Hyper Spectral HCA

Hyper Spectral Hierarchical Clustering Analysis (HSHCA) provides hierarchical clustering analysis (HCA) specialized for hyperspectral images that can be measured by techniques such as Raman microscopy.

Generally, when applying HCA to hyperspectral images, the numerous spectra composing the image are treated independently as vectors in multidimensional spaces. Therefore, information about spatial coordinates (example of unit: μm) at each measurement point of the spectra is lost.

HSHCA efficiently clusters spectra originating from physically adjacent measurement points by using both the distances between spectra ($d_{spectral}$) and the distances in real space between measurement points ($d_{spatial}$) as the definition of distance when performing HCA.

Principle

To see an overview of HSHCA, please refer to this file.

In HSHCA, the distance between cluster A and cluster B ( $d(A,B)$ ) is processed in HCA using the distance between spectra ( $d_{spectral}(A,B)$ ) and the distance in real space ( $d_{spatial}(A,B)$ ), i.e.:

$$d(A,B) = d_{spectral}(A,B) + \lambda\cdot d_{spatial}(A,B)$$

Since $d_{spectral}$ and $d_{spatial}$ have different dimensions, $\lambda$ is used as a coefficient to scale these values to the same magnitude. Note that $\lambda$ is a hyperparameter that needs to be adjusted according to measurement conditions and other factors.

$d_{spectral}$ is defined by metrics and methods commonly used in traditional HCA algorithms. For example, when using the Euclidean distance, $d_{spectral}$ corrensponds to the square root of the sum of squared differences of two spectra, and when using the cityblock distance, $d_{spectral}$ corresponds to the sum of the absolute differences of two spectra.

$d_{spatial}$ is defined as the Euclidean distance in real space, which is represented by the formula:

$$d_{spatial}(A,B) = \sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}$$

where $(x_A, y_A)$ and $(x_B, y_B)$ are the spatial coordinates of points A and B, respectively.

Installation

Install with pip (using Git, recommended)

Install Hyper Spectral HCA with:

$ python -m pip install git+https://github.com/MiLL4U/hshca.git

Install with pip

1. download a wheel package (*.whl) from Releases

2. Install Hyper Spectral HCA with pip:

$ python -m pip install hshca-x.y.z-py3-none-any.whl

(replace x.y.z with the version of HSHCA which you downloaded)

Install with git clone

1. Clone this repository

$ git clone https://github.com/MiLL4U/hshca.git

2. Go into the repository

$ cd hshca

3. Install Hyper Spectral HCA with setup.py

$ python setup.py install

Usage

Please refer to this script for an example of execution (need to install matplotlib).

Import HyperSpectralHCA, link method, and metric

from hshca import HyperSpectralHCA
from hshca.linkmethod import Ward
from hshca.metric import Euclidean

Load hyperspectral image as NumPy array

import numpy as np

image = np.load("./test/test_cell.npy")

Run HyperSpectralHCA

hshca = HyperSpectralHCA(
    data=image,  # hyperspectral image to analyze
    method=Ward,  # linkage method
    spectral_metric=Euclidean,  # metric
    spatial_dist_factor=1e-5,  # factor for spatial distance (lambda)
    spatial_scale=(1.0, 1.0),  # scale for each spatial axis (x, y, ...)
    show_progress=True  # set True here if you want to see progress bar
)
hshca.compute()

Get results

cluster_map = hshca.get_cluster_map(5)  # number of clusters
average_spectra = hshca.get_average_vectors(5)

Show results (using matplotlib)

import matplotlib.pyplot as plt

fig, ax = plt.subplots(1, 2, layout='constrained')
cluster_map = ax[0].imshow(cluster_map, cmap='Paired')
for cluster_idx, spectra in enumerate(average_spectra):
    ax[1].plot(spectra, label=f"Cluster {cluster_idx}")
ax[1].legend()
fig.colorbar(cluster_map, ax=ax[0], orientation='horizontal',
             label="Cluster index")
plt.show()

This script yields: