In this lab, you apply nearest neighbors technique to help a taxi company predict the length of their rides. Imagine that we are hired to consult for LiftOff, a limo and taxi service that is just opening up in NYC. Liftoff wants it's taxi drivers to target longer rides, as the longer the ride the more money it makes. LiftOff has the following theory:
the pickup location of a taxi ride can help predict the length of the ride.
LiftOff asks us to do some analysis to write a function that will allow it to **predict the length of a taxi ride for any given location **.
Our technique will be the following:
Collect the data to retrieve taxi data, and only select the attributes of taxi trips that we need
** Explore ** Exampine the attributes of our data, and plot some of our data on a map
** Train ** Write our nearest neighbors formula, and change the number of nearby trips to predict the length of a new trip
** Predict ** Use our function to predict trip lengths of new locations
Collect and Explore the data
Lucky for us, if we go to NYC Open Data information about NYC taxi trips is available on it's website .
For you're reading pleasure, the data has already been downloaded into the trips.json file in this lab which you can find here. We'll use Python's json
library to take the data from the trips.json
file and store it as a variable in our notebook.
import json
# First, read the file
trips_file = open ('trips.json' )
# Then, convert contents to list of dictionaries
trips = json .load (trips_file )
Press shift + enter
The next step is to explore the data. First, let's see how many trips we have.
Not bad at all. Now let's see what each individual trip looks like. Each trip is a dictionary, so we can see the attributes of each trip with the keys
function.
dict_keys(['dropoff_datetime', 'dropoff_latitude', 'dropoff_longitude', 'fare_amount', 'imp_surcharge', 'mta_tax', 'passenger_count', 'payment_type', 'pickup_datetime', 'pickup_latitude', 'pickup_longitude', 'rate_code', 'tip_amount', 'tolls_amount', 'total_amount', 'trip_distance', 'vendor_id'])
Ok, now that we have explored some of our data, let's begin to think through what data we need for our task.
Remember that our task is to use the trip location to predict the length of a trip . So let's just select the pickup_latitude
, pickup_longitude
, and trip_distance
from each trip. That will give us the trip location and related trip_distance
for each trip. Then based on these actual trip distances we can use nearest neighbors to predict an expected trip distance for a trip, provided an actual location.
** Add in about trip distance **
Write a function called parse_trips(trips)
that returns an list of the trips with only the following attributes:
trip_distance
pickup_latitude
pickup_longitude
def parse_trips (trips ):
return list (map (lambda trip : {'trip_distance' : trip ['trip_distance' ], 'pickup_latitude' : trip ['pickup_latitude' ], 'pickup_longitude' : trip ['pickup_longitude' ]},trips ))
parsed_trips = parse_trips (trips )
parsed_trips and parsed_trips [0 ]
# {'pickup_latitude': 40.64499,
# 'pickup_longitude': -73.78115,
# 'trip_distance': 18.38}
{'pickup_latitude': '40.64499',
'pickup_longitude': '-73.781149999999997',
'trip_distance': '18.379999999999999'}
Now, there's just one change to make. If you look at one of the trips, all of the values are strings. Let's change them to be integers.
def float_values (trips ):
return trips and list (map (lambda trip : {'trip_distance' : float (trip ['trip_distance' ]), 'pickup_latitude' : float (trip ['pickup_latitude' ]), 'pickup_longitude' : float (trip ['pickup_longitude' ])},trips ))
cleaned_trips = float_values (parsed_trips )
{'pickup_latitude': 40.64499,
'pickup_longitude': -73.78115,
'trip_distance': 18.38}
Now that we have paired down our data, let's get a sense of our trip data. We can use the folium
Python library to plot a map of Manhattan, and our data. We import folium
, and then use the Map
function to pass through a location
, and zoom_start
.
import folium
manhattan_map = folium .Map (location = [40.7589 , - 73.9851 ], zoom_start = 11 )
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Ok, now let's see how we could add a dot to mark a specific location. We'll start with Times Square.
marker = folium .CircleMarker (location = [40.7589 , - 73.9851 ], radius = 10 )
marker .add_to (manhattan_map )
<folium.features.CircleMarker at 0x11987ea90>
Above, we first create a marker. Then we add that circle marker to the manhattan_map
we created earlier.
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Do you see that blue dot near Time's Square? That is our marker.
