3,409 research outputs found
Euclidean Distance Matrices: Essential Theory, Algorithms and Applications
Euclidean distance matrices (EDM) are matrices of squared distances between
points. The definition is deceivingly simple: thanks to their many useful
properties they have found applications in psychometrics, crystallography,
machine learning, wireless sensor networks, acoustics, and more. Despite the
usefulness of EDMs, they seem to be insufficiently known in the signal
processing community. Our goal is to rectify this mishap in a concise tutorial.
We review the fundamental properties of EDMs, such as rank or
(non)definiteness. We show how various EDM properties can be used to design
algorithms for completing and denoising distance data. Along the way, we
demonstrate applications to microphone position calibration, ultrasound
tomography, room reconstruction from echoes and phase retrieval. By spelling
out the essential algorithms, we hope to fast-track the readers in applying
EDMs to their own problems. Matlab code for all the described algorithms, and
to generate the figures in the paper, is available online. Finally, we suggest
directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine
- change of title in the last revisio
Improving Semantic Embedding Consistency by Metric Learning for Zero-Shot Classification
This paper addresses the task of zero-shot image classification. The key
contribution of the proposed approach is to control the semantic embedding of
images -- one of the main ingredients of zero-shot learning -- by formulating
it as a metric learning problem. The optimized empirical criterion associates
two types of sub-task constraints: metric discriminating capacity and accurate
attribute prediction. This results in a novel expression of zero-shot learning
not requiring the notion of class in the training phase: only pairs of
image/attributes, augmented with a consistency indicator, are given as ground
truth. At test time, the learned model can predict the consistency of a test
image with a given set of attributes , allowing flexible ways to produce
recognition inferences. Despite its simplicity, the proposed approach gives
state-of-the-art results on four challenging datasets used for zero-shot
recognition evaluation.Comment: in ECCV 2016, Oct 2016, amsterdam, Netherlands. 201
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