Spectral, Probabilistic, and Deep Metric Learning: Tutorial and Survey

Ghojogh, Benyamin; Ghodsi, Ali; Karray, Fakhri; Crowley, Mark

doi:10.48550/arxiv.2201.09267

Cited by 5 publications

(7 citation statements)

References 74 publications

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“…Particularly well suited for this type of generalization is deep metric learning in which data are encoded as a high-dimensional representation, called an embedding, where one or more learned characteristics of the data are related to distance in the embedding space 29,30 . During training, the model is penalized for placing data from different classes near to one another and rewarded for placing data from the same class close together in the embedding space 31 .…”

Section: Main Text: Introductionmentioning

confidence: 99%

TomoTwin: Generalized 3D Localization of Macromolecules in Cryo-electron Tomograms with Structural Data Mining

Rice

Wagner

Stabrin

et al. 2022

Preprint

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Cryoelectron tomography enables the visualization of cellular environments in extreme detail through the lens of a benign observer; what remains lacking however are tools to analyze the full amount of information contained within these densely packed volumes. Detailed analysis of macromolecules through subtomogram averaging requires particles to first be localized within the tomogram volume, a task complicated by several factors including a low signal to noise ratio and crowding of the cellular space. Available methods for this task suffer either from being error prone or requiring manual annotation of training data. To assist in this crucial particle picking step, we present TomoTwin: a robust, first in class general picking model for cryo-electron tomograms based on deep metric learning. By embedding tomograms in an information-rich, high-dimensional space which separates macromolecules according to their 3-dimensional structure, TomoTwin allows users to identify proteins in tomograms de novo without manually creating training data or retraining the network each time a new protein is to be located. TomoTwin is open source and available at https://github.com/MPI-Dortmund/tomotwin-cryoet.

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Section: Main Text: Introductionmentioning

confidence: 99%

TomoTwin: Generalized 3D Localization of Macromolecules in Cryo-electron Tomograms with Structural Data Mining

Rice

Wagner

Stabrin

et al. 2022

Preprint

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“…This flexibility has resulted in the diversity of Metric Learning algorithms in the literature. For a broader exposition of different Metric Learning algorithms, see surveys [7,8,9].…”

Section: Literature Reviewmentioning

confidence: 99%

“…T where the scales are s = [2,4,8,16] and o = [0, 45,95,135]. The resulting covariance matrix C is size 24 × 24.…”

Section: K-nn Classification Testsmentioning

confidence: 99%

“…The learnt distance function may then be used in algorithms such as k-nearest-neighbours classification [1] or kmeans clustering [3]. These simple principles have spawned a large number of diverse algorithms suited to different tasks, datasets and disciplines [7,8,9].…”

Section: Introductionmentioning

confidence: 99%

“…While a significant amount of research has been devoted to training the Generalised Mahalanobis distance for Metric Learning, this is certainly not the only learnable distance function considered in Metric Learning. For instance, Deep Metric Learning [8,20] uses a neural network to transform input data, where the Euclidean distance between transformed datapoints serves as the distance function. While this is not strictly a distance function on the dataset, Deep Metric learning uses many of the principles of Metric Learning such as similarity and dissimilarity relations, and achieves superior performance on classification tasks.…”

Section: Introductionmentioning

confidence: 99%

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Applications of the Bures-Wasserstein Distance in Linear Metric Learning

Cooper¹

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Metric Learning has proved valuable in information retrieval and classification problems, with many algorithms using statistical formulations to their advantage. Optimal Transport, a powerful framework for computing distances between probability distributions, has seen significant uptake in Machine Learning and some applications in Metric Learning. The Bures-Wasserstein distance, a particular formulation of Optimal Transport, has seen limited application in Metric Learning despite being well suited to the field. In this thesis Linear Metric Learning algorithms incorporating the Bures-Wasserstein distance are developed, utilising its novel properties. The first set of algorithms we contribute use the Bures-Wasserstein distance for learning linear metrics using Cyclic Projections, Riemannian barycenters and gradient-based algorithms. The convergence properties and classification performance of these algorithms are then compared to benchmark Linear Metric Learning algorithms. Our algorithms achieve competitive classification performance on feature and image datasets and converge reliability. The second set of contributions extend Linear Metric Learning with the Bures-Wasserstein distance to a low-rank context to address issues related to scalability. An extension of the previous Cyclic Projections algorithm and a Riemannian optimisation method are developed. Convergence and classification experiments analogous to the full-rank case are conducted to examine how the reduced rank affects both of these performance metrics. Both algorithms converge reliably under a variety of synthetic conditions. Reduction in rank generally decreased the training time for algorithms until effects caused by the size of the training data dominated. Reducing rank either left classification error unchanged or increased it. With respect to other low-rank Linear Metric Learning algorithms our algorithms again performed competitively with respect to classification error. The last set of contributions consider Linear Metric Learning on Symmetric Positive Definite (SPD) matrices. Some datasets are expressed as or are suited to a SPD representation. As such, Metric Learning algorithms that respect the structure of these matrices have found success when adapted to this kind of data. Another extension of the Cyclic Projections algorithm is developed to use the Generalised Bures-Wasserstein distance on SPD matrices. Two other methods based on a ground metric formulation of the Bures-Wasserstein distance for learning linear metrics on SPD data are also introduced. One ground metric formulation uses an approximation (inspired by the Sinkhorn distance) to increase its scalability. Convergence experiments on synthetic problems adapted to SPD matrices are conducted on the ground metric algorithms to establish their convergence properties. Classification experiments are also conducted with respect to several types of SPD data. While the Cyclic Projections method is competitive, the ground metric algorithms have poor performance. Despite their poor classification performance, the approximation method does evaluate faster than the Generalised Bures-Wasserstein distance, potentially offering some scalability improvements.

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