Non-linear dimensionality reduction techniques for classification and visualization

Abstract

In this paper we address the issue of using local embeddings for data visualization in two and three dimensions, and for classification. We advocate their use on the basis that they provide an efficient mapping procedure from the original dimension of the data, to a lower intrinsic dimer~sion. We depict how they can accurately capture the user's perception of similarity in high-dimensional data for visualization purposes. Moreover, we exploit the low-dimensional mapping provided by these embeddings, to develop new classification techniques, and we show experimentally that the classification accuracy is comparable (albeit using fewer dimensions} to a number of other classification procedures.

Conformal predictions in multimedia pattern recognition

“…The work of Vlachos et al [171] -the WeightedIso method -is exactly the same in principle as the work of Li and Guo. For data samples belonging to the same class, the distance is scaled by a factor 1 α , where α > 1; else, the distance is left undisturbed.…”

“…Subsequently, these class-specific geodesic distance matrices are merged into a discriminative global distance matrix, which is used for the Multi-Dimensionality Scaling step. Vlachos et al [171] proposed the WeightedIso method, where the Euclidean distance between data samples is scaled with a constant factor λ (< 1), if the class labels of the samples are the same. Geng et al [172] extended the work from Vlachos et al towards visualization applications, and proposed the S-Isomap (supervised Isomap), where the dissimilarity between two points is defined differently from the regular geodesic distance.…”

A Note on the Locally Linear Embedding Algorithm

“…14. This paper focuses on the all-important LLE scheme, the utility of which can hardly be overestimated. Alongside earlier applications in visualisation 4,12,13 and classification, 17 the scheme has most recently found use to such tasks as 3D-object pose estimation, 20 face membership authentication, 11 multipose face synthesis, 18 facial animation, 10 image denoising, 15 hyperspectral image processing, 8 digital watermarking, 6 feature extraction, 7 gait recognition, 9 and manifold learning 19 -to name a few. In most applications, LLE is invoked as a ready-to-use dimensionality reduction tool.…”

Robust non-linear dimensionality reduction using successive 1-dimensional Laplacian Eigenmaps

“…Applications range from image compression (Ye et al, 2004) to visualization (Vlachos et al, 2002). Often the data lies on a low dimensional manifold embedded in a high dimensional space and the dimensionality of the data can be reduced without significant loss of information.…”