## Description
**Spectral Interpretation using Gaussian Mixtures and Autoencoder (SIGMA)** is an open-source Python library for phase identification and spectrum analysis for energy dispersive x-ray spectroscopy (EDS) datasets. The library mainly builds on the [**Hyperspy**](https://hyperspy.org/), [**Pytorch**](https://pytorch.org/), and [**Scikit-learn**](https://scikit-learn.org/stable/). The publication is available [**here**](https://doi.org/10.1002/essoar.10511396.1).<br />
**(UPDATE v0.2.0)** SIGMA now supports [**UMAP**](https://umap-learn.readthedocs.io/en/latest/index.html#) for dimensionality reduction and [**HDBSCAN**](https://scikit-learn.org/stable/modules/generated/sklearn.cluster.HDBSCAN.html) for clustering.
**Try your dataset on SIGMA with Colab in the cloud:**
| Type of data | Support format | Colab link
:---: | :---: | :---:
| SEM | `.bcf` `.hspy` | <a href="https://colab.research.google.com/github/poyentung/sigma/blob/master/tutorial/colab/tutorial_colab_sem.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a>|
| TEM | `.emi`/`.ser` `.emd`| <a href="https://colab.research.google.com/github/poyentung/sigma/blob/master/tutorial/colab/tutorial_colab_tem_emi_emd.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> |
| Images | `.tif` `.png` | <a href="https://colab.research.google.com/github/poyentung/sigma/blob/master/tutorial/colab/tutorial_colab_image.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a>|
This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 101005611: [**The EXCITE Network**](https://excite-network.eu/). If analysis using SIGMA forms a part of published work please cite the [manuscript](https://doi.org/10.1029/2022GC010530).
## Installation
1. Create a [**Python>=3.10**](https://www.python.org/) environment with [**conda**](https://docs.conda.io/en/latest/):
```bash
conda create -n sigma python=3.10
conda activate sigma
```
2. Install **SIGMA** with [**pip**](https://pypi.org/project/pip/):
```bash
pip install emsigma
```
3. Use the notebook in the tutorial folder to run **SIGMA**.
```bash
jupyter-lab
```
## Workflow of SIGMA
1. A neural network autoencoder is trained to learn good representations of elemental pixels in the 2D latent space. <br />
<div align="left">
<img width="650" alt="Autoencoder" src="https://user-images.githubusercontent.com/29102746/163899500-34ac68e2-9a38-44d9-a869-e40c024c420b.png">
</div><br />
2. The trained encoder is then used to transform high-dimensional elemental pixels into low-dimensional representations, followed by clustering using Gaussian mixture modeling (GMM) in the informative latent space.<br />
<div align="left">
<img width="650" alt="GMM" src="https://user-images.githubusercontent.com/29102746/163899758-6bd61544-fa91-44ac-8647-d249982b6607.png">
</div><br />
3. Non-negative matrix factorization (NMF) is applied to unmix the single-phase spectra for all clusters.<br />
<div align="left">
<img width="650" alt="NMF" src="https://user-images.githubusercontent.com/29102746/163899763-0fb4f835-3380-4504-9f3a-bb33089421f8.png">
</div><br />
In such a way, the algorithm not only identifies the locations of all unknown phases but also isolates the background-subtracted EDS spectra of individual phases.
## User-friendly GUI
### Check .bcf file
An example of checking the EDS dataset and the sum spectrum.
<details open>
<summary>Demo with Colab</summary>
</details>
### Dimensionality reduction and clustering
An example of analysing the latent space using the graphical widget.
<details open>
<summary>Demo with Colab</summary>
</details>
### Factor analysis on cluster-wise spectra
A demo of acquiring Background-substracted spectrum using Factor Analysis (FA).
<details open>
<summary>Demo with Colab</summary>
</details>
Raw data
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