePyKMMeffzNkW3b6oRRhgwgaHSKbLaizr+Z3vGAHmZPyEeEMRTgGnl6vjxWF00nIT9gxMsB5lu+XeyVvk4clbPdcnY62mbrDfYeZJVoQ1mQtGT9hBBsLSEGA24SAkMRThFEEjjwceeMCIL2ZhSqVWOBFhzsCk1uytDVL+Sa00Gbdemk3Y4LlNIjvfErQdR76w32Fm8SPCraZvkql2UhdF2KZ7d0/hDMPQhAMCvNCehYwQEh+KcAigTjhZUhXpsGZgctpdEzfKnCWn5YrRq415bRPPkFWdL1CEHaB22CGcYVmVJb7Nfvxj3x4wyv90jm9CigmKcIaAx4w6YiRyIaM6KOkITcMgxP3KD5ikLXjGXtt4GUU4T0HdsEtAw7CeV1zhW4B1KMddd09IMZAfIoxuVX37itx2m0iXLiLTptkrch+IL3pN33DDDaa86dlnnzXJW/h/BEVD02GXMF09vlIenrZHHnpvp0xdfEouGLlSbmtgzJginMfMmuUppEEMHjAEeOGCBfbBk6O6utqU8SG/Yvny5eY38sILL0RLAAkpdHJfhA9YF/kmTax3ar1Vp914I2qB7I1yE8xNDM8Xd/gzZsywl4oMGDAgJ6ZCTGQalp675LT5u7TinLScZH2Hjm1gFOE8p1s3T1H1Y0tKSgKFoFHu16tXL+MJK+jVjt8LblwJKQZyU4Th+WKqQEvEjNg6hffii2PPv/UtkdWr7Z0SgG2ef16kXbvIMdyGdTB423jNROh7w81BHOD9YuL/W265xTT2cDbwwDpcaDp16mTKmFKd+CEdTT3cdvGo1dK6dLvcOnGTfPBJrbz8/j7jNbeylk39dIf9TnIfirAH6P7WuLGnuCZj06zfY/9XXw3UhAO/C5TzDRw40F4SAR3o0OAGvxVCCp3cFOEnn4yJrAouRFKBCOq6REIMoUQIW4+RjN1/v71zHPS9NbAd7vJRN+wEy+ABo4kH7v4RgkNoGt6y345aTtLR1KMhQ2nTyzP3y5whC+TYiJn2O8ltKMJxuO8+T4FtyOABQ4BTATep8HzdrV0xZShyKAgpdCw1yQy+RBgeq1MY4a26gfCqEH/vexEP1Qk8WqfXjG1wHIwpq+cLQXV6xDC7D3RcIL44XkNi7QJ39RqaRptL9X6xHN21vHpO+yGdoelEtnT2AVm99LR8/dlK+52QvOOZZzxFNpFpCDqIB+y8OYU3jN8EfgNOEI7WHu2EFDKWmmSGwCL8t38bf+x32bLIemwH71hxCzDCzGHxb/8WOSbE3AeLFi0yHjD+D+hBjYtOWVmZSUAZN26cdcjzUg6/ZSI07bbp/++Pcvrqm2XvqAVybuVa+52QvGLHDk+hjWdBQtA4z+H1YggGLV9btmxpvF1EgBARQlgaQziEFBuWmmQGXyJ8zTUxAX39dXthHKwftNkOYWfgFuCwftinT4vcdVfsuI0aNew1O0AjD+fdPjxhPB8xYoTxkFP1hJVMh6anduxnLsxHf/+6nLvip1IzZibce/vdkLyhfft6YutlyYag3eFleLYYitEIkJ7/EGWA7SHEhBQblppkhqRFGGFl9W4Rbob4JQJhZWyLNnwYA06HAAN403pcp0H8G0rmskB/aVxkkJCFO3/Y1q1bpVu3biZbWi9OyKgeZnn1zmQuv4TdbzqRqQjDjrd/TjaW75EzAxxRCZIfNCDCNeefb0qQIMAN9YFes2aNKTXCuax06dKlXjMOhKWvv/76aHh6+vTp0d8BIcWCpSKZIWkRRg2wChzGaBsCYWhsizFfhIh137BDW6+8Ejs2Elkg+vocnnsS4AKDhCxcoLzGwebNm2eWwzNOtUQjXU093PbSs5PqXbC3la6Xc3MX2u+E5DxJNO7w24TDPZ4LEfZqxIGQNLplEVKsWAqSGZIWYQiTilsyIgyx1e21nhhjymECD1uTwCC46p1rpjTMnRiWAIz9uu/4UbYEcUbIDuIMrxkh6lQ8g0yEpjv2La93wa4aMkfOdOtlv4vCBlM6bjl0So59ccZekodgbNf1HTrNTxa0M68BOQ+I+IDS0tI64WgF4WiKMClmLPXIDEmLsLOkyK8IwxvG34bGkf2iNwbuJDGE2/S1A76mTvwP0V2CuV5tcLHCshYtWqTUPSgToemT/1RS56Jd+8OmUt23NOJhFTidymPTQZZMWCMdF+6U8WsPypdn8qzj009+Uuc7hNU0biw9r7wyqRA0QDtWdIQDCDHj3EYy4rJly6LDMaj/1XI8CHb79u1TauNKSL5jqUdmSFqEnWO6fsLRMA0RO2uKUwVer3rBXhnRmhiGbRI08HCDcB08XXi/CD97ebzwHLAuVdIdmp7z6951Lt61198uu0cvxZduv4PCBZ6w1//khtL1Uns2j4R4zpw63yGsp/X789sFCzeUCDtjWAXiinMcjzE+jHNc6+QR7cG5DW+ZkGLGUo/MkDYR1nFgCDC2x2MIY1ggA1rfj1cCFjxjTSTTDO0GeOWVV8yFSENxKNlwhvHwePDgwcZzcIbqUglNa7/pMKdCVLux39w6F++z3/9X2fPyO3JmdQPfdR5Ra3m2MDcHTkbaerrtry37PyNXGs94b00DyYW5AELSF15ovr+qH/zACPDChf7H9bt37279FM6TSZMmmec4Z7Gsc+fO5jnObXTEQrXA+vXr2SOaFD2WcmSGQCKcqCEGPFQkcan3C+FVQYZXGhYIMzd0TN0G5uiDGw+EnVVQcVGCRwAPYe7cucaLwHMIsFN0daYZ/B9TIR1TIcIOXHZ1TIRLrpItZVvlzAzLuyoAXv1kd/Rz9lq0014a4Z53K+v8H7zsB2NWmXHjnKdbNyPAza66yrcHrEyZMqWO96tgWIVjv4TUx1KNzJC0CDtrhP/932PdrZzm1YoSY8NOrzWsmZa0cUhDGdCaFIabAp9oaBoXLhgE2Sm2aGKA5dhm9+7d9tJgpCs0/Wnzu6IirHZuWn60s0zE6r019T5r+2kbzfL1+z+Xb42ouy6RjfzTHjl77mv7yDmIJcJBQtBuMOaLG0mU2il4jGWpRHMIKUQs1cgMSYuwhpSTNSRjQZgVFUN4rslM7tAQ6ml7jQcr6NzlzJR+9NHkJoNwceLEiehFCn8RsoMg/+IXvzACjOdt2rQxyS2pzkkcdmj6t51ei4rvn//5clm34KjUvJvfZUqrqmvkMsuL9fq8sP/tQ4Bhf2PZT0srZcH2YzknxrgR7Hn//b5D0BBcCCyGVlADr/Xt8ILh/ao3fPjwYbON0zsmhFiSYf9NO0mLsNPL/Yd/iIiy2xB6RgjYS2QXLYqN0eIvxNPpRcNjTjaBCsfX9/LAAzEvXN+HCnQ8C1gqBQGG0MJzQOmSE6xDWA+lH6lM+gDCDE3/eNDHdbxg2JkX+tuvlH9AJP9ldHwBTsW+bYl3iSXuR3OkrAkC3KxZs0AecNu2bc1ECzgfkWyFul9FvV+cr0OGDLGXEkKcWEqRGZIWYetHHRWxoKVGCEtrRnM8g8esAu3ltSLhymse40SGKeHw93/8D5EbbggcEkfiymuvvVYndAfPF7134RnD4FXgAtizZ8862/mhau9+I8Rh9Zte1vq/owKMhh27p1far5R/QCC9PmOYdvnba+XdykNy8nT22nxCgF988cVAEzEsWLBAevToYT8T+fDDD022v479IrIDUYZHHCTJi5BiwFKMzJC0CN96a0zUUgknw9tFfa/Tg04kzE6v1dmcA3b55XWPg23Vs4bg6/uEkOs+jvGwVNHkLYwLO2dgAijxQKg6FcKaganlwI/qeMJmwvg8puecbZ6fMx2G8eVMgwRBeMBBBBjA88UQCdDJ+N955x3z1x3BIYR4Y6lFZkhahDt1iojY3/2dvSBkIJQQSIS0ncLq9FohrngPEGK/3riG0+FFhwRCfXphg+ji4qdCjDIPrAvqDSthhab32glayI7eMje1BJ9sgy5Y6QpJu61kbGYzqFMJQSvI5B81apSZfEHPT52aEDeNqfQ/J6RYyD0RhvcKEYMwZgt4tnh9eLl+cfa+DilDG94GPGCAukoVYvxF6RIaJDjrjIMQVmj6v14ok3P/63w5eceDcnLgOPvo+QuSs1Dv6/VZ02Fo8jF63cG0hqiDhqDRBQvn4htvvGESrDBEsmfPHlPzju5YADeDEGHUwn/yySdmGSEkPrknwlonHDCpKSfQseSQbiTU23VOD4eLHYQYY3CpJmg5CSM0vehn91jeu8iBt2NtOPOZR+Zt9/yc6TaUQu048oX9LoKx53itKY26yxL3lxbvlFnzFwcKQUOAcQ4iHwHNZTTcrOcmhF2fpzo8QkgxkVsi7BxTRRZzvuLsZ43ypRCA14sLIJKxkDmNbFN4v87/J8KD2AbJMNu2bbOX+mfglIUpCfG/Dlwslc9PkNq+hZERu+7A556fM1P2k4lr5b4PtsjvPqmSXiv2yaBV+2XGpsOy3RJoJJCha1fFnhqzDDZ3+zFz43DdO+vrHOebj/WXLs827AHDy0W50eefx8ap+/btGz3nnFEXbIPzEc1lcN7de++9DEMT4oPcEmGM1UK4UFrU0DzCuQzeu04mkajrVwBwAfQa/4U3jLA01mEMGfXEqZDqDEyF5AmDyav2+WrMkXPWfbQ89kwf+9PEByFmeLUY08VvVkE2vs6IpOBce+utt8xjRGmwPpX6dUKKkdwSYW07GWJSU9aAB4xwdBJtLIOCECH68gJcEK+55pqoQHtNou6XVGZgum/KLlkz7kP7SIXBKMsL9fqsOW0DF8tf39HeCPDJLxLPagUP9tZbb5WtW7caMcVvVb3a5557Tvr0qSvi2AaRGUJIcHJLhDEODBHOZlJWHoGkLGdzBFwQdazO+TgVgra5hNM0+oNq+yiFw4MfZq5sKQyDAC/fkNzQBIYzcPOmDBo0yAxv4MZOx35xzjnp2rWr/YgQEgSKcB6D8J9ThOEVa1IM5nBVrzhVgoSmyxafkh5lu7PaiCId9Ph0j+fnzUlLMgSt4KYNogsgtvjNQnghzhgGQSIgnmuYGucfPWFCUoMinOdAdJG0hf8vuhdpuRJs6dKlpo4T43nYDhfNoFPH+Q1Nd3h/n7SctEWmbDxsH6Ew+HjXcdMD2usz54z5CEHjRm369On2M5HWrVubc+iFF14w5xBKkpCBP2/ePBN+RivKu+66ywgyBJtJWISkBkU4z8FFFAILDwUZqlqupPO6Yh3aCOoUidrhKAh+QtPqCSOrt5BAT2mvz5tL5icEjfOnV69e9jMxmc7q/SrwkNF6khASPhThAgEXUw0/jxgxQm655RYZMGCAPPbYY1FvBZ7M448/bh4HRWdgaqiEST3hb49cKVXHE3tj+caCbUc9P3PWrW+5EeDJ7/tLiIPHiygJxn3XrVsn7777rvF+0dZSwaT86FOObQkh4UERLjAgxPBkEIoGKDeBECsII4ZBQ009Rs89JkNnHzaPb5+0zt6rcHh10c56nzmrZgnw/7z48qQ9YDc63ouMewDvF16xgtphrOfE/ISEC0W4wFARhlejwCNGeBEX1jATafz0m16y45i9V2GAvtJenzNb9k0fIWgvtP8z8gsUjA3DQ1acjwkh4ZBbIgwvDSKMSRBIYDDui/Chhhg3bNhghBgXVef/H1Mj4nsJSqJ+04NmH5L3P/oi+vxfx66WmtrCCmV2XZgD3rDlAUOAJ/kMQQOcGzhXtMcznt9o3QDr8AX6QaMvNL1fQtJHbokweiNDgEOa+KCYQTYrPBuYM6wI4PUg/AhRDqPvdLzQ9BWjV8sFjskPygosUxpj3c7Pm3HrPlq+cfEPZdrSWNQjWXCDhnMD54Gzuxpu1rQ2GCCxz5mkRQgJl9wSYRIqWqqkZUkY70PXI3g3qC9GLSguss8++6wMHjzYbBMUd7/pJuPWy4JPz8jV4yujy/7L8hwLjbfX7I9+vozaY/3l/t89J5v2HLLfSfLgnPj1r38dHf/FczxG4p62P8WNG/pCMxGLkPRCES4CcCGFNwPPR5sxuMGFV72foHg19YAY6+Mb3620tyws0Ffa+ZnTbpYHDAEOCr5nzQ1A4h5uwjRqAg8ZQoxyNo4BE5J+KMJFwPz586OhR/V+nOCiDO/YLcJI5PLbjMEZmu49o1qGzomV81wyZpW9VeHR5r2Yx59Ws0PQQTxgJ6gp14xofPe4SUNURMU5pwT4xAmR118Xef75SN4IEjcT2Z13RiaDwX5+0Nfp21fkwAF7ISHphSJcBCAcjf+/G5SdICwNr0fH/ZYvXy4///nPzUUaXvPatWvNcj9oaBrjwe3e2yk3vb05KiKYdq8QQXvOn5amWYhTCEG7we8Q3dRwg3bCFit4wJiKMOd48knrSmVdqvzat74lsnq1fZAkgMjrviHPfkZIPKyzLTNQhHMLZLyiIUO/fv2iHjC8HwgvvCMIs07UHgQNTWM2paUV56JCUmilSk4WbD8m5ztFM0xLMQSN8X94vu4JGJyJeTgX0JYy59DSRYgqPF0IJATTyzABxTXXxMQUU4om69UiMRTTqGI/vCYhGYAiXGScPn3azHyDNoTIoAYIOT9peRsYF8YsOtXV1aZ0xct79gO6a7UYukBum1ApL886JP88dp30XbTDXlt4nPv6L/JGxV5vEQ1qAxfLN+541AjwkZov7FdKHny3aNaCSfrffvttmT17tr0mMgyBvuK33Xab+YvMaJwfoQEPG6K+a5e9IAA4xg03RITRT+kiPqcKKqZG9QpNu98fvGYVb1ZokAxBES5yNGFL5yV2glKmIOFoJ9pvetKCmmimdKEDb7+emAY1S4CDlCApGOfF2L4TfK/IhFa2b99uPwoZDSOnEtrVY3z3u/6FcezYmKhCiN03GBj7xTp42PCi0VkOzyHeXqJNSBqwzrjMQBHOPfCdaMKWOykL4Wqsg+FCnko9sYamH5psnQOWsGw5dMpeU7i0LttQX1D9WoohaOAUYfSC1uEGd+14WgijA16qx4Cni/1hSLpygvAzBFjXMxRNsoB1xmUGinDuAeFFNuwjjzxiHiNRC8k62m1r69atZhk6a7Vs2TIlr3hZxVoZU15lxKVD+WYTui1k1h88JVdNWFNfWJOxFEPQqO/VrHZ8ZxhmuPPOO+UXv/iFlJaWmu8WDTqmTp1qtkkbYYpwKsIILxjH8ApnIwQNLxvrYRBiP8lchKSIddZlBopwbgMRRjIWDBdn/IWHrM0a4E1hXDEV1lfuk9vGRISpoqrww33w+OsJbDKWQggaoWaUHGmEIx4YfnCHqUMnDBGGcOIYqYiwhp2RpOXFpZdG1n/zmxwLJhmHIkwMBw8eNBduvTBDfNHMv3fv3qaMBWHMP/zhD2adAuHG9+ocX0zEmTMin3y2Tm57s1x+NGmdbLS8xULn0embvIXWy/qWGwEe9m7Dcz57JVANHTrUeL0VFRXG20X2u5ae6feJ/tDwhnv06JH+blhhiDD2xTGQ9RwUCCuOAXPjDFfDwkxMIyQJPM7K9EARzn0wfggP2NnQAx6Tjgvjog3hhYeFi7uOL7rLXpKh5ZsfyA9GrzKzERUySNL6Wy/BdRsE+OIfyjsfJxfyxzACvF5FpxrUZRjTx3epTVhgEGj9LpO9cUqJMERYQ8lInArKokUxkXWCDGpdrkZPmGQY11mZPijCuQ9EFvMQv/TSS6ZZBy7gGB/GdwfQ9AMeFpJ6cDHHjDtOwfZzYd9efUh++MePpcV7lfLV2T/bSwuPit3H5a+8RNdplgD/8KEusn73QXuvhsHYPb4jnbIS3xG+E9R2o+EKxvmxrFu3bub7wmMIcUbEVwlDhC++OHIMhJSD4iXCqB1GeBrL8BqNGkUep+JxExIAx1mZXijC+YN6VW4P9/XXXzfL4QnD43rttdeiWdMqAhr+TIbas+fkiaFT0p8glEW6z97qLbxqdhvKhRv32nskD74H/M/xXeAGSqcc/O1vf2sEF6DeGx4xtvPbgjRlwhBhFUqUGwVFQ85IulJQNqXLli2LPUe2tNYNE5IBrLMuM1CE8wt4vAou6BBXjDF6JfPA+4KHhTCnM0SaLM8884zU1tbazwoLT+FVs0PQz021RCAA+F/rTZGC70L7PwOM/0KcVaAzShgijP1hqYgwekk734dzjFg9bHjLWqKEv3jvAc5lQvxinXGZgSKcn0CMEZbGhR3foRPUnSLUibAoumwFBftCiOER67SLhcCqvTXxx4MtAb74/s5Je8AIO6OtJG504N2iDEmX4/+vEYjdu3eb3t/4rmBPPfWUWZ4VwhThAHkHBgipiivGldGEQ71rdwMPCL2zbhiPKcQkzVhnWmagCOcnOgOT08N1esZBkrLigTmNCyk0PfJPe7wF2GcIGsKL76Cv5bVpCNp5Q4TvRhOwAG6YsA3MGdHIOGGIsIpiEE8YAquJXRBijAMjSoDnf/VX1hc0sn5NMEQaYq2vi/0JSSPWWZYZKML5CTxTeF5I2MJYMXoMo3GHesZYhvWoIcY6JAyl0l1rwoQJRojTXj6TAVpMWldfgB/rLz/r8GTSAjzSEgr0+XaKrldyFbxkRCUw7ovyJfz1mrYyo4QhwpqYFUSEtcZY93f2hnYaPGO8V4wdIywN69Mntv7BBzm1IUkb1hmWGSjC+Q9KXOCVqcjCy4K3hcQfTA6A5/CQU22JCI+4ffv2eS3EZ899XV+ALQ8YAuwH/C+Tmc0KXjC+B5SN5cz/LUwR9luipA06nPvq+wli2JeQNGCdXZmBIpz/VFZW2o8iQCAQHnV7vvCSUw2D5nto+ugXZ+oJcJAsaIz3apjZC9z0aNIVkuZwU5TxLOh4hCHCl13mXwSR3azjwPraCE3rMgg7krOwDH+R2KZh63g2dGjkOISEjHV2ZQaKcGGBWtTbb7/d0+vCtIjjxo2znwUnn0PT2458ERNgnyFoJxDheLW9CDdjPfpAKzkjwCAMEUbdLo4Rr+WkGwgrXg/76DgwcHrGySZbYXzYmdRFSBqwzq7MQBEuLOB9YQzYC3jIYfUlztfQ9NxtR6MesN8QtJOG/peatJWT/58wRNjZ1aqhblYQVxVgmM6a5PSMUa7kBx1XTuUzEJIA6+zKDBThwgIX/V//+tcmexrf7YYNG2TYsGFGNCAMChK3sDyVTk3ohTxkyJC8EuL+S7aaPtA3dXhKdh4+aS/1zx//+EeT+ewV3sf/A7MjOT3hnEJFGOFfeJLJGDxWiKYTDRXHC0lDqPW11Jzb4rhYBiF2H7shwriRICQB1tmVGSjChQdCn1oyA0NSkNNrg7esZUyJxjWTAUIMjzhfmnr86rHfBW7C4QRCqx2v8BtygvFgLM9qGVIiMNYKAfNrbrFFVjM8UogtDKKKMDWE0VnXC0PYGlnOTtRDDlJORxEmacY6uzIDRbhwQfauc65hCAdKZiAQ8OJUqEeMGGFvEYx8CU2jiUmnp16wn6UO/r8QYpQqoSYYNzQzZsww/1Nt0pGTQPwgnhAwP+YOO2Oc98kn6wuu09TbxrZhQhEmacY6uzIDRbjwgTggPI2QdDvr4oXH6gHjbxfLe0FYORVyOTSNkHvPnj2lf//+8tVXX9lLwwHHfvnll02ZGJKx7rnnntz1gMPGmVQFgxhDFNHvGcKbzkn41ZvHzQQhaYAiTEIBoqhTG8brU4yGHs4+x0HJ1dA0BHjvXv8Z0KQB0DwDoguvFI8zCSZ3wGuH2BmOECcUYRIa8NaQiOUEHjA6akGgW7duHVoJDYRY+01nG4SLIcALFy60lxBCSHJQhElaSWXi/2SYM2eO/Sg7YPy3WbNm9IAJIYGgCJO0gPFKCDDGL4NMb5gPwAOmABNCUoEiTNICQtOYzOHQoUP2ksICAvziiy/KyZPBa4AJIYQiTIhPNARNASaEpApFmBAfoPQI9c4UYEJIGFCECSGEkCxBESaEEEKyBEWYEEIIyRIUYUIISYL33nvPfkRIeFCECSEkCa677jq57LLL5JFHHjEZ8oSEAUWYEEKSACKMa5ga2rBSjEmqZEyEjx49au4gcSLTaDRavlmjRo3qiDDswgsvlOnTp9tXOUL8kzERJoSQfAZC7BRfTB6SazN5kfyDIkwIIUmgIoxuaWvXrrWXEpIaFGFCCEmCkSNHmpwWzJ1NSFhQhAkhhJAsQREmhBBCsgRFmBBCCMkSFGFCCCEkS1CECSFJU1paKs8//7ynrVixwt4qdaqrq+1H2eHLL7+UUaNGyYkTJ+wlhKQHijAhJGmuvfZaOe+88zxt8eLF9lapgeO0bdvWfpZ5IMB33323+Ux4TEg6oQgTQpJi6dKlRpjmzp1rL0kPAwcOlM6dO9vPMkdNTY3Mnz9fmjRpYj5nmzZt7DWEpA+KMCEkKYYPH27ECX3gEwFP9umnnzbbduzYsZ6HjP3V07zoooukvLzcLIcIYpkajgHatWsX3UbB/ggXA7yv7t27y+TJk81+8NYB9tHXwbGqqqrMci/g8error0u/rpfk5B0QBEmhCQFBBXidOTIEXtJfdavXx8VM6ft2rXL3kKkefPm9dZDSLGNexlo1aqVbNq0yTwG6EOP9fBaAQS2S5cudfbDOn2uBnGOF17GZ8Lng/DqZwgrvE5IIijChJAGgXjBa3ULm9qUKVPMdvA8J06cGBVd/IVn2b9/f/McXvCYMWOiYnj69Gkjjuq9ash7w4YN5jm6U5WUlNQRz5kzZ0a30fd1//33y759+8x6eNQ33nijEWI8BhBWbJfMZAv4LO7XJCRdUIQJIQ2iXmq/fv3sJfWBt6qi7DZ4qgomPkDo2JnkBfEGGsZWAcQx4Qk7cW4DbxWPId4KvFk9rts0hJ0IhLY1FE5IuqEIE0IaBPPmQsScYucG4nrVVVd5li/Nnj3beMEIRd98881G5LD88ccfN8cdO3as8XrhrUIElWHDhslvfvMb+5mYkiFso0lTSOLC/ghRK127djWv434PsJUrV9pbxefee+9N+DkJCROKMCGkQeBBusXODTxQd2mRJnPBk4YXjcfOMWUNLaPGWL1t51gsvGWn96rba9IU1qsXrUDgO3XqZD+LoOPZyYSYIeCJPichYUIRJoQ0CMLJbrFzg+xjeKnatENDxRBAoIKs67G9JmlB9DQhSpOwIJh4DuEF2K9p06bRbXS9JnApEGhsp0IKD91ru3i0bNnSfkRI+qEIE0IaBOFfhIwbYvDgwUaIIXqXXnqpSdJS7xOJUyg3aty4sVkPAX744YfNY3jHW7duNQlReI4xY/DCCy9Et8dNAELK2Aah6+3bt5vlXqHjZ5991qyDYR5gzaRuiDVr1kjr1q3tZ4SkH4owIYQQkiUowoQQQkiWoAgTQgghWYIiTAghhGQJijAhhBCSJSjChBBCSJagCBNCCCFZgiJMCCGEZAmKMCGEEJIlKMKEEEJIlqAIE0IIIVmCIkwIIYRkCYowIYQQkiUowoQQQkiWoAgTQgghWYIiTAghhGQFkf8PrQqXqBXQtAIAAAAASUVORK5CYII=\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image('./image/feature.PNG')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3. PCA(Principal Components Analysis) : 주성분 분석\n",
