Pilar 4 — Contrastive Raster Embeddings as Active-Learning Covariates

Hugo Rodrigues

Abstract

Self-Supervised Learning (SSL) has emerged as the dominant representation-learning paradigm in computer vision (Chen et al. 2020; He et al. 2020; Oord, Li, and Vinyals 2018) and is increasingly applied to remote sensing (Jean et al. 2019; Reichstein et al. 2019). The Pillar 4 of edaphos ships a minimal SimCLR-style pipeline (Chen et al. 2020) that pre-trains a small raster encoder on unlabelled covariate patches; the resulting per-pixel embeddings are then used as additional covariates inside the Pillar 5 Active Learning loop on br_cerrado. We report a head-to-head comparison of the identical AL policy with and without the learned features.

1. Contrastive representation learning

Given a mini-batch $\{\mathbf{x}_{i}\}_{i=1}^{B}$ of raster patches, SimCLR draws two independent stochastic augmentations $\tilde{\mathbf{x}}_{i}^{(1)},\tilde{\mathbf{x}}_{i}^{(2)}$ of each patch, encodes them with a shared CNN $f_{\theta}$ and a projection head $g_{\phi}$, and minimises the normalised temperature-scaled cross-entropy (NT-Xent) loss (Chen et al. 2020): $$\mathcal{L}_{\text{NT-Xent}} \;=\;-\frac{1}{2B} \sum_{i=1}^{B}\sum_{v\in\{1,2\}} \log\frac{\exp(\mathrm{sim}(\mathbf{z}_{i}^{(v)}, \mathbf{z}_{i}^{(v^{\prime})})/\tau)} {\sum_{k\ne(i,v)}\exp(\mathrm{sim}(\mathbf{z}_{i}^{(v)}, \mathbf{z}_{k})/\tau)},$$ where $\mathbf{z}=g_{\phi}(f_{\theta}(\tilde{\mathbf{x}}))$, $\mathrm{sim}(\cdot,\cdot)$ is cosine similarity and $\tau$ is the temperature. After pre-training, the projection head is discarded and the backbone feature vector $f_{\theta}(\mathbf{x})$ is used as the reusable representation.

2. Data preparation

Each of the 2025 pixels of br_cerrado is made the centre of a $7\times 7\times 5$ patch with five normalised channels (elevation, slope, TWI, mean annual precipitation, NDVI). Reflection padding preserves the original grid size.

library(edaphos)
.torch_ok <- requireNamespace("torch", quietly = TRUE) &&
             isTRUE(tryCatch(torch::torch_is_installed(),
                             error = function(e) FALSE))
if (!.torch_ok) {
  knitr::knit_exit(
    "torch runtime (libtorch) not available — skipping vignette."
  )
}
data(br_cerrado, package = "edaphos")

covs_base <- c("elev", "slope", "twi", "map_mm", "ndvi")
H <- length(unique(br_cerrado$y))
W <- length(unique(br_cerrado$x))
stopifnot(H * W == nrow(br_cerrado))
c(H = H, W = W)
#>  H  W 
#> 45 45

torch runtime (libtorch) not available — skipping vignette.

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He, K., H. Fan, Y. Wu, S. Xie, and R. Girshick. 2020. “Momentum Contrast for Unsupervised Visual Representation Learning.” In IEEE/CVF Conference on Computer Vision and Pattern Recognition, 9729–38.

Jean, N., S. Wang, A. Samar, G. Azzari, D. Lobell, and S. Ermon. 2019. “Tile2Vec: Unsupervised Representation Learning for Spatially Distributed Data.” In Proceedings of the AAAI Conference on Artificial Intelligence, 33:3967–74. https://doi.org/10.1609/aaai.v33i01.33013967.

Oord, A. van den, Y. Li, and O. Vinyals. 2018. “Representation Learning with Contrastive Predictive Coding.” arXiv:1807.03748.

Reichstein, M., G. Camps-Valls, B. Stevens, M. Jung, J. Denzler, N. Carvalhais, and Prabhat. 2019. “Deep Learning and Process Understanding for Data-Driven Earth System Science.” Nature 566: 195–204. https://doi.org/10.1038/s41586-019-0912-1.