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‎Logistic Regression.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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"metadata": {},
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"source": [
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"# Definition"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"It is a sorting regression which uses the outputs between 0 to 1 for classification of the input data given"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Sigmoid function:\n",
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"s(z) = 1 / (1+e**(-z))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"As z->-(1/0):s(z)->0 ||\n",
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"As z->(1/0):s(z)->1 ||\n",
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"At z=0:s(z)=0.5"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Generally,z is a function"
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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": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import pandas as pd"
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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": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"from sklearn import datasets\n",
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"from sklearn.linear_model import LogisticRegression"
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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": 3,
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"metadata": {},
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"outputs": [
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{
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"data": {
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" 8.758e-02],\n",
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" 'target_names': array(['malignant', 'benign'], dtype='<U9'),\n",
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" 'DESCR': '.. _breast_cancer_dataset:\\n\\nBreast cancer wisconsin (diagnostic) dataset\\n--------------------------------------------\\n\\n**Data Set Characteristics:**\\n\\n :Number of Instances: 569\\n\\n :Number of Attributes: 30 numeric, predictive attributes and the class\\n\\n :Attribute Information:\\n - radius (mean of distances from center to points on the perimeter)\\n - texture (standard deviation of gray-scale values)\\n - perimeter\\n - area\\n - smoothness (local variation in radius lengths)\\n - compactness (perimeter^2 / area - 1.0)\\n - concavity (severity of concave portions of the contour)\\n - concave points (number of concave portions of the contour)\\n - symmetry \\n - fractal dimension (\"coastline approximation\" - 1)\\n\\n The mean, standard error, and \"worst\" or largest (mean of the three\\n largest values) of these features were computed for each image,\\n resulting in 30 features. For instance, field 3 is Mean Radius, field\\n 13 is Radius SE, field 23 is Worst Radius.\\n\\n - class:\\n - WDBC-Malignant\\n - WDBC-Benign\\n\\n :Summary Statistics:\\n\\n ===================================== ====== ======\\n Min Max\\n ===================================== ====== ======\\n radius (mean): 6.981 28.11\\n texture (mean): 9.71 39.28\\n perimeter (mean): 43.79 188.5\\n area (mean): 143.5 2501.0\\n smoothness (mean): 0.053 0.163\\n compactness (mean): 0.019 0.345\\n concavity (mean): 0.0 0.427\\n concave points (mean): 0.0 0.201\\n symmetry (mean): 0.106 0.304\\n fractal dimension (mean): 0.05 0.097\\n radius (standard error): 0.112 2.873\\n texture (standard error): 0.36 4.885\\n perimeter (standard error): 0.757 21.98\\n area (standard error): 6.802 542.2\\n smoothness (standard error): 0.002 0.031\\n compactness (standard error): 0.002 0.135\\n concavity (standard error): 0.0 0.396\\n concave points (standard error): 0.0 0.053\\n symmetry (standard error): 0.008 0.079\\n fractal dimension (standard error): 0.001 0.03\\n radius (worst): 7.93 36.04\\n texture (worst): 12.02 49.54\\n perimeter (worst): 50.41 251.2\\n area (worst): 185.2 4254.0\\n smoothness (worst): 0.071 0.223\\n compactness (worst): 0.027 1.058\\n concavity (worst): 0.0 1.252\\n concave points (worst): 0.0 0.291\\n symmetry (worst): 0.156 0.664\\n fractal dimension (worst): 0.055 0.208\\n ===================================== ====== ======\\n\\n :Missing Attribute Values: None\\n\\n :Class Distribution: 212 - Malignant, 357 - Benign\\n\\n :Creator: Dr. William H. Wolberg, W. Nick Street, Olvi L. Mangasarian\\n\\n :Donor: Nick Street\\n\\n :Date: November, 1995\\n\\nThis is a copy of UCI ML Breast Cancer Wisconsin (Diagnostic) datasets.\\nhttps://goo.gl/U2Uwz2\\n\\nFeatures are computed from a digitized image of a fine needle\\naspirate (FNA) of a breast mass. They describe\\ncharacteristics of the cell nuclei present in the image.\\n\\nSeparating plane described above was obtained using\\nMultisurface Method-Tree (MSM-T) [K. P. Bennett, \"Decision Tree\\nConstruction Via Linear Programming.