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 as hyp
import numpy as np
import scipy
import pandas as pd
from scipy.linalg import toeplitz
from copy import copy
%matplotlib inline
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()
.
mushrooms.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
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
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)
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')
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}})
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)
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)
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:
data2[i,j]=np.nan
# reduce the data
data1_r,data2_r = hyp.reduce([data1, data2], ndims=3)
# pull out missing inds
missing_inds = hyp.tools.missing_inds(data2)
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/format_data.py:141: UserWarning: Missing data: Inexact solution computed with PPCA (see https://github.com/allentran/pca-magic for details)
warnings.warn('Missing data: Inexact solution computed with PPCA (see https://github.com/allentran/pca-magic for details)')
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)
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')
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):
hyper
- hyperalignment algorithm (default) See:
http://haxbylab.dartmouth.edu/publications/HGC+11.pdf
SRM
- shared response model algorithm. See:
https://papers.nips.cc/paper/5855-a-reduced-dimension-fmri-shared-response-model.pdf
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 = [hyp.tools.procrustes(source, target), target]
# after alignment
geo_aligned = hyp.plot(aligned, ['-','--'], title='After alignment')
To save a plot created with hypertools, simply pass the save_path
argument.
# geo_cluster = hyp.plot(mushrooms, '.', save_path='cluster_plot.pdf')
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.
geo.plot()
<hypertools.datageometry.DataGeometry at 0x11448fcc0>