# Generation and Optimization of Spectral Cluster Maps to Enable Data Fusion of CaSSIS and CRISM Datasets

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Source

#### 2.2. Data and Location

#### 2.3. Preprocessing

#### 2.4. Dimensionality Reduction Techniques

**Autoencoder**

**t-SNE**

**UMAP**

#### 2.5. Clustering Algorithms

## 3. Results

#### 3.1. Experiment

#### 3.2. Evaluation

## 4. Discussion

^{2+}iron-bearing minerals that produce diagnostic absorptions between 700 and 1100 nm (e.g., mafic minerals such as olivine and pyroxene). The CaSSIS sensitivity range also includes diagnostic broad absorptions which arise from intervalence charge-transfer transitions of ferric iron Fe

^{3+}and O

^{2−}and are present in altered ferric (Fe

^{3+}) iron-bearing minerals (e.g., hematite, nontronite, etc.) [26].

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CaSSIS | Color and Stereo Surface Imaging System |

CH | Calinski–Harabasz |

CRISM | Compact Reconnaissance Imaging Spectrometer |

DB | Davies–Bouldin |

GMM | Gaussian Mixture model |

HiRISE | High Resolution Imaging Science Experiment |

MRO | Mars Reconnaissance Orbiter |

MTRDR | Map-projected Targeted Reduced Data Record |

PCA | Principal omponent analysis |

SC | Silhouette Coefficient |

SCM | Spectral Cluster Map |

SOM | Self-organizing map |

t-SNE | t-distributed Stochastic Neighbor Embedding |

TGO | ExoMars Trace Gas Orbiter |

UMAP | Uniform Manifold Approximation and Projection |

## Appendix A

**Table A1.**Mean of the Davies–Bouldin criterion over a range of three to seven clusters, split by method and region. The best score for each dataset is in bold.

Regions | |||
---|---|---|---|

Methods | FRT0000d3a4 | FRT0001c479 | FRT0001c71b |

Autoencoder + K-Means | 0.8775 | 0.9128 | 0.7967 |

Autoencoder + GMM | 2.9242 | 2.2085 | 0.8964 |

Autoencoder + SOM | 1.2979 | 1.1723 | 0.9601 |

Autoencoder + Fuzzy-c-Means | 1.0237 | 0.9387 | 0.8412 |

PCA + K-Means | 0.8678 | 0.9009 | 0.8000 |

PCA + GMM | 1.9057 | 1.7879 | 0.8214 |

PCA + SOM | 1.2301 | 1.1618 | 0.9572 |

PCA + Fuzzy-c-Means | 1.0105 | 0.9256 | 0.8434 |

t-SNE + K-Means | 0.8332 | 0.8347 | 0.8369 |

t-SNE + GMM | 0.8454 | 0.8614 | 0.8660 |

t-SNE + SOM | 0.9658 | 0.9936 | 1.0490 |

t-SNE + Fuzzy-c-Means | 0.8673 | 0.8438 | 0.8507 |

UMAP + K-Means | 0.7425 | 0.6971 | 0.6523 |

UMAP + GMM | 0.7322 | 0.7178 | 0.7142 |

UMAP + SOM | 1.0230 | 0.8936 | 0.7817 |

UMAP + Fuzzy-c-Means | 0.7682 | 0.7178 | 0.6542 |

## Appendix B. Citation of PDS Data Products

## Appendix C. HiRISE and CaSSIS Filter Bandpasses

**Table A2.**A comparison of the HiRISE and CaSSIS filter bandpasses. HiRISE data taken from McEwen et al. [1]. The filters are not perfect top-hat functions and cut-off values can be +/−5 nm depending on the definition used.

HiRISE Name | HiRISE Color Band | CaSSIS Name | CaSSIS Color Band | CaSSIS Effective Central Wavelength |
---|---|---|---|---|

BG | <580 nm | BLU | <570 nm | 494 nm |

RED | 570–830 nm | PAN | 550–800 nm | 678 nm |

NIR | >790 nm | RED | 785–880 nm | 836 nm |

NIR | >870 nm | 939 nm |

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**Figure 1.**Location map of the used cubes in the present work.

