Deep Unsupervised Embedding for Remotely Sensed Images Based on Spatially Augmented Momentum Contrast

Convolutional neural networks (CNNs) have achieved great success when characterizing remote sensing (RS) images. However, the lack of sufficient annotated data (together with the high complexity of the RS image domain) often makes supervised and transfer learning schemes limited from an operational perspective. Despite the fact that unsupervised methods can potentially relieve these limitations, they are frequently unable to effectively exploit relevant prior knowledge about the RS domain, which may eventually constrain their final performance. In order to address these challenges, this article presents a new unsupervised deep metric learning model, called spatially augmented momentum contrast (SauMoCo), which has been specially designed to characterize unlabeled RS scenes. Based on the first law of geography, the proposed approach defines spatial augmentation criteria to uncover semantic relationships among land cover tiles. Then, a queue of deep embeddings is constructed to enhance the semantic variety of RS tiles within the considered contrastive learning process, where an auxiliary CNN model serves as an updating mechanism. Our experimental comparison, including different state-of-the-art techniques and benchmark RS image archives, reveals that the proposed approach obtains remarkable performance gains when characterizing unlabeled scenes since it is able to substantially enhance the discrimination ability among complex land cover categories. The source codes of this article will be made available to the RS community for reproducible research.

semantic variety of RS tiles within the considered contrastive learning process, where an auxiliary CNN model serves as an updating mechanism. Our experimental comparison, including different state-of-theart techniques and benchmark RS image archives, reveals that the proposed approach obtains remarkable performance gains when characterizing unlabeled scenes, since it is able to substantially enhance the discrimination ability among complex land cover categories. The source codes of this paper will be made available to the RS community for reproducible research.

Index Terms
Deep learning, metric learning, self-supervised learning, unsupervised learning, remote sensing, scene characterization.

I. INTRODUCTION
With the growing development of deep learning (DL) technologies, these kinds of methods have achieved tremendous success in many important Remote Sensing (RS) applications [1], [2], such as scene classification [3]- [7], object localization [8]- [12] and change detection [13]- [15], owing to their prominent capabilities to uncover highly representative features from RS scenes [16]. In general, DL techniques aim at projecting the visual content of input images onto a particular label space, using a hierarchy of nonlinear layers to generate a high-level semantic abstraction that is very useful to characterize RS data. Most available DL-based image characterization methods in the RS field rely on a supervised learning scheme, in which a large amount of labeled scenes is required to properly train the models and prevent over-fitting [17].
However, the task of obtaining relevant annotations for vast volumes of RS data can be very difficult and time consuming. This may severely constrain the applicability and potential of the supervised DL paradigm in operational RS environments, especially under the most challenging conditions [18].
In order to mitigate the need for labeled RS data, different strategies have been effectively explored in the literature, e.g. [19]- [22]. One of the most popular schemes is based on the use of pre-trained convolutional neural networks (CNNs) [23], where different pre-defined CNN architectures (e.g. AlexNet [24], VGGNet [25], GoogleNet [26] and ResNet [27]), trained on large-scale computer vision datasets (e.g. ImageNet [28]) are directly used as feature extraction methods for RS data. Despite its remarkable success [29]- [32], the existing limitations on the number of spectral bands and the data complexity make this transfer learning scheme unable to fully exploit the advantages of RS imagery [33]. An attractive option to relieve these limitations consists of using unsupervised methods to characterize unlabeled RS scenes. As a result, different methods have been successfully proposed within and outside the DL field [34]- [37]. However, the general unsupervised framework is often unable to introduce appropriate prior knowledge about the RS image domain, eventually constraining the resulting performance. Although a recently developed deep metric learning method -the Tile2Vec [38]-is certainly able to obtain promising results by using the geospatial information as prior knowledge, the unprecedented availability of massive RS archives, together with the constant development of the acquisition technology, still make unsupervised DL-based image characterization a major challenge in RS.
Note that the integration of the unsupervised mode into the deep metric learning approach [39] is highly limited by the contrasting land cover types that can be sampled in a single batch, which may eventually reduce the capacity of the model to distinguish a broader range of complex RS categories, and also motivates the development of novel techniques useful to deal with the large-scale variance complexity of the RS image domain [40].
With all these considerations in mind, this paper proposes a new unsupervised deep metric learning approach, called spatially augmented momentum contrast (SauMoCo), which has been specially designed to characterize unlabeled RS scenes. Inspired by Tobler's first law of geography [41], the proposed approach provides a new perspective on unsupervised land cover characterization in which not only the semantic similarities among nearby scenes are exploited to learn the corresponding feature embeddings, but also the inherent diversity within RS semantic concepts. To achieve this goal, we define a spatial augmentation criteria to uncover enhanced semantic relationships among RS tiles for the embedding space. Then, we build a queue of deep embeddings, where the size of queue is forced to be larger than the batch size in order to further increase the semantic variety of contrasting land cover tiles during the training process. Moreover, we introduce an auxiliary CNN into our model to consistently update the deep embeddings of the RS tiles in the queue. With the objective of validating the proposed approach, we conduct a comprehensive experimental comparison, using two benchmark datasets and different state-ofthe-art characterization techniques, which demonstrates the superior performance of the presented method in the task of categorizing RS scenes without using any land cover class information.
In short, the main contributions of this paper can be summarized as follows: 1) We propose a new unsupervised deep metric learning model (SauMoCo) to characterize unlabeled RS images. The presented approach pursues to exploit not only the semantic similarities among nearby geospatial locations, but also the inherent diversity within land cover concepts, by using a newly defined spatial augmentation criteria with a contrastive loss formulation and a momentum update-based optimization.
2) We investigate how the proposed SauMoCo model performs with large-scale training data, which gives us important insights about the working mechanism and practical advantages of the proposed method with respect to other unsupervised RS image characterization techniques available in the literature. The codes of this work will be released for reproducible research inside the research community.
The rest of this paper is organized as follows. Section II reviews some related works on RS scene characterization while highlighting their main limitations. Section III details the proposed unsupervised deep metric learning model for RS images. Section IV presents the experimental part of the work. Finally, Section V concludes the paper with some remarks and hints at plausible future research lines.