"\n",
"- 분산을 최대한 보존하면서 서로 직교하는 새 기저(축)을 찾아, 고차원 공간의 표본들을 선형 연관성이 없는 저차원 공간으로 변환하는 기법.\n",
"\n",
"\n",
"- PC(주성분) : data의 분산을 가장 잘 설명하는 방향들\n",
"\n",
"\n",
"- 데이터의 **최적 표현**의 견지에서 데이터를 축소\n",
"\n",
"\n",
"- 대개 차원축소, data de-noising, data visualization에 사용\n",
"\n",
"**PCA 알고리즘**\n",
"- 최대 분산의 직교 방향을 찾는 것이 목적이다.\n",
" - 데이터 포인트를 새 subspace에 투영시킨다.\n",
"\n",
"\n",
"- Eigenvector와 Eigenvalue를 구해서 여러개의 eigenvalue중 가장 큰 eigenvalue 공간으로 정사영시킨다.\n",
" - 예를 들어) n차원을 3차원으로 n 개의 eigenvector와 eigenvalue 중 큰 순서대로 3개를 뽑아 그 세 벡터로 이루어진 공간에 점을 매핑(사영)시키는 것이다.\n",
"\n",
"\n",
"**PCA는 공분산 행렬의 고유벡터를 사용하기 때문에 유니모달 가우시안을 따르는 자료들에 있어서 서로 독립적인 축을 찾는데 사용될 수 있다. 즉, 가우시안이 아니거나 비선형인 멀티 모달 패턴에는 적용하기가 곤란하다.**"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image('./image/pca.PNG')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- $x_1, x_2, ...,x_n$ : 원래의 데이터\n",
"- $v_1, v_2, ...,v_n$ : PCA의 변환행렬(새로운 저차원으로 변환하기 위한)\n",
"\n",
"원래의 데이터 X에 V변환 행렬을 곱해서 만든 새롭게 생성된 저차원 데이터 Z를\n",
"$$ z^i = v_1x_1^i + v_2x_w^i + ... + v_nx_n^i $$\n",
"\n",
"\n",
"## 분산\n",
"$\\mu$: 새로 생성된 데이터의 평균. 이 평균을 0으로 만들고 싶다.\n",
"$$Z= XV$$\n",
"$$\\mu_z = \\frac{1}{n}\\sum^n_{i=1}z^i$$\n",
"\n",
"분산식을 구해보면\n",
"\n",
"$$max_{V\\in R^n}\\frac{1}{m}\\sum^m_{i=1}(z^i-\\mu_z)^2$$\n",
"\n",
"여기서 평균$\\mu$을 0으로 만들기 위해\n",
"\n",
"$$\\mu_z = v_1(\\frac{1}{m}\\sum^m_{i=1}x^i_1 \\ \\Longrightarrow \\ 0) +v_2(\\frac{1}{m}\\sum^m_{i=1}x^i_2 \\ \\Longrightarrow \\ 0)....v_p(\\frac{1}{m}\\sum^m_{i=1}x^i_p \\ \\Longrightarrow \\ 0)$$\n",
"\n",
"이처럼 각 feature의 평균을 0으로 만드는 것을 **Centering**이라한다.\n",
"\n",
"위 식으로 인해\n",
"\n",
"$$max_{V\\in R^n}\\frac{1}{m}\\sum^m_{i=1}(z^i)^2$$\n",
"$$=max_\\vec{v}\\frac{1}{m}\\vec{z}^T \\vec{z}$$\n",
"$$=max_\\vec{v}\\frac{1}{m}(X\\vec{v})^T(X\\vec{v})$$\n",
"$$=max_\\vec{v}\\frac{1}{m}\\vec{v}^T(X^T X)\\vec{v} : 정사영 \\ 후 \\ 분산$$\n",
"$$\\frac{1}{m}(X^TX) : 공분산 \\ 행렬 \\ :S$$\n",
"\n",
"**\\*공분산이 높아지면 feature가 같이 움직인다**\n",
"\n",
"\n",
"PCA에서 풀고자하는 문제는 $\\vec{v}^TS\\vec{v}$를 최대화하는 $v_1$을 구하는 문제이다. \n",
"\n",
"\n",
"$v_1$=1이라 가정하면 **Rayleigh Qutien**에 의해 $v^T_1Sv_1$의 최댓값은 S의 **가장 큰 eigenvalue**와 같다. 이때 $v_1$은 S이 가장 큰 eigenvalu와 대응되는 **eigenvector**이며 크기는 1이다.\n",
