Nearly all of the hypertools functionality may be accessed through the main plot function. This design enables complex data analysis, data manipulation, and plotting to be carried out in a single function call. To use it, simply pass your samples by features dataset(s) [in the form of a numpy array, pandas dataframe, or (mixed) list] to the plot function. Let’s explore!

Import Hypertools and other libraries for tutorial

import hypertools as hyp
import numpy as np
import scipy
import pandas as pd
from scipy.linalg import toeplitz
from copy import copy

%matplotlib inline

Load your data

We will load one of the sample datasets. This dataset consists of 8,124 samples of mushrooms with various text features.

geo = hyp.load('mushrooms')
mushrooms = geo.get_data()

We can peek at the first few rows of the dataframe using the pandas function head().

bruises cap-color cap-shape cap-surface gill-attachment gill-color gill-size gill-spacing habitat odor ... ring-type spore-print-color stalk-color-above-ring stalk-color-below-ring stalk-root stalk-shape stalk-surface-above-ring stalk-surface-below-ring veil-color veil-type
0 t n x s f k n c u p ... p k w w e e s s w p
1 t y x s f k b c g a ... p n w w c e s s w p
2 t w b s f n b c m l ... p n w w c e s s w p
3 t w x y f n n c u p ... p k w w e e s s w p
4 f g x s f k b w g n ... e n w w e t s s w p

5 rows × 22 columns

Plot with default settings

Hypertools can plot your high-dimensional data quickly and easily with little user-generated input. By default, hypertools automatically reduces your data via incremental principal component analysis (if dimensions > 3) and plots plots a 3D line plot where the axes represent the top 3 principal components of the dataset.

geo = hyp.plot(mushrooms) # plots a line

By default, hypertools assumes you are passing in a timeseries, and so it plots a trajectory of the data evolving over time. If you aren’t visualizing a timeseries, you can instead plot the individual observations as dots or other symbols by specifying an appropriate format style.

To show the individual points, simply pass the '.' format string in the second argument position, or in any position using fmt='.'; the format string is parsed by matplotlib.

geo = hyp.plot(mushrooms, '.') # plots dots
geo = hyp.plot(mushrooms, fmt = 'b*') # plots blue asterisks

Plot in 2D

We can also opt to plot high dimensional data in two dimensional space, rather than 3D, by passing the ndims argument.

geo = hyp.plot(mushrooms, '.', ndims=2)

Using other dimensionality reduction algorithms

To explore a data reduction method aside from the default (PCA), use reduce argument. Here, we pass the reduce argument a string.

Other supported reduction models include: PCA, IncrementalPCA, SparsePCA, MiniBatchSparsePCA, KernelPCA, FastICA, FactorAnalysis, TruncatedSVD, DictionaryLearning, MiniBatchDictionaryLearning, TSNE, Isomap, SpectralEmbedding, LocallyLinearEmbedding, MDS, UMAP

geo = hyp.plot(mushrooms, '.', reduce='SparsePCA')

Parameter Specifications

For finer control of the parameters, you can pass the reduce argument a dictionary (see scikit learn documentation about parameter options for specific reduction techniques).

geo = hyp.plot(mushrooms, '.', reduce={'model' : 'PCA', 'params' : {'whiten' : True}})

Coloring by hue

To color your datapoints by group labels, pass the hue argument. It accepts strings, ints, and floats, or a list of these. You must pass hue the same number of labels as you have rows in your data matrix.

Here, we group the data in five different chunks of equal size (size #points / 5) for simplicity. Note that we pass ints, strings, floats, and None in the same list to the hue argument.

split = int(mushrooms.shape[0]/ 5)
hue = [1]*split + ['two']*split + [3.0]*split + [None]*split + ['four']*split
geo_group = hyp.plot(mushrooms, '.', hue=hue)

Adding a legend

When coloring, you may want a legend to indicate group type. Passing legend=True will generate the legend based on your groupings.

split = int(mushrooms.shape[0]/5)
hue = [1]*split + ['two']*split + [3.0]*split + [None]*split + ['four']*split
geo_hue = hyp.plot(mushrooms, '.', hue=hue, legend=True)

Interpolating missing data

Missing data points? No problem! Hypertools will fill missing values via probabalistic principal components analysis (PPCA). Here, we generate a small synthetic dataset, remove a few values, then use PPCA to infer those missing values. Then, we plot the original data and the interpolated data, for comparison. The one exception is that in cases where the entire data sample (row) is nans. In this scenario, there is no data for PPCA to base its guess on, so the inference will fail.