II. RELATED WORK
Different strategies have been successfully adopted within the RS field to relieve the need for labeled data when characterizing aerial scenes. This section reviews some of the most relevant trends, including pre-trained (Section II-A), unsupervised (Section II-B) and deep metric learningbased (Section II-C) methods. Additionally, we also analyze their main limitations in the context of RS problems (Section II-D).

A. Pre-trained Methods
One of the most popular schemes to characterize RS data is based on the use of pre-trained convolutional neural networks (CNNs). In more details, these approaches make use of pre-defined CNN models, such as AlexNet [24], VGGNet [25], GoogleNet [26] or ResNet [27], which are pre-trained on large-scale computer vision datasets, such as the ImageNet [28] collection. In this way, the amount of labeled RS scenes can be substantially reduced by transferring the knowledge from the standard image domain to the RS field. For instance, Hu et al. define in [42] two different schemes to take advantage of the VGGNet model pre-trained on ImageNet. In the first scheme, the authors employ the last fully connected layers as image descriptors. In the second one, an additional encoding procedure is used to fuse the last convolutional feature maps.
In both cases, a support vector machine (SVM) is adopted to finally classify the RS images.
Precisely, Marmanis et al. analyze in [29] the effectiveness of classifying remotely sensed scenes using different CNN-based representations transferred from ImageNet. Similarly, Li et al. present in [31] a multi-layer feature fusion framework which integrates several pre-trained DL models for RS scene classification. Zheng et al. build in [43] a holistic representation of RS images using a multi-scale pooling over pre-trained features. Kang et al. also combine in [44] several pre-trained CNN architectures to define a building-instance level land-use classification framework. In [30], the authors propose using a sparse autoencoder (AE) over pre-trained features to generate the final representation of RS scenes.
Despite the remarkable performance achieved by these and other pre-trained models, there are still some important limitations that substantially reduce the applicability of such transfer learning strategies within the RS field. On the one hand, standard image collections, such as ImageNet, are often made up of RGB imagery, which makes existing pre-trained networks unable to take advantage of the additional spectral bands provided by air-borne and space-borne optical sensors [45]. Note that RS instruments are often designed to provide valuable information outside the visible spectrum, and these data are essential in may important applications, such as biophysical parameter analysis [46] and land cover material study [47]. On the other hand, standard images often contain natural object-centric photographs that hardly represent the complexity of RS scenes, comprising fully focused multi-band shots of the Earth surface with plenty of complex spatio-spectral details within the same acquisition frame [48]. Precisely, these important differences often make necessary to consider broader strategies than pre-tranined DL models.