**Left**: color-coded MGS MOLA hillshade over Coprates Chasma and surrounding plateau; the white outline indicates the extent of the right panel (data).

**Right**: location of the three overlapping CRISM observations used here; the background imagery consists of HRSC Level4 Nadir imagery, orbit h7201.

**Figure 2.**Examples of produced spectral cluster maps with a predefined number of 10 clusters from the FRT0001c71b dataset. (

**a**) Autoencoder + GMM; (

**b**) PCA + K-Means; (

**c**) UMAP + Fuzzy-c-Means.

**Figure 3.**Calinski–Harabasz and Davies–Bouldin index as a function of the number of clusters for the FRT0001c71b dataset. Each subfigure (

**a**–

**c**) represents quantitative analysis for the same combinations of the dimensionality reduction technique and clustering algorithm as in Figure 2.

**Figure 4.**Silhouette Score UMAP + K-Means as a function of the number of clusters for all three datasets.

**Figure 5.**Silhouette coefficient for the identified number of clusters for each dataset across all examined methods. The scores are grouped by clustering algorithm. The UMAP algorithm has the highest SC score in all but one case. (

**a**) FRT0000d3a4; (

**b**) FRT0001c479; (

**c**) FRT0001c71b.

**Figure 6.**Spectral cluster maps generated for a configuration of six clusters and the FRT0001c71b dataset. In (

**a**) Spectral cluster map, UMAP + K-Means is applied, in (

**b**) Cluster map based on four selected summary products and in (

**c**) Cluster map based on CaSSIS bands.

**Table 1.**Mean of the Calinski–Harabasz criterion over a range of 3 to 7 clusters, split by method and region. The best score for each dataset is in bold.

Regions | |||
---|---|---|---|

Methods | FRT0000d3a4 | FRT0001c479 | FRT0001c71b |

Autoencoder + K-Means | 96.371 | 135.768 | 221.408 |

Autoencoder + GMM | 49.838 | 62.005 | 185.458 |

Autoencoder + SOM | 69.396 | 108.513 | 192.581 |

Autoencoder + Fuzzy-c-Means | 81.773 | 133.995 | 214.217 |

PCA + K-Means | 97.718 | 138.611 | 220.849 |

PCA + GMM | 50.756 | 82.344 | 202.702 |

PCA + SOM | 71.086 | 110.939 | 192.436 |

PCA + Fuzzy-c-Means | 83.132 | 136.640 | 213.769 |

t-SNE + K-Means | 137.141 | 138.955 | 138.998 |

t-SNE + GMM | 132.889 | 128.090 | 127.752 |

t-SNE + SOM | 120.052 | 114.351 | 113.640 |

t-SNE + Fuzzy-c-Means | 134.679 | 138.300 | 137.684 |

UMAP + K-Means | 207.836 | 246.825 | 284.543 |

UMAP + GMM | 178.341 | 216.898 | 224.978 |

UMAP + SOM | 162.585 | 198.219 | 222.445 |

UMAP + Fuzzy-c-Means | 206.015 | 245.274 | 284.117 |

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**MDPI and ACS Style**

Fernandes, M.; Pletl, A.; Thomas, N.; Rossi, A.P.; Elser, B.
Generation and Optimization of Spectral Cluster Maps to Enable Data Fusion of CaSSIS and CRISM Datasets. *Remote Sens.* **2022**, *14*, 2524.
https://doi.org/10.3390/rs14112524

**AMA Style**

Fernandes M, Pletl A, Thomas N, Rossi AP, Elser B.
Generation and Optimization of Spectral Cluster Maps to Enable Data Fusion of CaSSIS and CRISM Datasets. *Remote Sensing*. 2022; 14(11):2524.
https://doi.org/10.3390/rs14112524

**Chicago/Turabian Style**

Fernandes, Michael, Alexander Pletl, Nicolas Thomas, Angelo Pio Rossi, and Benedikt Elser.
2022. "Generation and Optimization of Spectral Cluster Maps to Enable Data Fusion of CaSSIS and CRISM Datasets" *Remote Sensing* 14, no. 11: 2524.
https://doi.org/10.3390/rs14112524