"\n",
"\n",
"만약 d차원 -> 1차원으로 축소한다면, 가장 큰 eigenvalue와 대응하는 $w_1$을 찾으면 되고, \n",
"만약 d차원 -> p차원으로 ㅊ축소한다면, 큰 순서대로 p개의 eigenvalue와 대응하는 $w_1, \\ w_2, \\ ..w_p$를 찾으면 된다.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" ## Rayleigh Quotient\n",
" $$R(\\Sigma,v)=\\frac{v^T \\Sigma v}{v^T v} \\ , \\ \\ \\ \\ \\ \\ \\ \\ \\Sigma : \\ 공분산$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" \n",
" \n",
" \n",
" \n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 4. LDA(Linear Discriminant Analysis)\n",
"- 데이터 분포를 학습해 결정경계(Decision Boundary)를 만들어 데이터를 분류하는 모델.\n",
"\n",
"\n",
"- 데이터의 **최적 분류**의 견지에서 데이터를 축소.\n",
"\n",
"\n",
"- 데이터를 특정한 축에 사영한 후에, 두 범주를 잘 구분할 수 있는 직선을 찾는 것이 목표.\n",
"\n",
"\n",
"**클래스간 분산(between-class scatter)과 클래스내 분산(within-class scatter)** 의 비율을 최대화하는 방식으로 데이터에 대한 특징벡터의 차원을 축소.\n",
"\n",
"\n",
"- 즉, 클래스 간 분산은 최대로 하고, 클래스 내 분산은 최소화.\n",
"\n",
"\n",
"## LDA의 가정\n",
"1. feature들이 정규분포이어야 한다.\n",
"\n",
"\n",
"2. feature들이 서로 독립이어야 한다.\n",
"\n",
"\n",
"3. 개개 클래스들의 공분산이 모두 동일해야 한다."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image('./image/lda.PNG')"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image('./image/lda_02.PNG')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"p차원의 입력벡터 x를 w라는 벡터(축)에 사영시킨 후 생성되는 1차원상의 좌표값을 아래와 같이 y라고 정의하자. \n",
"\n",
"\n",
"$$y=w^T\\vec{x}$$\n",
"\n",
"\n",
"각각 $N_1$개와 $N_2$개의 관측치를 갖는 $C_1$과 $C_2$ 두 범주에 대해 원래 입력공간(2차원)에서 각 범주의 중심(평균) 벡터도 아래와 같이 m1, m2로 정의한다. \n",
"\n",
"\n",
"$$m_1=\\frac{1}{N_1}\\sum_{n\\in C_1}x_n$$\n",
"$$m_2=\\frac{1}{N_2}\\sum_{n\\in C_2}x_n$$\n",
"\n",
"\n",
"일단 사영 후, 두 범주의 중심에서 멀리 떨어져 위치하는 벡터 w를 찾아야 한다. \n",
"\n",
"\n",
"$$m_2 - m_1 = w^T(m_2-m_1) \\ , \\ \\ \\ \\ \\ \\ \\ m_k = w^Tm_k$$ \n",
"\n",
"\n",
"사영 후, 범주에 속한 관측치들은 해당 범주 중심에 가까이 있을 수록 좋다. 즉, 분산이 작을수록 좋다.\n",
"\n",
"\n",
"사영 후 클래스 간 분산은\n",
"\n",
"\n",
"$$S^2_k = \\sum_{n \\in C_k}(y_n - m_k)^2$$\n",
"\n",
"**두 범주의 중심은 최대화하고, 범주 내에 분산은 최소화하는 것이 목표**\n",
"\n",
"따라서 목적함수는 \n",
"\n",
"$$J(w)=\\frac{(m_1 - m_2)^2}{S_1^2 + S_2^2} = \\frac{w^TS_Bw}{w^TS_ww}$$\n",
"$$S_B=(m_1 - m_2)(m_1-m_2)^T$$\n",
"$$S_w=\\sum_{n \\in C_1}(x_n-m_1)(x_n-m_1)^T + \\sum_{n \\in C_2}(x_n-m_w)(x_n-m_2)^T$$\n",
"\n",
"$$따라서 \\ 이 \\ 목적함수를 \\ 다음 \\ 식으로 \\ 바꿔 \\ 볼 \\ 수 \\ 있다.$$\n",
"\n",
"$$max_w w^T(S_w^{-1}S_B)w$$\n",
