# Install hypertools (run this first on Colab)
%pip install -q "hypertools[interactive]"

Normalization

The normalize function is a helper to z-score your data. This is useful if your features (columns) are scaled differently within or across datasets. By default, hypertools normalizes across the columns of all datasets passed, but also affords the option to normalize columns within individual lists. Alternatively, you can also normalize each row. The function returns an array or list of arrays where the columns or rows are z-scored. Note that a list containing a single array is returned as a bare array; lists of two or more arrays come back as lists.

Import packages

import hypertools as hyp
import numpy as np

%matplotlib inline

Generate synthetic data

First, we generate two sets of synthetic data. We pull points randomly from a multivariate normal distribution for each set, so the sets will exhibit unique statistical properties.

np.random.seed(123)  # seed the RNG so this tutorial is reproducible

x1 = np.random.randn(10,10)
x2 = np.random.randn(10,10)

c1 = np.dot(x1, x1.T)
c2 = np.dot(x2, x2.T)

m1 = np.zeros([1,10])
m2 = 10 + m1

data1 = np.random.multivariate_normal(m1[0], c1, 100)
data2 = np.random.multivariate_normal(m2[0], c2, 100)

data = [data1, data2]

Visualize the data

fig = hyp.plot(data, '.')

Normalizing (Specified Cols or Rows)

By default, calling hyp.normalize(data) z-scores the columns across all passed lists (equivalent to passing normalize='across'). To specify a different normalization, pass one of the following arguments as a string, as shown in the examples below.

• ‘across’ - columns z-scored across passed lists (default)

• ‘within’ - columns z-scored within passed lists

• ‘row’ - rows z-scored

Normalizing ‘across’

When you normalize ‘across’, all of the data is stacked/combined, and the normalization is done on the columns of the full dataset. Then the data is split back into separate elements.

norm = hyp.normalize(data, normalize = 'across')
fig = hyp.plot(norm, '.')

Normalizing ‘within’

When you normalize ‘within’, normalization is done on the columns of each element of the data, separately.

norm = hyp.normalize(data, normalize = 'within')
fig = hyp.plot(norm, '.')

Normalizing by ‘row’

norm = hyp.normalize(data, normalize = 'row')
fig = hyp.plot(norm, '.')