# simulate data
K = 10 - toeplitz(np.arange(10))
data1 = np.cumsum(np.random.multivariate_normal(np.zeros(10), K, 250), axis=0)
data2 = copy(data1)

# randomly remove 5% of the data
missing = .01
inds = [(i,j) for i in range(data1.shape[0]) for j in range(data1.shape[1])]
missing_data = [inds[i] for i in np.random.choice(int(len(inds)), int(len(inds)*missing))]
for i,j in missing_data:

# reduce the data
data1_r,data2_r = hyp.reduce([data1, data2], ndims=3)

# pull out missing inds
missing_inds =
missing_data = data2_r[missing_inds, :]

# plot
geon_nan = hyp.plot([data1_r, data2_r, missing_data], ['-', '--', '*'],
         legend=['Full', 'Missing', 'Missing Points'])
/Users/andyheusser/Documents/github/hypertools/hypertools/tools/ UserWarning: Missing data: Inexact solution computed with PPCA (see for details)
  warnings.warn('Missing data: Inexact solution computed with PPCA (see for details)')

Labeling plotted points

The labels argument accepts a list of labels for each point, which must be the same length as the data (the number of rows). If no label is wanted for a particular point, simply input None. In this example, we have made use of None in order to label only three points of interest (the first, second, and last in our set).

num_unlabeled = int(mushrooms.shape[0])-3
labeling = ['a','b'] + [None]*num_unlabeled + ['c']
label = hyp.plot(mushrooms, '.', labels = labeling)

Data Clustering

Hypertools can also auto-cluster your datapoints with the n_clusters argument. To implement, simply set n_clusters to an integer.

geo_cluster = hyp.plot(mushrooms, '.', n_clusters = 6)


For quick, easy data normalization of the input data, pass the normalize argument.

You can pass the following arguments as strings: + across - columns z-scored across lists (default) + within - columns z-scored within each list + row - each row z-scored

geo_cluster = hyp.plot(mushrooms, '.', normalize = 'within')

Aligning datasets with different coordinate systems

You can also align multiple datasets using the hypertools plot function in order to visualize data in a common space. This is useful, if you have more than one high-dimensional dataset that is related to the same thing. For example, consider a brain imaging (fMRI) dataset comprised of multiple subjects watching the same movie. Voxel A in subject 1 may not necessarily be Voxel A in subject 2. Alignment allows you to rotate and scale multiple datasets so they are in maximal alignment with one another.

To do so, pass one of the following strings to the align argument (as shown below):

Below, is a simple example of a spiral.

# load example data
geo = hyp.load('spiral')
geo.plot(title='Before Alignment')

# use procrusted to align the data
source, target = geo.get_data()
aligned = [, target), target]

# after alignment
geo_aligned = hyp.plot(aligned, ['-','--'], title='After alignment')
../_images/plot_43_0.png ../_images/plot_43_1.png


To save a plot created with hypertools, simply pass the save_path argument.

# geo_cluster = hyp.plot(mushrooms, '.', save_path='cluster_plot.pdf')

Plotting text using semantic models

In addition to numerical data, hypertools supports the plotting of text data by fitting the data to a semantic model. We’ll load in an example text dataset to get started which is comprised of all State of the Union Addresses from 1989-2017.

geo = hyp.load('sotus')

By default, the text data will be transformed using a Latent Dirichlet Model trained on a sample of wikipedia pages. Simply pass the list of text data to the plot function, and under the hood it will be transformed to a topic vector and then reduced for plotting.

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