\" Proceedings of the 4th\\nMidwest Artificial Intelligence and Cognitive Science Society,\\npp. 97-101, 1992], a classification method which uses linear\\nprogramming to construct a decision tree. Relevant features\\nwere selected using an exhaustive search in the space of 1-4\\nfeatures and 1-3 separating planes.\\n\\nThe actual linear program used to obtain the separating plane\\nin the 3-dimensional space is that described in:\\n[K. P. Bennett and O. L. Mangasarian: \"Robust Linear\\nProgramming Discrimination of Two Linearly Inseparable Sets\",\\nOptimization Methods and Software 1, 1992, 23-34].\\n\\nThis database is also available through the UW CS ftp server:\\n\\nftp ftp.cs.wisc.edu\\ncd math-prog/cpo-dataset/machine-learn/WDBC/\\n\\n.. topic:: References\\n\\n - W.N. Street, W.H. Wolberg and O.L. Mangasarian. Nuclear feature extraction \\n for breast tumor diagnosis. IS&T/SPIE 1993 International Symposium on \\n Electronic Imaging: Science and Technology, volume 1905, pages 861-870,\\n San Jose, CA, 1993.\\n - O.L. Mangasarian, W.N. Street and W.H. Wolberg. Breast cancer diagnosis and \\n prognosis via linear programming. Operations Research, 43(4), pages 570-577, \\n July-August 1995.\\n - W.H. Wolberg, W.N. Street, and O.L. Mangasarian. Machine learning techniques\\n to diagnose breast cancer from fine-needle aspirates. Cancer Letters 77 (1994) \\n 163-171.',\n",
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" 'feature_names': array(['mean radius', 'mean texture', 'mean perimeter', 'mean area',\n",
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" 'mean smoothness', 'mean compactness', 'mean concavity',\n",
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" 'mean concave points', 'mean symmetry', 'mean fractal dimension',\n",
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" 'radius error', 'texture error', 'perimeter error', 'area error',\n",
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" 'smoothness error', 'compactness error', 'concavity error',\n",
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" 'concave points error', 'symmetry error',\n",
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" 'fractal dimension error', 'worst radius', 'worst texture',\n",
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" 'worst perimeter', 'worst area', 'worst smoothness',\n",
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" 'worst compactness', 'worst concavity', 'worst concave points',\n",
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" 'worst symmetry', 'worst fractal dimension'], dtype='<U23'),\n",
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" 'filename': 'C:\\\\Users\\\\Psyfer\\\\Anaconda3\\\\lib\\\\site-packages\\\\sklearn\\\\datasets\\\\data\\\\breast_cancer.csv'}"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"cancer_ds = datasets.load_breast_cancer()\n",
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"cancer_ds"
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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": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"text": [
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"C:\\Users\\Psyfer\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\logistic.py:433: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.\n",
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" FutureWarning)\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
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" intercept_scaling=1, max_iter=100, multi_class='warn',\n",
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" n_jobs=None, penalty='l2', random_state=None, solver='warn',\n",
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" tol=0.0001, verbose=0, warm_start=False)"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"clf = LogisticRegression()\n",
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"clf.fit(cancer_ds.data,cancer_ds.target)"
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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": 6,
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"data": {
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"clf.score(cancer_ds.data,cancer_ds.target)"
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]
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{
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"cell_type": "code",
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"execution_count": 10,
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"execution_count": 10,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"clf.predict_proba(cancer_ds.data)[13]"
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]
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},
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{
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"cell_type": "code",
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],
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"source": [
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"clf.predict(cancer_ds.data) - cancer_ds.target"
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]
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},
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{
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