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‎Other/ML0101EN-16 Distance Metric.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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"nteract": {
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"transient": {
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"deleting": false
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}
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}
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},
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"source": [
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"### DistanceMetric\n",
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"\n",
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"This class provides a uniform interface to fast distance metric functions. The various metrics can be accessed via the get_metric class method and the metric string identifier"
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]
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},
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{
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"cell_type": "markdown",
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"transient": {
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"deleting": false
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}
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}
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},
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"source": [
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"**Available Metrics**\n",
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"\n",
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"The following lists the string metric identifiers and the associated distance metric classes:\n",
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"\n",
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"* Metrics intended for real-valued vector spaces:\n",
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"\n",
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"|**Identifier**|**Class name in scikit-learn**|**Args**|**Distance function**|\n",
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"|--------------|------------|------------|------------|\n",
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"|`Euclidean`|EuclideanDistance|.|$sqrt(sum((x - y)^2))$|\n",
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"|`Manhattan`|ManhattanDistance|.|$sum(x - y)$|\n",
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"|`chebyshev`|ChebyshevDistance|.|$max(x - y)$|\n",
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"|`minkowski`|MinkowskiDistance|p|$sum(x - y^p)^(1/p)$|\n",
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"|`wminkowski`|WMinkowskiDistance|p, w|$sum(w * (x - y)^p)^(1/p)$|\n",
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"|`seuclidean`|SEuclideanDistance|V|$sqrt(sum((x - y)^2 / V))$|\n",
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"|`mahalanobis`|MahalanobisDistance|V or VI|$sqrt((x - y)' V^-1 (x - y))$|\n",
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"\n",
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"\n",
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"\n",
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"**Metrics intended for two-dimensional vector spaces:**\n",
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"\n",
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"* Note that the haversine distance metric requires data in the form of [latitude, longitude] and both inputs and outputs are in units of radians.\n",
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"\n",
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"|**Identifier**|**Class name in scikit-learn**|**Distance function**|\n",
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"|--------------|------------|------------|------------|\n",
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"|`haversine`|HaversineDistance|$2 arcsin(sqrt(sin^2(0.5*dx) + cos(x1)cos(x2)sin^2(0.5*dy)))$|"
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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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"nteract": {
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"transient": {
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"deleting": false
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}
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}
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[0, 1, 2],\n",
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" [3, 4, 5]])"
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]
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},
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"execution_count": 2,
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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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"from sklearn.neighbors import DistanceMetric\n",
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"import numpy as np\n",
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"\n",
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"euclidean_dist = DistanceMetric.get_metric('euclidean')\n",
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"X = np.array([[0, 1, 2],[3, 4, 5]])\n",
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"X"
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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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"nteract": {
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"transient": {
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"deleting": false
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}
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}
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[0. , 5.19615242],\n",
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" [5.19615242, 0. ]])"
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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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"euclidean_dist.pairwise(X)"
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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": 4,
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"metadata": {
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"nteract": {
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"transient": {
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"deleting": false
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}
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}
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},
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"outputs": [],
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"source": [
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"Manhattan_dist = DistanceMetric.get_metric('manhattan')"
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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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"nteract": {
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"transient": {
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"deleting": false
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}
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}
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[0., 9.],\n",
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" [9., 0.]])"
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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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"Manhattan_dist.pairwise(X)"
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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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"metadata": {
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"nteract": {
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"transient": {
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"deleting": false
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}
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}
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},
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"outputs": [],
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"source": [
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"ChebyshevDistance = DistanceMetric.get_metric('chebyshev')"
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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": 7,
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"metadata": {
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"nteract": {
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"transient": {
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"deleting": false
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}
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}
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[0., 3.],\n",
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" [3., 0.]])"
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]
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},
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"execution_count": 7,
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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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"ChebyshevDistance.pairwise(X)"
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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": 8,
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"metadata": {
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"nteract": {
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"transient": {
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"deleting": false
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}
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}
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[0. , 5.19615242],\n",
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" [5.19615242, 0. ]])"
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]
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},
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"execution_count": 8,
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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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"MinkowskiDistance = DistanceMetric.get_metric('minkowski')\n",
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"MinkowskiDistance.pairwise(X)"
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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": 10,
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"metadata": {
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"nteract": {
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"transient": {
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"deleting": false
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}
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}
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"2.0"
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]
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},
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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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"from scipy.spatial import distance\n",
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"distance.wminkowski([1, 0, 0], [0, 1, 0], 1, np.ones(3))"
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]
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}
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],
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"metadata": {
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"kernel_info": {
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"name": "python3"
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},
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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": "3.6.8"
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},
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"version": "0.24.0"
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}
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"nbformat": 4,
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"nbformat_minor": 4
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}

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