We examine the algebraic and geometric properties of a uni-directional GRU and word embeddings trained end-to-end on a text classification task. A hyperparameter search over word embedding dimension, GRU hidden dimension, and a linear combination of the GRU outputs is performed. We conclude that words naturally embed themselves in a Lie group and that RNNs form a nonlinear representation of the...

Abstract. In this paper we propose the generalization of the recently introduced Neighbor Embedding Exploratory Observation Machine (NEXOM) for dimension reduction and visualization. We provide a general mathematical framework called Self Organized Neighbor Embedding (SONE). It treats the components, like data similarity measures and neighborhood functions, independently and easily changeable. ...

This paper presents a generalization of the random dot product model for networks whose edge weights are drawn from a parametrized probability distribution. We focus on the case of integer weight edges and show that many previously studied models can be recovered as special cases of this generalization. Our model also determines a dimension–reducing embedding process that gives geometric interp...

In this paper we propose the generalization of the recently introduced Neighbor Embedding Exploratory Observation Machine (NE-XOM) for dimension reduction and visualization. We provide a general mathematical framework called Self Organized Neighbor Embedding (SONE). It treats the components, like data similarity measures and neighborhood functions, independently and easily changeable. And it en...

We propose an automated system for out-of-sample predictions of a set of European stock indices. The system performs on piecewise linear representations of the time series. An automated segmentation algorithm converges to an optimum segmented time series representation, which achieves considerable data compression and allows variable sampling rate of the time series depending on different segme...

Analyzing and forecasting the financial market based on the theory of phase space reconstruction of support vector regression. The key point of the phase space reconstruction is to choose the optimal delay time, and to find the optimal embedding dimension of space. This paper proposes the use of false nearest neighbor method to construct the error function for all the variables to determine the...

A major open problem in the field of metric embedding is the existence of dimension reduction for n-point subsets of Euclidean space, such that both distortion and dimension depend only on the doubling constant of the pointset, and not on its cardinality. In this paper, we negate this possibility for `p spaces with p > 2. In particular, we introduce an n-point subset of `p with doubling constan...

A major open problem in the field of metric embedding is the existence of dimension reduction for n-point subsets of Euclidean space, such that both distortion and dimension depend only on the doubling constant of the pointset, and not on its cardinality. In this paper, we negate this possibility for `p spaces with p > 2. In particular, we introduce an n-point subset of `p with doubling constan...

where 0 ≤ λ ≤ 1 is the host-rejection parameter, ν is a parameter for fixing the embedding distortion, and Mi ∈ {0, 1} is the binary message (equiprobable) embedded in Xi. The vector Xi denotes the host signal, whereas s0 is the secret spreading vector, both of dimension n. The classical additive spread spectrum modulation (add-SS) is a particular case of (1) for λ = 0. In our statistical model...

In this paper we consider the problem of embedding the input and hypotheses of boolean function classes in other classes, such that the natural metric structure of the two spaces is approximately preserved. We rst prove some general properties of such embedding and then suggest and discuss possible approximate embedding in the class of \half-spaces" (single layer perceptrons) with dimension pol...