So now thar we can plot one marker on a map, we should have a sense of how we can plot many markers on a map to display our taxi ride data. We simply plot a map, and then we add a marker for each location of a taxi trip.
So now let's write some functions to allow us to plot maps and add markers a little more easily.
Writing some map plotting functions
As a first step towards this, note that the functions to create both a marker and map each take in a location as two element list, representing the latitude and longitude values. Take another look:
marker = folium .CircleMarker (location = [40.7589 , - 73.9851 ])
manhattan_map = folium .Map (location = [40.7589 , - 73.9851 ])
So let's write a function called to create this two element list from a trip. Write a function called location
that takes in a trip as an argument and returns a list where the first element is the latitude and the second is the longitude. Remember that a location looks like the following:
first_trip = {'pickup_latitude' : 40.64499 , 'pickup_longitude' : - 73.78115 , 'trip_distance' : 18.38 }
first_trip
{'pickup_latitude': 40.64499,
'pickup_longitude': -73.78115,
'trip_distance': 18.38}
def location (trip ):
return [trip ['pickup_latitude' ], trip ['pickup_longitude' ]]
first_location = location (first_trip ) # [40.64499, -73.78115]
first_location # [40.64499, -73.78115]
Ok, now that we can turn a trip into a location, let's turn a location into a marker. Write a function called to_marker
that takes in a location (in the form of a list) as an argument, and returns a folium circleMarker
for that location. The radius of the marker should always equal 6.
def to_marker (location ):
return folium .CircleMarker (location , radius = 6 )
import json
times_square_marker = to_marker ([40.7589 , - 73.9851 ])
times_square_marker and times_square_marker .location # [40.7589, -73.9851]
times_square_marker and json .loads (times_square_marker .options )['radius' ] # 6
Ok, now that we know how to produce a single marker, let's write a function to produce lots. We can write a function called markers_from_trips
that takes in a list of trips, and returns a marker object for each trip.
def markers_from_trips (trips ):
locations = list (map (lambda trip : location (trip ), trips ))
return list (map (lambda location : to_marker (location ),locations ))
trip_markers = markers_from_trips (cleaned_trips )
trip_markers and len (trip_markers ) # 1000
marker_locations = None
if trip_markers :
marker_locations = list (map (lambda marker : marker .location ,trip_markers ))
trip_markers and marker_locations == list (map (lambda trip : location (trip ), cleaned_trips )) # True
Ok, now that we have a function that creates locations, and a function that creates markers, it is time to write a function to plot a map.
Write a function called map_from
that, provided the first argument of a list location and second argument an integer representing the zoom_start
, returns a folium
map the corresponding location and zoom_start
attributes.
Hint: The following is to write a map with folium:
folium.Map(location=location, zoom_start=zoom_amount)
def map_from (location , zoom_amount ):
return folium .Map (location = location , zoom_start = zoom_amount )
times_square_map = map_from ([40.7589 , - 73.9851 ], 15 )
times_square_map and times_square_map .location # [40.7589, -73.9851]
times_square_map and times_square_map .zoom_start # 15
times_square_marker and times_square_marker .add_to (times_square_map )
times_square_map
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Now that we have a marker and a map, now let's write a function that adds a lot of markers to a map.
manhattan_map = map_from ([40.7589 , - 73.9851 ], 13 )
def add_markers (markers , map_obj ):
for marker in markers :
marker .add_to (map_obj )
return map_obj
map_with_markers = add_markers (trip_markers , manhattan_map )
<bound method Map.choropleth of <folium.folium.Map object at 0x10b7aa1d0>>
Ok, let's write a function that given a latitude and longitude will predict the fare distance for us. We'll do this by first finding the nearest trips given a latitude and longitude.
As a first step, write a function named distance_location
that calculates the distance in pickup location between two trips.
import math
def distance_location (selected_trip , neighbor_trip ):
distance_squared = (neighbor_trip ['pickup_latitude' ] - selected_trip ['pickup_latitude' ])** 2 + (neighbor_trip ['pickup_longitude' ] - selected_trip ['pickup_longitude' ])** 2
return math .sqrt (distance_squared )
first_trip = {'pickup_latitude' : 40.64499 , 'pickup_longitude' : - 73.78115 , 'trip_distance' : 18.38 }
second_trip = {'pickup_latitude' : 40.766931 , 'pickup_longitude' : - 73.982098 , 'trip_distance' : 1.3 }
distance_first_and_second = distance_location (first_trip , second_trip )
distance_first_and_second and round (distance_first_and_second , 3 ) # 0.235
Ok, next write a function called distance_between_neighbors
that adds a new key-value pair, called distance_from_selected
, that calculates the distance of the neighbor_trip
from the selected_trip
.
