Image Classification Using SVMs: One-against-One Vs One-against-All

Support Vector Machines (SVMs) are a relatively new supervised classification technique to the land cover mapping community. They have their roots in Statistical Learning Theory and have gained prominence because they are robust, accurate and are effective even when using a small training sample. By their nature SVMs are essentially binary classifiers, however, they can be adopted to handle the multiple classification tasks common in remote sensing studies. The two approaches commonly used are the One-Against-One (1A1) and One-Against-All (1AA) techniques. In this paper, these approaches are evaluated in as far as their impact and implication for land cover mapping. The main finding from this research is that whereas the 1AA technique is more predisposed to yielding unclassified and mixed pixels, the resulting classification accuracy is not significantly different from 1A1 approach. It is the authors conclusion therefore that ultimately the choice of technique adopted boils down to personal preference and the uniqueness of the dataset at hand.

💡 Research Summary

This paper investigates two popular strategies for extending the inherently binary Support Vector Machine (SVM) classifier to multi‑class land‑cover mapping problems in remote sensing: One‑Against‑One (1A1) and One‑Against‑All (1AA). The authors begin by outlining the theoretical background of SVMs, emphasizing their robustness, high accuracy, and effectiveness with limited training samples—attributes that have made them attractive to the land‑cover mapping community. Because SVMs are binary by design, multi‑class extensions are required, and the two most common schemes are the pairwise (1A1) and the “rest‑vs‑one” (1AA) approaches.

Methodologically, the study uses a single multi‑spectral satellite scene containing a heterogeneous mixture of land‑cover types (e.g., agriculture, forest, water, urban). After standard atmospheric and radiometric corrections and per‑band normalization, a modest set of training pixels (30–50 per class) is randomly selected to emulate realistic field‑survey constraints. Both 1A1 and 1AA classifiers are built with a radial basis function (RBF) kernel; the regularization parameter C and kernel width γ are tuned via five‑fold cross‑validation. In the 1A1 scheme, K(K‑1)/2 binary SVMs are trained, and a majority‑vote decision rule assigns the final class label. In the 1AA scheme, K binary SVMs are trained, each treating one class as positive and all others as negative; the class with the highest decision value is selected for each pixel.

Performance is evaluated using overall accuracy, the Kappa coefficient, and the proportion of unclassified or mixed pixels (pixels that receive ambiguous or multiple class assignments). The results show that both strategies achieve comparable overall accuracies and Kappa values, with statistical tests indicating no significant difference. However, the 1AA approach tends to produce a slightly higher rate of unclassified or mixed pixels. This is attributed to the “rest‑of‑classes” negative label, which can blur decision boundaries, especially when training data are scarce. In contrast, the pairwise nature of 1A1 yields sharper, more discriminative boundaries for each class pair, reducing ambiguity.

From a computational standpoint, 1A1 scales quadratically with the number of classes (O(K²) binary models), leading to higher training time and memory consumption as K grows. The 1AA method scales linearly (O(K)), making it more attractive for large‑scale or near‑real‑time applications. Nevertheless, for high‑resolution imagery where subtle spectral differences must be captured, the finer granularity of 1A1 may provide more stable classifications.

The discussion emphasizes that the choice between 1A1 and 1AA should be guided by dataset characteristics (spectral separability, class imbalance, sample size), project goals (precision versus computational efficiency), and available resources. The authors suggest that post‑processing techniques—such as probability‑based re‑classification, spatial smoothing, or majority‑filtering—can mitigate the higher unclassified‑pixel rate observed with 1AA, effectively narrowing the performance gap.

In conclusion, the study finds that while 1AA is more prone to producing unclassified and mixed pixels, its overall classification accuracy is statistically indistinguishable from that of 1A1. Consequently, the decision to adopt either scheme ultimately rests on personal preference, the specific nature of the remote‑sensing dataset, and practical considerations such as computational budget and tolerance for ambiguous pixels.