Related papers: From Average Embeddings To Nearest Neighbor Search
Neighbor Embedding (NE) aims to preserve pairwise similarities between data items and has been shown to yield an effective principle for data visualization. However, even the best existing NE methods such as Stochastic Neighbor Embedding…
Proximities are at the heart of almost all machine learning methods. If the input data are given as numerical vectors of equal lengths, euclidean distance, or a Hilbertian inner product is frequently used in modeling algorithms. In a more…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…
We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from…
Graph-based algorithms have shown great empirical potential for the approximate nearest neighbor (ANN) search problem. Currently, graph-based ANN search algorithms are designed mainly using heuristics, whereas theoretical analysis of such…
We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
Person re identification is a challenging retrieval task that requires matching a person's acquired image across non overlapping camera views. In this paper we propose an effective approach that incorporates both the fine and coarse pose…
We investigate the problem of finding reverse nearest neighbors efficiently. Although provably good solutions exist for this problem in low or fixed dimensions, to this date the methods proposed in high dimensions are mostly heuristic. We…
A common technique for compressing a neural network is to compute the $k$-rank $\ell_2$ approximation $A_{k,2}$ of the matrix $A\in\mathbb{R}^{n\times d}$ that corresponds to a fully connected layer (or embedding layer). Here, $d$ is the…
Given a metric space (X, d), we continue our study of the distance function x\mapsto d(x,-) and its relation to bi-Lipschitz embeddings of (X, d) into R^N. As application, given a compact metric-measure space (X, d,\mu), we give three…
We propose a general framework for end-to-end learning of data structures. Our framework adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned…
Nearest neighbor search is a problem of finding the data points from the database such that the distances from them to the query point are the smallest. Learning to hash is one of the major solutions to this problem and has been widely…
Ensembling word embeddings to improve distributed word representations has shown good success for natural language processing tasks in recent years. These approaches either carry out straightforward mathematical operations over a set of…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
Oblivious low-distortion subspace embeddings are a crucial building block for numerical linear algebra problems. We show for any real $p, 1 \leq p < \infty$, given a matrix $M \in \mathbb{R}^{n \times d}$ with $n \gg d$, with constant…
Nearest neighbor search is a very active field in machine learning for it appears in many application cases, including classification and object retrieval. In its canonical version, the complexity of the search is linear with both the…
Vector retrieval systems exhibit significant performance variance across queries due to heterogeneous embedding quality. We propose a lightweight framework for predicting retrieval performance at the query level by combining quantization…