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‎README.md

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1) Naive Bayes classifier for categorical data from scratch in Python
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2) Naive Bayes classifier for continuous data from scratch in Python
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3) Data Visualization: Showing Iris dataset with Blender API
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4) Norms in vector space: A review of norms, and reminding p-norms are included. Finally, we compare some special p-norms.
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4) Norms in vector space: A review of norms, and reminding p-norms are included. Finally, we compare some special p-norms.
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5) Inner products in vector space: Reminding dot product and Frobenius inner product, and then canonical norms based on them. There are examples with module *numpy*.

‎inner product-ML- background.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "58525ac6",
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"metadata": {},
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"source": [
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"### Machine Learning (Background): Inner products\n",
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"$\\mathbf{u}\\cdot\\mathbf{v}=\\sum_{i=1}^n u_i v_i \\,\\rightarrow \\lVert \\mathbf{u} \\rVert_{canonical}=\\sqrt{\\mathbf{u}\\cdot\\mathbf{u}}$ <br>\n",
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"$<A,B>_F=tr(A^HB) \\, \\rightarrow\\lVert A \\rVert_F=\\sqrt{<A,A>_F}$\n",
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"###### by Hamed Shah-Hosseini\n",
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"Explanation at: https://www.pinterest.com/HamedShahHosseini/Machine-Learning/Background-Knowledge\n",
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"<br>Explanation in Persian: https://www.instagram.com/words.persian\n",
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"<br>Code that: https://github.com/ostad-ai/Machine-Learning"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 98,
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"id": "ddd68127",
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"metadata": {},
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"outputs": [],
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"source": [
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"# importing the required module\n",
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"# درون‌بَری سنجانه نیازداشته\n",
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"import numpy as np"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 99,
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"id": "b12e168b",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"vector 1: [2 1 1 3]\n",
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"vector 2: [1 2 4 3]\n",
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"dot product: 17\n",
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"1-norm of vector 1: 7.0\n",
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"1-norm of vector 2 10.0\n",
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"2-norm of vector 1: 3.872983346207417\n",
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"2-norm of vector 2 5.477225575051661\n",
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"canonical norm of vector 1: 3.872983346207417\n",
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"canonical norm of vector 2 5.477225575051661\n"
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]
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}
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],
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"source": [
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"# dot product and p-norms, example\n",
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"# فرآورد خجک و پ-هنجارها: نمونه\n",
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"vec1=np.random.randint(1,5,4)\n",
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"vec2=np.random.randint(1,5,4)\n",
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"print('vector 1:',vec1)\n",
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"print('vector 2:',vec2)\n",
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"print('dot product: ',np.dot(vec1,vec2))\n",
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"print('1-norm of vector 1:',np.linalg.norm(vec1,ord=1))\n",
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"print('1-norm of vector 2',np.linalg.norm(vec2,ord=1))\n",
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"print('2-norm of vector 1:',np.linalg.norm(vec1,ord=2))\n",
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"print('2-norm of vector 2',np.linalg.norm(vec2,ord=2))\n",
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"print('canonical norm of vector 1:',np.sqrt(np.dot(vec1,vec1)))\n",
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"print('canonical norm of vector 2',np.sqrt(np.dot(vec2,vec2)))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 102,
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"id": "1a0b718b",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The matrix:\n",
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" [[3 2 2]\n",
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" [3 1 4]\n",
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" [1 3 2]]\n",
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"---------------------\n",
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"Eigenvalues of matrix: [ 6.92434399 1.21506597 -2.13940996]\n",
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"Trace of matrix: 6\n",
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"sum of eigenvalues: 5.999999999999998\n",
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"-------------\n",
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"Determinant of matrix: -18.000000000000004\n",
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"Product of eigenvalues: -18.0\n",
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"------------------\n",
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"Frobenius norm of matrix: 7.54983443527075\n",
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"Norm using Frobenius inner product: 7.54983443527075\n"
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]
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}
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],
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"source": [
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"# Example for trace, determinant, and norm of a matrix\n",
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"# نمونه برای رآس، بَریهنده، و هنجار یک ماتکدان\n",
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"M=np.random.randint(1,5,(3,3))\n",
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"eigs=np.linalg.eigvals(M)\n",
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"detM=np.linalg.det(M)\n",
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"print('The matrix:\\n',M)\n",
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"print('---------------------')\n",
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"print('Eigenvalues of matrix:',eigs)\n",
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"print('Trace of matrix:',np.trace(M))\n",
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"print('sum of eigenvalues:',np.sum(eigs))\n",
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"print('-------------')\n",
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"print('Determinant of matrix: ',detM)\n",
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"print('Product of eigenvalues: ',np.prod(eigs))\n",
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"print('------------------')\n",
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"print('Frobenius norm of matrix:',np.linalg.norm(M,ord='fro'))\n",
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"print('Norm using Frobenius inner product:',np.sqrt(np.trace(M.T@M)))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "0df1d5e9",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.15"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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