We introduce and study methods for inferring and learning from correspondences among neurons. The approach enables alignment of data from distinct multiunit studies of nervous systems. We show that the methods for inferring correspondences combine data eectively from cross-animal studies to make joint inferences about behavioral decision making that are not possible with the data from a single animal. We focus on data collection, machine learning, and prediction in the representative and long-studied invertebrate nervous system of the European medicinal leech. Acknowledging the computational intractability of the general problem of identifying correspondences among neurons, we introduce ecient computational procedures for matching neurons across animals. The methods include techniques that adjust for missing cells or additional cells in the dierent data sets that may reect biological or experimental variation. The methods highlight the value harnessing inference and learning in new kinds of computational microscopes for multiunit neurobiological studies.
The work described in this paper builds upon many different sub-areas of machine learning. In particular, the key ingredients include metric learning, correspondence matching and probabilistic dimensionality reduction . Distance metric learning is a fairly active research area. Most of the work in distance metric learning focus on @math -Nearest Neighbor ( @math -NN) classification scenario and often aim to learn a Mahalanobis metric that is consistent with the training data . The distance metric learning method employed in this paper is closest to the work of @cite_1 and @cite_2 , but modified to just consider the sets of similar cells given by the user.
@cite_1 @cite_2
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The accuracy of k-nearest neighbor (kNN) classification depends significantly on the metric used to compute distances between different examples. In this paper, we show how to learn a Mahalanobis distance metric for kNN classification from labeled examples. The Mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes kNN classification using Euclidean distances. In our approach, the metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. As in support vector machines (SVMs), the margin criterion leads to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our approach requires no modification or extension for problems in multiway (as opposed to binary) classification. In our framework, the Mahalanobis distance metric is obtained as the solution to a semidefinite program. On several data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification. Sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster. We show how to learn and combine these local metrics in a globally integrated manner. We are interested in supervised metric learning of Mahalanobis like distances. Existing approaches mainly focus on learning a new distance using similarity and dissimilarity constraints between examples. In this paper, instead of bringing closer examples of the same class and pushing far away examples of different classes we propose to move the examples with respect to virtual points. Hence, each example is brought closer to a a priori defined virtual point reducing the number of constraints to satisfy. We show that our approach admits a closed form solution which can be kernelized. We provide a theoretical analysis showing the consistency of the approach and establishing some links with other classical metric learning methods. Furthermore we propose an efficient solution to the difficult problem of selecting virtual points based in part on recent works in optimal transport. Lastly, we evaluate our approach on several state of the art datasets. Abstract Distance metric learning has been a hot research spot recently due to its high effectiveness and efficiency in improving the performance of distance related methods, such as k nearest neighbors ( k NN). Metric learning aims to learn a data-dependent metric to make intra-class distance smaller and inter-class larger. A large number of methods have been proposed for various applications and a survey to evaluate and compare these methods is imperative. The existing surveys just analyze the algorithms theoretically or compare them experimentally with a narrow time scope. Therefore, the paper reviews classical and influential methods that were proposed between 2003 and 2017 and presents a taxonomy based on the most distinct character of each method. All the methods are categorized into five classes, including pairwise cost, probabilistic framework, boost-like approaches, advantageous variants and specific applications. A comprehensive experimental study is made to compare all the selected methods, exploring the ability in improving accuracy, the relation between distance change and accuracy, the relation between accuracy and k NN neighbor size. We show how to learn a Mahanalobis distance metric for k-nearest neighbor (kNN) classification by semidefinite programming. The metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. On seven data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification—for example, achieving a test error rate of 1.3 on the MNIST handwritten digits. As in support vector machines (SVMs), the learning problem reduces to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our framework requires no modification or extension for problems in multiway (as opposed to binary) classification.