{
"cells": [
{
"attachments": {},
"cell_type": "markdown",
"metadata": {
"id": "8GTL9Gqaxlg4"
},
"source": [
"# Nonlinear Methods\n",
"\n",
"ใน tutorial ก่อนหน้า เราได้เห็นถึงความสามารถของเทคนิค PCA ในการ transform ข้อมูล รวมถึงความสามารถในการลดมิติลงอย่างมีประสิทธิภาพ แต่ก็ยังมีข้อมูลอีกจำนวนมากที่ไม่เหมาะกับเทคนิค PCA\n",
"\n",
"\n",
"\n",
"[Slides: Nonlinear Dimensionality Reduction](https://github.com/ichatnun/brainCodeCamp2023_lectures/blob/main/DimensionalityReduction/dim_reduction_part4_nonlinear.pdf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## ตัวอย่างแรก\n",
"\n",
"เราจะลองใช้ PCA กับข้อมูลชุดใหม่ที่ถูกสร้างไว้ตาม code ด้านล่าง"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "GQZLjejKQvxQ"
},
"outputs": [],
"source": [
"import sys\n",
"import numpy as np\n",
"from sklearn.decomposition import PCA\n",
"from numpy.random import multivariate_normal\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import colors\n",
"\n",
"np.random.seed(42) # ตั้งค่า random seed เอาไว้ เพื่อให้การรันโค้ดนี้ได้ผลเหมือนเดิม"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 472
},
"id": "HQFGgXfJJ7AC",
"outputId": "65880ce4-80f4-4dba-ea1d-fcdd9e8a61d6"
},
"outputs": [
{
"data": {
"image/png": 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",
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