def distance_between_neighbors (selected_trip , neighbor_trip ):
neighbor_with_distance = neighbor_trip .copy ()
neighbor_with_distance ['distance_from_selected' ] = distance_location (selected_trip , neighbor_trip )
return neighbor_with_distance
distance_between_neighbors (first_trip , second_trip )
# {'distance_from_individual': 0.23505256047318146,
# 'pickup_latitude': 40.766931,
# 'pickup_longitude': -73.982098,
# 'trip_distance': 1.3}
{'distance_from_selected': 0.23505256047318146,
'pickup_latitude': 40.766931,
'pickup_longitude': -73.982098,
'trip_distance': 1.3}
Ok, now our neighbor_trip has another attribute called distance_from_selected
, that indicates the distance from the neighbor_trip
's pickup location from the selected_trip
.
** Understand the data:** Our dictionary now has a few attributes, two of which say distance. Let's make sure we understand the difference.
distance_from_selected
: This is our calculation of the distance of the neighbor's pickup location from the selected trip.
trip_distance
: This is the attribute we were provided initially. It tells us the length of the neighbor's taxi trip from pickup to dropoff.
Next, write a function called distance_all
that provided a list of neighbors, returns each of those neighbors with their respective distance_from_individual
numbers.
def distance_all (selected_individual , neighbors ):
remaining_neighbors = filter (lambda neighbor : neighbor != selected_individual , neighbors )
return list (map (lambda neighbor : distance_between_neighbors (selected_individual , neighbor ), remaining_neighbors ))
cleaned_trips and distance_all (first_trip , cleaned_trips [0 :4 ])
Now write the nearest neighbors formula to calculate the distance of the selected_trip
from all of the cleaned_trips
in our dataset. If no number is provided, it should return the top 3 neighbors.
def nearest_neighbors (selected_trip , trips , number = 3 ):
neighbor_distances = distance_all (selected_trip , trips )
sorted_neighbors = sorted (neighbor_distances , key = lambda neighbor : neighbor ['distance_from_selected' ])
return sorted_neighbors [:number ]
new_trip = {'pickup_latitude' : 40.64499 ,
'pickup_longitude' : - 73.78115 ,
'trip_distance' : 18.38 }
nearest_three_neighbors = nearest_neighbors (new_trip , cleaned_trips or [], number = 3 )
nearest_three_neighbors
# [{'distance_from_individual': 0.0004569288784918792,
# 'pickup_latitude': 40.64483,
# 'pickup_longitude': -73.781578,
# 'trip_distance': 7.78},
# {'distance_from_individual': 0.0011292165425673159,
# 'pickup_latitude': 40.644657,
# 'pickup_longitude': -73.782229,
# 'trip_distance': 12.7},
# {'distance_from_individual': 0.0042359798158141185,
# 'pickup_latitude': 40.648509,
# 'pickup_longitude': -73.783508,
# 'trip_distance': 17.3}]
[{'distance_from_selected': 0.0004569288784918792,
'pickup_latitude': 40.64483,
'pickup_longitude': -73.781578,
'trip_distance': 7.78},
{'distance_from_selected': 0.0011292165425673159,
'pickup_latitude': 40.644657,
'pickup_longitude': -73.782229,
'trip_distance': 12.7},
{'distance_from_selected': 0.0042359798158141185,
'pickup_latitude': 40.648509,
'pickup_longitude': -73.783508,
'trip_distance': 17.3}]
Ok great! Now that we can provide a new trip location, and find the distances of the three nearest trips, we can take calculate an estimate of the trip distance for that new trip location.
