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"cell_type": "code",
"execution_count": 1,
"id": "8af97296-7b17-4c97-b62f-dce80b6ab1ac",
"metadata": {},
"outputs": [
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"data": {
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"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Age | \n",
" Blood Pressure | \n",
" Specific Gravity | \n",
" Albumin | \n",
" Sugar | \n",
" Red Blood Cells | \n",
" Pus Cell | \n",
" Pus Cell clumps | \n",
" Bacteria | \n",
" Blood Glucose Random | \n",
" ... | \n",
" Packed Cell Volume | \n",
" White Blood Cell Count | \n",
" Red Blood Cell Count | \n",
" Hypertension | \n",
" Diabetes Mellitus | \n",
" Coronary Artery Disease | \n",
" Appetite | \n",
" Pedal Edema | \n",
" Anemia | \n",
" Class | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 48 | \n",
" 70 | \n",
" 1.005 | \n",
" 4 | \n",
" 0 | \n",
" normal | \n",
" abnormal | \n",
" present | \n",
" notpresent | \n",
" 117 | \n",
" ... | \n",
" 32 | \n",
" 6700 | \n",
" 3.9 | \n",
" yes | \n",
" no | \n",
" no | \n",
" poor | \n",
" yes | \n",
" yes | \n",
" 1 | \n",
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" \n",
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" 53 | \n",
" 90 | \n",
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" abnormal | \n",
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" \n",
" | 2 | \n",
" 63 | \n",
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" 3 | \n",
" 0 | \n",
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" abnormal | \n",
" present | \n",
" notpresent | \n",
" 380 | \n",
" ... | \n",
" 32 | \n",
" 4500 | \n",
" 3.8 | \n",
" yes | \n",
" yes | \n",
" no | \n",
" poor | \n",
" yes | \n",
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3 rows × 25 columns
\n",
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Glucose | \n",
" Hemoglobin | \n",
" WBCC | \n",
" Class | \n",
" Glucose_in_std | \n",
" WBCC_in_std | \n",
" Hemoglobin_in_std | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 117 | \n",
" 11.2 | \n",
" 6700 | \n",
" 1 | \n",
" -0.220847 | \n",
" -0.567962 | \n",
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" 1 | \n",
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" -1.452826 | \n",
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" 10.8 | \n",
" 4500 | \n",
" 1 | \n",
" 3.829056 | \n",
" -1.271539 | \n",
" -1.001783 | \n",
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" \n",
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"
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},
"metadata": {},
"output_type": "display_data"
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],
"source": [
"# Let us see if we can make a prediction using the Glucose and Hemoglobin readings only\n",
"# First, we do a scatter plot where we color every data point with the class (ckd/no ckd)\n",
"# to see if there is a pattern that points to the success of the nearest neighbor classifier\n",
"fig, ax = subplots(figsize = (5, 5))\n",
"scatter = ax.scatter(data['Hemoglobin_in_std'], data['Glucose_in_std'], c = data['Class'], alpha = 0.5)\n",
"ax.set_xlabel('Hemoglobin')\n",
"ax.set_ylabel('Glucose')\n",
"handles, labels = scatter.legend_elements()\n",
"# You can define custom labels here if \"1\", \"2\", etc. are not descriptive enough\n",
"custom_labels = [\"No CKD\", \"CKD\"] \n",
"# Add the legend using the generated handles and custom labels\n",
"ax.legend(handles = handles, labels=custom_labels, loc=\"upper right\", title=\"Classes\");"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "5626649c-b1c4-4cea-9066-1f921b14daac",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.69932398, -1.07588608, 0.38289209, ..., -0.13803762,\n",
" -1.39723815, -0.01613155])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rng = np.random.default_rng()\n",
"d = 10000 #dimension\n",
"x = np.array(rng.normal(0, 1, d))\n",
"y = np.array(rng.normal(0, 1, d))"
]
},
{
"cell_type": "markdown",
"id": "49d4717a-b8d9-4893-bfd4-c5185a01334c",
"metadata": {},
"source": [
"The Euclidean distance between $(x_1, x_2, ..., x_d)$ and $(y_1, y_2, ..., y_d)$ is given by $\\sqrt{\\sum_i (x_i - y_i)^2}$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "6e2ed8d1-4386-4789-9f59-29bc6ebc9342",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.62 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 10 loops each)\n"
]
}
],
"source": [
"%%timeit -n 10 -r 1\n",
"s = 0\n",
"for i in range(d):\n",
" s = s + (x[i] - y[i])**2\n",
"dist1 = np.sqrt(s)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "e2fa0453-3615-41a2-8a6e-35bcde52d52b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"146 µs ± 0 ns per loop (mean ± std. dev. of 1 run, 10 loops each)\n"
]
}
],
"source": [
"%%timeit -n 10 -r 1\n",
"dist2 = np.linalg.norm(x - y)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "905ea96b-0a1f-4e07-a233-31b2d9559543",
"metadata": {},
"outputs": [
{
"data": {
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