B. Unsupervised Methods
A more general option to relieve the need for annotated RS data is based on using unsupervised image characterization methods. In more details, these techniques work for characterizing aerial scenes without using any class label information, which becomes particularly attractive in RS problems [18]. Consequently, different unsupervised models (both within and outside the DL field) have been proposed to learn informative representations from unlabeled RS scenes. For instance, Cheriyadat presented in [49] a feature learning approach for aerial scenes which adopts a sparse coding framework to generate unsupervised data representations based on a set of basis functions derived from low-level measurements. Following this idea, other authors proposed using different unsupervised decomposition frameworks instead. This is the case of the works presented in [37], [50], [51], which make use of probabilistic topic models to represent the RS data as probability distributions of feature patterns. In [52] [34] a greedy layer-wise unsupervised pre-training method for learning sparse features from aerial images. In the case of [36], the authors define a shallow weighted deconvolution network for extracting features from RS scenes by minimizing the Euclidean distance between the original and the reconstructed images. Alternatively, some works in the literature also show the utility of convolutional generative adversarial networks to characterize standard and remotely sensed imagery [53], [54].

C. Unsupervised Deep Metric Learning
Notwithstanding the positive results of these and other important unsupervised methods, all these works mainly rely on generic clustering, decomposition or encoding procedures that are often unable to introduce relevant prior knowledge about the RS domain without using supervised information. Among all the conducted research, one of the most promising trends to adequately characterize RS images is based on the so-called deep metric learning approach [39]. In particular, deep metric learning aims at learning a low-dimensional metric space based on CNN models, where the feature embeddings of similar images should be close, and those of dissimilar images should be separated. Despite its great potential in RS problems [55]- [58],

D. Current Limitations in RS
Certainly, the Tile2Vec algorithm sets a path for learning more informative CNN-based characterizations of RS data from a completely unsupervised perspective. However, the task of generating highly meaningful representations of aerial scenes without using any kind of class label information still remains a very important challenge in RS [59], [60]. The recent availability of massive data archives, together with the constant development of the airborne and space acquisition technology, are steadily increasing the complexity of RS data and, hence, their semantic understanding. Precisely, this growing complexity often produces a huge within-class diversity and between-class similarity that introduce important limitations within the aforementioned learning scheme [39]. When integrating the unsupervised mode into the deep metric learning approach [38], it is logically necessary to train the CNN model by sampling negative RS image tiles within each batch. However, this strategy significantly reduces the capacity of the model to distinguish between a broader range of contrasting land cover types, since the learning process is constrained by the tiles that can be sampled in a single batch. Note that this point may become particularly critical in complex large-scale archives, which stimulates the development of more advanced unsupervised characterization techniques within the RS field [18], and ultimately motivates the research conducted in this work.

E. Novelty of the Proposed Method
To address all these challenges, this paper proposes a new unsupervised deep metric learning model that jointly exploits two different aspects: a spatially augmented contrastive loss and a momentum update-based optimization. In contrast to Tile2Vec [38], the proposed approach integrates a new spatial augmentation criteria that allows considering not only semantic similarities among nearby RS scenes but also the inherent semantic diversity of land cover concepts when learning the corresponding metric space in an unsupervised fashion. Note that this within-class variability has not yet been exploited in the context of characterizing unlabelled RS scenes despite the fact it may become very useful to relieve the large-scale variance problem of RS data [40]. Using this methodological improvement, the proposed approach is able to avoid the triplet loss limitations with scalable data while also taking advantage of additional contrastive RS image pairs during training. In order to further improve such contrasting land cover variety, the proposed approach also utilizes a momentum update-based optimization [61]. The general idea behind the momentum update is based on managing a dynamic dictionary of encoders to enhance the contrastive learning process. Following this idea, we build a queue of deep embeddings of RS scenes in order to force the length of such queue to be larger than the mini-batch size.
Unlike the standard momentum scheme which shows limited results with large-scale data [61], the proposed end-to-end approach is designed to exploit vast unlabeled RS archives by using a CNN-based backbone architecture to jointly characterize land cover scenes and update the queue. Compared with different state-of-the-art methods to characterize unlabelled RS scenes, the proposed approach is able to achieve a better performance than the methods in [29], [38], [54], [62], which also reveals the novelty and advantages provided by this work for the RS community.

