Plot multidimensional vectors in Python

Question

I have a Matrix that contains N users and K items. I want to plot that matrix in Python by considering each line as a vector with multiple coordinates. For example a simple point plot require X,Y. My vector hasK coordinates and I want to plot each one of those N vectors as a point to see there similarities. Can anyone help me with that ?

UPDATE:

#Matrix M shape = (944, 1683)
plt.figure()
plt.imshow(M, interpolation='nearest', cmap=plt.cm.ocean)
plt.colorbar()
plt.show()

but this gave me as result : enter image description here

What I want is something like that: enter image description here

SO is not a code writing service, please provide any code that you have written so far in a MCVE — Ffisegydd
– Ffisegydd, Commented Nov 3, 2014 at 9:41
I should've told you that I am a beginer in Python. I search like everywhere but I did not find anything that can resolve my problem. — deltascience
– deltascience, Commented Nov 3, 2014 at 9:48
Before searching or asking for implementations, you should think about what you are hoping to see as a result. Your example is a simple 2D scatter plot. But for plotting k-dimensional data you need some other concept, like euclidean embedding or parallel coordinates. — Falko
– Falko, Commented Nov 3, 2014 at 10:11

Matt L. · Accepted Answer · 2019-07-30 20:02:35Z

It is difficult from this question to be sure if my answer is relevant, but here's my best guess. I believe deltascience is asking how multidimensional vectors are generally plotted into two-dimensional space, as would be the case with a scatter plot. I think the best answer is that some kind of dimension reduction algorithm is generally performed. In other words, you don't do this by finding the right matplotlib code; you get your data into the right shape (one list for the X axis, and another list for the Y axis) and you then plot it using a typical matplotlib approach:

import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA

M = np.random.rand(944, 1683)

pca = PCA(n_components=2)
reduced = pca.fit_transform(M)

# We need a 2 x 944 array, not 944 by 2 (all X coordinates in one list)
t = reduced.transpose()

plt.scatter(t[0], t[1])
plt.show()

Here are some relevant links:

https://stats.stackexchange.com/questions/63589/how-to-project-high-dimensional-space-into-a-two-dimensional-plane

http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html

https://towardsdatascience.com/the-art-of-effective-visualization-of-multi-dimensional-data-6c7202990c57

https://www.evl.uic.edu/documents/etemadpour_choosingvisualization_springer2016.pdf

July 2019 Addendum: It didn't occur to me at the the time, but another way people often visualize multi-dimensional data is with network visualization. Each multi-dimensional array in this context would be a node, and the edge weight would be something like the cosine similarity of two nodes, or the Euclidian distance. Networkx in python has some really nice visualization options.

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