Histograms are simple; yet it's important to get the right data into them. We will cover histograms in 2D for now.
Histograms are used to visualize estimations of distribution of data. Generally, we use a few terms when speaking of histograms. Vertical rectangles represent frequencies of data points within a particular interval called a bin. Bins are created at fixed intervals, so the total area of a histogram sums to the number of data points.
Instead of using absolute values of data, histograms can display relative frequencies of data. When this is the case, the total area equals 1.
Histograms are often used in image manipulation software as a way to visualize image properties such as distribution of light in a particular color channel. Further, these image histograms can be used in computer vision algorithms to detect peaks aiding in edge detections, image segmentation, and so on.
In Chapter 5, Making 3D Visualizations, we have recipes that deal with 3D histograms.
The number of bins is the value we want to get right, but it is hard to get them right as there are no strict rules on what is the optimal number of bins. There are different theories on how to calculate the number of bins, the simplest being the one based on a ceiling function, where the number of bins (k) is equal to the ceiling (max(x) – min(x))/h,where x is the dataset plotted and h is the desired bin width. This is just one option as the number of bins required to display data properly is dependent on real data distribution.
We create a histogram calling matplotlib.pyplot.hist() with a set of parameters. Here are some of the most useful ones:
bins: This is either an integer number of bins or a sequence giving the bins. The default is10.range: This is the range of bins and is not used if bins are given as a sequence. Outliers are ignored and the default isNone.normed: If the value for this isTrue, histogram values are normalized and form probability density. The default isFalse.histtype: This parameter allows us to specify the type of histogram that we want. The default value is 'bar' and the other options are shown here:barstacked: This gives stacked-view histograms for multiple datastep: This creates a line plot that is left unfilledstepfilled: This creates line plot that is filled by default
align: This centers bars between bin edges. The default ismid. Other values areleftandright.color: This specifies the color of the histogram. It may be a single value or have a sequence of colors. If multiple datasets are specified, the color sequence will be used in the same order. If not specified, a default line color sequence is used.orientation: This allows the creation of histograms that are horizontal by settingorientationtohorizontal. The default isvertical.
The following code demonstrates how hist() is used:
import numpy as np
import matplotlib.pyplot as plt
mu = 100
sigma = 15
x = np.random.normal(mu, sigma, 10000)
ax = plt.gca()
# the histogram of the data
ax.hist(x, bins=35, color='r')
ax.set_xlabel('Values')
ax.set_ylabel('Frequency')
ax.set_title(r'$mathrm{Histogram:} mu=%d, sigma=%d$' % (mu, sigma))
plt.show()This creates a neat, red-colored histogram for our data sample:
We start by generating some normally distributed data. The histogram is plotted with the specified number of bins—35—and it is normalized by setting normed to True (or 1); we set the color to red (r).
After that, we set labels and a title for the plot. Here we used the ability to write LaTeX expressions to write math symbols and mixed that with Python format strings.