III. SPATIALLY AUGMENTED MOMENTUM CONTRAST
Our newly proposed end-to-end unsupervised deep metric learning model for characterizing unlabeled RS scenes (SauMoCo) can be summarized in the following three parts: • A backbone architecture (called anchor CNN) which is used to generate the corresponding feature embedding of the input RS scenes. Note that this CNN architecture can be defined according to a specific off-the-shelf topology, such as AlexNet [24], VGGNet [25], GoogleNet [26] and ResNet [27].
• A spatially augmented loss, based on the contrastive loss formulation and a newly defined spatial augmentation criteria, which exploits not only the semantic similarities among nearby RS scenes but also the inherent diversity within land cover semantic concepts.
• The corresponding optimization algorithm, which learns the proposed model parameters using a momentum contrast update. To achieve this goal, a queue of deep embeddings is constructed, and an additional CNN model (called momentum CNN) is introduced to update such queue. It is important to highlight that this network should be defined with the same architecture with regards to the one of the anchor CNN for a scalable training. Figure 1 illustrates in a graphical manner the proposed unsupervised deep metric learning framework. In the following sections, we detail the newly defined loss function and the considered optimization algorithm.

A. Spatially Augmented Loss
x i , an anchor patch x a i (located in its center) can be cropped with a certain size W × W . With a certain distance d of the anchor patch x a i , a neighborhood patch cropped from x i is defined as its spatial augmentation, which is x n i . If the distance is 100 pixels (in both vertical and horizontal directions), the center of x n i should be within 100 pixels with respect to the center of x a i . Let f a i ∈ R D denote the deep embedding of x a i obtained by a CNN model F(·; θ) on the unit sphere (i.e., f a i = F(x a i ; θ)/ F(x a i ; θ) 2 ), where D is its dimension and θ represents the parameters of the CNN model. We identify this model as anchor CNN.
As noted by the first law of geography [41], everything is related to everything else, but nearby things are more related than distant things. Following this rule, the proposed method relies on the assumption that images that are geographic neighbors should be semantically more similar than distant images [38]. Therefore, the embeddings of nearby images should be closer than those of distant images in the metric space. However, it is important to highlight that the proposed spatial augmentation criteria is different from the one considered in other works, such as in [38]. Specifically, we do not fix the position of the spatially augmented patches to a specific neighbour position, but to a neighbourhood region of the anchor patch. As a result, our augmentation criteria allows certain spatial variations on the cropped areas in order to increase the variety of spatially augmented patches that are extracted on-line. To achieve this in a scalable way, we adopt a contrastive learning mechanism [63], [64], where the contrastive loss of x a i can be defined as: In this equation, the inner product f a i , f n i measures the cosine similarity between the embedding f a i of the anchor patch x a i and the one f n i of its spatial augmented patch x n i . Besides, τ represents a temperature parameter controlling the concentration level of the sample distribution [65]. Intuitively, Equation (1) describes the log-likelihood of the spatial augmented patch, which can be classified as its anchor patch among all the anchor patches in X . Then, the corresponding contrastive loss over the whole dataset can be formally expressed as: By optimizing Equation (2), we can obtain the deep embeddings of X and the trained CNN model, which is useful for characterizing unlabeled RS scenes and conducting the corresponding downstreaming land-cover categorization tasks.