We do so simply by calculating an average of it's nearest neighbors.
import statistics
def median_distance (neighbors ):
nearest_distances = list (map (lambda neighbor : neighbor ['trip_distance' ], neighbors ))
return round (statistics .median (nearest_distances ), 3 )
nearest_three_neighbors = nearest_neighbors (new_trip , cleaned_trips or [], number = 3 )
distance_estimate_of_selected_trip = mean_distance (nearest_three_neighbors ) # 12.593
Choosing the correct number of neighbors
Now, as we know from the last lesson, one tricky element is to determine how many neighbors to choose, our $k$ value, before calculating the average. We want to choose our value of $k$ such that it properly matches actual data, and so that it applies to new data. There are fancy formulas to ensure that we train our algorithm so that our formula is optimized for all data, but here let's see different $k$ values manually. This is the gist of choosing our $k$ value:
If we choose a $k$ value too low, our formula will be too heavily influenced by a single neighbor, whereas if our $k$ value is too high, we will be choosing so many neighbors that our nearest neighbors formula will not be adjust enough according to locations.
Ok, let's experiment with this.
First, let's choose a midtown location, to see what the trip distance would be. A Google search reveals the coordinates of 51st and 7th avenue to be the following.
midtown_trip = dict (pickup_latitude = 40.761710 , pickup_longitude = - 73.982760 )
seven_closest = nearest_neighbors (midtown_trip , cleaned_trips , number = 12 )
seven_closest
[{'distance_from_selected': 0.00037310588309379025,
'pickup_latitude': 40.761372,
'pickup_longitude': -73.982602,
'trip_distance': 0.58},
{'distance_from_selected': 0.00080072217404248,
'pickup_latitude': 40.762444,
'pickup_longitude': -73.98244,
'trip_distance': 0.8},
{'distance_from_selected': 0.0011555682584735844,
'pickup_latitude': 40.762767,
'pickup_longitude': -73.982293,
'trip_distance': 1.4},
{'distance_from_selected': 0.0012508768924205918,
'pickup_latitude': 40.762868,
'pickup_longitude': -73.983233,
'trip_distance': 8.3},
{'distance_from_selected': 0.0018118976240381972,
'pickup_latitude': 40.760057,
'pickup_longitude': -73.983502,
'trip_distance': 1.26},
{'distance_from_selected': 0.002067074502774709,
'pickup_latitude': 40.760644,
'pickup_longitude': -73.984531,
'trip_distance': 0.0},
{'distance_from_selected': 0.0020684557041472677,
'pickup_latitude': 40.762107,
'pickup_longitude': -73.98479,
'trip_distance': 1.72},
{'distance_from_selected': 0.0024634057725016426,
'pickup_latitude': 40.760442,
'pickup_longitude': -73.980648,
'trip_distance': 12.7},
{'distance_from_selected': 0.00250734760254793,
'pickup_latitude': 40.763684,
'pickup_longitude': -73.981214,
'trip_distance': 2.1},
{'distance_from_selected': 0.002609860149511136,
'pickup_latitude': 40.759663,
'pickup_longitude': -73.981141,
'trip_distance': 2.2},
{'distance_from_selected': 0.0026676605856094052,
'pickup_latitude': 40.759347,
'pickup_longitude': -73.981522,
'trip_distance': 2.73},
{'distance_from_selected': 0.0028054840937036273,
'pickup_latitude': 40.75906,
'pickup_longitude': -73.983681,
'trip_distance': 3.3}]
Looking at the distance_from_selected
it appears that our our trips are still fairly clses to our selected trip. Notice that most of the data is a distance of .0045 away, so going to the top 7 nearest neighbors didn't seem to give us neighbors too far from each other, which is a good sign.
Still, it's hard to know what distance in latitude and longitude really look like, so let's map the data.
midtown_location = location (midtown_trip ) # [40.76171, -73.98276]
midtown_map = map_from (midtown_location , 16 )
closest_markers = markers_from_trips (seven_closest )
add_markers (closest_markers , midtown_map )
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Ok. These locations stay fairly close to our estimated location of 51st street and 7th Avenue. So they could be a good estimate of a trip distance.
median_distance (seven_closest )
Ok, now let's try a different location
charging_bull_closest = nearest_neighbors ({'pickup_latitude' : 40.7049 , 'pickup_longitude' : - 74.0137 }, cleaned_trips , number = 12 )
median_distance (charging_bull_closest ) # 3.515
Ok, so there appears to be a significant difference between choosing a location around 51st street versus choosing a location at Wall Street.
Ok, so in this lab, we used the nearest neighbors function to predict the length of a taxi ride. To do so, we selected a location, then found a number of closest taxi rides to that location, and then took the median trip lengths of the nearest neighbors to find an estimate of the new ride's trip length. You can see that even with just a little bit of math and programming we can begin to make meaningful predictions with data.