"$$(S_w^{-1}S_B)w = \\lambda w$$\n",
"\n",
"\n",
"$$v가 \\ 가장 \\ 큰 \\ eigenvalue \\ \\lambda를 \\ 갖는 \\ eigenvector일 \\ 때 \\ w=S_B^{-\\frac{1}{2}}v$$\n",
"\n",
"\n",
"$$=(S_w^{-1}S_B)(S_B^{-\\frac{1}{2}}v) = \\lambda (S_B^{-\\frac{1}{2}}v) $$\n",
"$$=S_w^{-1}S_B^{\\frac{1}{2}}v = \\lambda S_B^{-\\frac{1}{2}}v$$\n",
"$$=(S_B^{\\frac{1}{2}}S_w^{-1}S_B^{\\frac{1}{2}})v = \\lambda v$$\n",
"$$S_B^{\\frac{1}{2}}S_w^{-1}S_B^{\\frac{1}{2}}은 \\ symmetric$$\n",
"\n",
"\n",
"$$ 이렇게 \\ eigenvalue와 \\ eigenvector에 \\ 대한 \\ 식으로 \\ 나타낼 \\ 수 \\ 있다.$$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image('./image/lda_03.PNG')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 커널 함수와 커널 트릭\n",
"\n",
"## 커널 PCA\n",
"선형 분리가 불가능한 데이터 포인트를 고차원 feature space로 사영하고, 그 후 새 feature space에 기존 PCA를 적용하는 것.\n",
"\n",
"$$기존 \\ 공분산 \\ 식: \\ \\Sigma = \\frac{1}{n}\\sum^n_{i=1}x^i(x^i)^T $$\n",
"\n",
"$$커널 \\ PCA의 \\ 공분산: \\ \\Sigma = \\frac{1}{n}\\sum^n_{i=1}\\Phi(x^i)\\phi(x^i)^T $$\n",
"\n",
"주성분 v를 얻기 위해, eigenvalue 문제를 고려\n",
"\n",
"$$\\Sigma_{k\\times k}v = \\lambda v$$\n",
"\n",
"$$\\frac{1}{n}\\sum^n_{i=1}\\Phi(x^i)\\phi(x^i)^T v = \\lambda v$$\n",
"\n",
"$$ * \\ 즉, \\ v= \\frac{1}{n\\lambda}\\sum^n_{i=1}\\Phi(x^i)\\phi(x^i)^T v = \\frac{1}{n}\\sum^n_{i=1}a^i\\Phi(x^i)$$\n",
"$$where \\ a^i = \\frac{1}{\\lambda}\\Phi(x^o)^Tv$$\n",
"\n",
"\n",
"**따라서 v는 주성분이 되고, $a^i$를 v로 사영된, feature space 내의 $x^i$의 좌표라 볼 수 있다.**\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\\Sigma v = \\lambda v로 \\ 부터$$\n",
"$$\\frac{1}{n}\\Phi(X)^T\\Phi(X)\\Phi(X)^T\\vec{a}=\\lambda \\Phi(X)^T \\vec{a}$$\n",
"\n",
"$$ 양 \\ 측에 \\ \\Phi(X)를 \\ 곱하면$$\n",
"$$\\frac{1}{n}\\Phi(X)\\Phi(X)^T\\Phi(X)\\Phi(X)^T \\ \\vec{a}=\\lambda \\Phi(X)\\Phi(X)^T \\ \\vec{a}$$\n",
"\n",
"\n",
"$$\\frac{1}{n}\\Phi(X)\\Phi(X)^T \\ \\vec{a}=\\lambda \\vec{a}$$\n",
"\n",
"\n",
"$$ * 여기서 \\ \\Phi(X)\\Phi(X)^T가 \\ 커널행렬 \\ k_{m\\times m}$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
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"language_info": {
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"name": "ipython",
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
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"nbformat_minor": 2
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