B. Optimization via Momentum Update
In order to sufficiently train the CNN model based on Equation (2) in an unsupervised fashion, a scalable dataset is logically required to be fed into the deep model. For scalable datasets, how to sufficiently sample the negative patches, (i.e., x a j ) with respect to x a i should be carefully defined, since the number of spatially augmented patches and their consistency are both critical aspects within the proposed contrastive unsupervised learning scheme.
One common strategy adopted in the literature is based on sampling the negative patches within each mini-batch [39]. However, this optimization mechanism has important limitations for training our deep model with scalable spatially augmented data. In more details, this minibatch sampling process assumes that each patch can be seen once during one epoch of training and hence x a i only exists in one mini-batch for the current iteration. Consequently, the CNN model is only able to see its corresponding negative patches x a j belonging this mini-batch, while other important samples outside the mini-batch cannot be considered. Precisely, this fact can substantially reduce the semantic variety of contrasting land cover types during training, which is a key factor to allow learning more informative RS image representations from an unsupervised perspective.
To solve this problem, we adopt the momentum update rule [61], [66] for training our newly proposed unsupervised RS image characterization model. Specifically, a queue of the deep embeddings of image patches x a j is constructed, where the size of the queue is forced to be larger than that of the mini-batch. In this way, the unsupervised learning process can be substantially enhanced by considering contrasting patches beyond a single batch. During the training phase, the embeddings of the current mini-batch are compared with the ones in the queue, as they are progressively replaced. The embeddings of the current mini-batch are enqueued and the oldest ones are dequeued. Moreover, in order to consistently update the deep embeddings in the queue, an auxiliary CNN model with parameter set θ aux is introduced. We identify the θ aux model as momentum CNN and it is updated as follows: where m ∈ [0, 1) is a momentum coefficient. It is worth noting that only the CNN with θ is updated by means of back-propagation. The momentum CNN with parameters θ aux can be evolved more smoothly than the CNN with θ. Then, the embeddings in the queue (encoded by the momentum CNN) are updated by:f In this expression,f i denotes the features generated by the momentum CNN. In other words, the embeddings in the queue are replaced by the ones encoded by the momentum CNN after each training epoch. To this end, the proposed optimization mechanism is detailed in Algorithm 1.

A. Dataset Description
In this work, we use two benchmark RS image datasets to validate the effectiveness of the proposed method. A detailed description of the datasets is provided below: Sample a mini-batch of x i .

4:
Within x i , randomly generate the center pixels of x n i .

5:
Crop the patches x n i and x a i online. Crop, Residential, River, and Sea Lake. The EuroSAT archive is also publicly available 2 .
These two RS archives have been selected to evaluate the performance of the unsupervised RS image characterization process from a single-source land cover acquisition perspective because  Figure 2(a). Then, we randomly select a total of 100,000 images (with a size of 250 × 250 pixels) from the downloaded tiles.
2) In the case of EuroSAT, we downloaded 100 Sentinel-2 Level-1C image products which have been globally sampled from the entire globe. Figure 2(b) illustrates the geo-locations of the downloaded Sentinel-2 products. Then, we select 100,000 random images (with a size of 264 × 264 pixels) from the downloaded products. centers is 100 pixels, according to the defined spatial augmentation criteria.

B. Experimental Setup
The proposed method is implemented in PyTorch [68].  [54], 2) MARTA GAN [62], 3) the ResNet18 model pre-trained on ImageNet while considering the most discriminating principal components (pretrained CNN+PCA) [29] and 4) the Tile2Vec [38]. In the case of the pre-trained CNN+PCA, it is important to highlight that we make use of the PCA method after extracting the pre-trained features to generate the corresponding deep embeddings with the same dimensionality as the other methods. All the experiments are conducted on an NVIDIA Tesla P100 graphics processing unit (GPU).
To measure the effectiveness of the proposed approach as compared with the other methods, we extract the deep embeddings for the NAIP and EuroSAT collections after training. Then, we use the available annotations to compute the corresponding classification results for each dataset.
In more details, we provide five different experiments for validating and analyzing the results from several perspectives: 1) Evaluation of deep embeddings based on random forest (RF) classification: We first utilize the random forest (RF) classifier to measure the classification performance based on the extracted feature embeddings of the two datasets obtained by the considered methods. For each dataset, we randomly select 80% images for training the classifier and evaluate its performance on the rest 20% images. In order to obtain a mean score of the overall accuracy, a total of 100 trials are conducted. Then, we calculate the mean and standard deviation values of the obtained accuracy scores.
2) Visualization of image retrieval: In this experiment, we conduct a retrieval test to explore, from a qualitative perspective, the performance of the considered characterization methods. In particular, we extract one query image patch from a complete NAIP scene. Then, we use the pretrained CNN+PCA, Tile2Vec and SauMoCo models to obtain the deep embeddings of the selected patch as well as the rest of the patches in the scene. Finally, we calculate their corresponding similarity maps with respect to the query and retrieve the 10 nearest neighbor patches within the whole scene.      images are cropped on-line, which also provides additional advantages as data augmentation strategy. By doing so, a higher semantic variety of similar images can be generated during the training phase (with respect to the anchor images). In comparison, the triplet set utilized in Tile2Vec is constructed beforehand and it does not exhibit any data augmentation capability during the training. Therefore, the proposed approach can also take advantage of the proposed spatial augmentation criteria. To analyze the differences between Tile2Vec and SauMoCo in more details, Table II provides the corresponding class-wise F1 scores obtained by the RF classifier on the EuroSAT dataset,

