相关论文: Binarized Johnson-Lindenstrauss embeddings

This paper describes a new method of data encoding which may be used in various modern digital, computer and telecommunication systems and devices. The method permits the compression of data for storage or transmission, allowing the exact…

Two-dimensional constrained coding is a problem that is much more difficult than its one-dimensional counterpart. Indeed, in two dimensions, obtaining the answers to very natural questions becomes uncomputable. In particular, it is…

By replacing the lens with a thin optical element, lensless imaging enables new applications and solutions beyond those supported by traditional camera design and post-processing, e.g. compact and lightweight form factors and visual…

Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…

Deep embedding methods have influenced many areas of unsupervised learning. However, the best methods for learning hierarchical structure use non-Euclidean representations, whereas Euclidean geometry underlies the theory behind many…

Clark Hash is a small method for storing neural embeddings in less space. It normalizes each database vector, applies a deterministic sparse signed Johnson-Lindenstrauss projection, clips the result, and stores a fixed-width…

We study the precise computational complexity of deciding satisfiability of first-order quantified formulas over the theory of fixed-size bit-vectors with binary-encoded bit-widths and constants. This problem is known to be in EXPSPACE and…

With the emergence of new storage and communication methods, the insertion, deletion, and substitution (IDS) channel has attracted considerable attention. However, many topics on the IDS channel and the associated Levenshtein distance…

Information distances like the Hellinger distance and the Jensen-Shannon divergence have deep roots in information theory and machine learning. They are used extensively in data analysis especially when the objects being compared are high…

Although much effort has recently been devoted to training high-quality sentence embeddings, we still have a poor understanding of what they are capturing. "Downstream" tasks, often based on sentence classification, are commonly used to…

The paper presents a binarization scheme that converts non-binary data into a set of binary strings. At present, there are many binarization algorithms, but they are optimal for only specific probability distributions of the data source.…

In continuation to earlier works where the problem of joint information embedding and lossless compression (of the composite signal) was studied in the absence \cite{MM03} and in the presence \cite{MM04} of attacks, here we consider the…

The Johnson--Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be flattened to lower dimensions while…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

This paper introduces a methodology based on Euclidean information theory to investigate local properties of secure communication over discrete memoryless wiretap channels. We formulate a constrained optimization problem that maximizes a…

Vectors of data are at the heart of machine learning and data mining. Recently, vector quantization methods have shown great promise in reducing both the time and space costs of operating on vectors. We introduce a vector quantization…

We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…

For natural language understanding and generation, embedding concepts using an order-based representation is an essential task. Unlike traditional point vector based representation, an order-based representation imposes geometric…

We consider the task of lossy compression of high-dimensional vectors through quantization. We propose the approach that learns quantization parameters by minimizing the distortion of scalar products and squared distances between pairs of…

This paper presents an improved analysis of a structured dimension-reduction map called the subsampled randomized Hadamard transform. This argument demonstrates that the map preserves the Euclidean geometry of an entire subspace of vectors.…