Smoothing

Smoothing can help to discover trends that otherwise might be hard to see in raw data.

import pandas as pd

from lets_plot import *

LetsPlot.setup_html()

mpg_df = pd.read_csv('https://raw.githubusercontent.com/JetBrains/lets-plot-docs/master/data/mpg.csv')
mpg_df

	Unnamed: 0	manufacturer	model	displ	year	cyl	trans	drv	cty	hwy	fl	class
0	1	audi	a4	1.8	1999	4	auto(l5)	f	18	29	p	compact
1	2	audi	a4	1.8	1999	4	manual(m5)	f	21	29	p	compact
2	3	audi	a4	2.0	2008	4	manual(m6)	f	20	31	p	compact
3	4	audi	a4	2.0	2008	4	auto(av)	f	21	30	p	compact
4	5	audi	a4	2.8	1999	6	auto(l5)	f	16	26	p	compact
...	...	...	...	...	...	...	...	...	...	...	...	...
229	230	volkswagen	passat	2.0	2008	4	auto(s6)	f	19	28	p	midsize
230	231	volkswagen	passat	2.0	2008	4	manual(m6)	f	21	29	p	midsize
231	232	volkswagen	passat	2.8	1999	6	auto(l5)	f	16	26	p	midsize
232	233	volkswagen	passat	2.8	1999	6	manual(m5)	f	18	26	p	midsize
233	234	volkswagen	passat	3.6	2008	6	auto(s6)	f	17	26	p	midsize

234 rows × 12 columns

The default smoothing method is 'linear model' (or 'lm')

mpg_plot = ggplot(mpg_df, aes(x='displ', y='hwy'))
mpg_plot + geom_point() + geom_smooth(seed=42)

LOESS model does seem to better fit MPG data than the linear model.

mpg_plot + geom_point() + geom_smooth(method='loess', size=1, seed=42)

Applying smoothing to groups

Let’s map the vehicle drivetrain type (variable ‘drv’) to the color of points.

This makes it easy to see that points with the same type of the drivetrain are forming some kind of groups or clusters.

mpg_plot + geom_point(aes(color='drv'))\
         + geom_smooth(aes(color='drv'), method='loess', size=1, seed=42)

Apply linear model with 2nd degree polynomial.

As LOESS prediction looks a bit weird let’s try 2nd degree polinomial regression.

mpg_plot + geom_point(aes(color='drv'))\
         + geom_smooth(aes(color='drv'), method='lm', deg=2, size=1, seed=42)

Using as_discrete() function with numeric data series

In the previous examples we were using a discrete (or categorical) variable 'drv' to split the data into a groups.

Now let’s try to use a numeric variable 'cyl' for the same purpose.

mpg_plot + geom_point(aes(color='cyl'))\
         + geom_smooth(aes(color='cyl'), method='lm', deg=2, size=1, seed=42)

Easy to see that the data wasn’t split into groups. Lets-Plot offers two solutions in this situation:

• Use the group aesthetic

• Use the as_discrete() function

The group aesthetic helps to create a groups.

mpg_plot + geom_point(aes(color='cyl'))\
         + geom_smooth(aes(color='cyl', group='cyl'), method='lm', deg=2, size=1, seed=42)

The as_discrete(‘cyl’) function will “annotate” the 'cyl' variable as discrete.

This leads to creation of the groups and to assigning of a discrete color scale instead of a continuous.

mpg_plot + geom_point(aes(color='cyl'))\
         + geom_smooth(aes(color=as_discrete('cyl')), method='lm', deg=2, size=1, seed=42)

Effect of span parameter on the “wiggliness” the LOESS smoother.

The span is the fraction of points used to fit each local regression. Small numbers make a wigglier curve, larger numbers make a smoother curve.

import math
import numpy as np

n = 150
np.random.seed(42)
x_range = np.arange(-2 * math.pi, 2 * math.pi, 4 * math.pi / n)
y_range = np.sin(x_range) + np.array([np.random.uniform(-.5, .5) for i in range(n)])
df = pd.DataFrame({'x': x_range, 'y': y_range})

p = ggplot(df, aes(x='x', y='y')) + geom_point(shape=21, fill='yellow', color='#8c564b')
p1 = p + geom_smooth(method='loess', size=1.5, color='#d62728', seed=42) + ggtitle('default (span = 0.5)')
p2 = p + geom_smooth(method='loess', span=.2, size=1.5, color='#9467bd', seed=42) + ggtitle('span = 0.2')
p3 = p + geom_smooth(method='loess', span=.7, size=1.5, color='#1f77b4', seed=42) + ggtitle('span = 0.7')
p4 = p + geom_smooth(method='loess', span=1, size=1.5, color='#2ca02c', seed=42) + ggtitle('span = 1')

gggrid([p1, p2, p3, p4], ncol=2) + ggsize(800, 600)