3) Evaluation of CNN model initialization
where the two best results are highlighted in bold and gray-shaded font. As it is possible to observe, the proposed approach obtains the best and second best performances in 2 and 5 landcover classes, respectively. Although Tile2Vec also exhibits positive results in 5 categories, the performance for the rest of the classes is rather limited, being even worse than that of the pre-trained CNN+PCA and MARTA GAN in some cases. Precisely, these important differences make SauMoCo more stable and accurate from a global perspective, indicating that the proposed approach is able to extract more relevant information about a wider range of semantic concepts.
2) Visualization of image retrieval: As shown in Figure 5, we extract one query image patch from a NAIP tile. Then, we obtain its deep embedding and the ones of the rest of the patches in the tile based on the considered methods. Subsequently, we calculate their similarities and obtain the corresponding heatmaps for SauMoCo (b), Tile2Vec (c) and the pre-trained CNN+PCA (d), where brighter colors denote a higher similarity in the embedding space. Additionally, the 10 nearest neighbor patches are illustrated in (e). As it is possible to observe in the heatmaps, the locations of the most similar patches with respect to the query can be more clearly identified in (b). Precisely, these results indicate that the semantic information of the RS scene is not properly encoded based on Tile2Vec and the pre-trained CNN+PCA model, since there are larger parts in the image that are considered to be similar to the query in the embedding space. Regarding the nearest neighbor results, it is possible to see that the image patches retrieved from the embedding space generated by SauMoCo are the most visually similar with regards to the query. That is, the proposed approach is able to model the semantic content of the query more accurately than the other methods, since all the retrieved images display similar land-cover patterns.
3) Evaluation of CNN model initialization: Figure 6 shows the learning curves of the ResNet18 model over the EuroSAT collection when using two different initialization strategies: with the parameters obtained by the proposed approach and with the pre-trained ImageNet parameters.
According to the displayed results, it can be seen that the classification accuracy can be slightly improved when the parameters of the CNN model are initialized via the proposed approach.
Although the pre-trained ImageNet initialization exhibits higher classification accuracies at the beginning of the training process, SauMoCo is able to consistently achieve better results after 30 epochs. This fact reveals that the proposed approach is able to capture richer semantic information in the corresponding embedding space, since a better minimum location of the loss function can be discovered by the parameters pre-trained via SauMoCo.  ResNet50 is slightly improved in comparison with ResNet18. As shown in Table III, compared with ResNet18, the classification accuracy based on the deep embeddings from ResNet50 can be improved with a score of 0.5% on the NAIP dataset.

V. CONCLUSIONS AND FUTURE LINES
This paper presents a new unsupervised deep metric learning framework (SauMoCo) to characterize unlabeled RS scenes. Specifically, the proposed approach initially defines a spatial augmentation criterion to uncover semantically similar RS images based on the the first law of geography. Then, a queue of deep embeddings is built such that the size of queue is forced to be substantially larger than the batch size, to improve the semantic variety of contrasting land cover types during the training. To achieve this goal, an auxiliary CNN model is also used to consistently update the deep embeddings in the queue. The experimental part of the work, conducted over two benchmark datasets and based on the use of different characterization methods, reveals that the proposed unsupervised deep metric learning model is able to provide competitive advantages with respect to other state-of-the-art techniques in the task of representing unlabeled RS images.
One of the main conclusions that arises from this work is the relevance of considering a broader variety of land cover types when learning unsupervised RS image characterizations.
In this regard, the proposed approach takes advantage of the defined spatial augmentation criteria and the considered queue of deep embeddings to enrich the semantic information of different RS categories during the contrastive learning process. Precisely, this feature allows our SauMoCo to enhance the global discrimination ability among unsupervised land-cover classes, and also to provide a more robust behavior with different datasets and settings. Owing to the remarkable performance achieved by the presented method, our future work will be directed towards adapting it to inter-sensor data and other important RS tasks, such as dimensionality reduction of hyperspectral imagery or fine-grained land-use categorization.