Overlap Removal of Dimensionality Reduction Scatterplot Layouts

Dimensionality Reduction (DR) scatterplot layouts have become a ubiquitous visualization tool for analyzing multidimensional data items with presence in different areas. Despite its popularity, scatterplots suffer from occlusion, especially when markers convey information, making it troublesome for users to estimate items' groups' sizes and, more importantly, potentially obfuscating critical items for the analysis under execution. Different strategies have been devised to address this issue, either producing overlap-free layouts, lacking the powerful capabilities of contemporary DR techniques in uncover interesting data patterns, or eliminating overlaps as a post-processing strategy. Despite the good results of post-processing techniques, the best methods typically expand or distort the scatterplot area, thus reducing markers' size (sometimes) to unreadable dimensions, defeating the purpose of removing overlaps. This paper presents a novel post-processing strategy to remove DR layouts' overlaps that faithfully preserves the original layout's characteristics and markers' sizes. We show that the proposed strategy surpasses the state-of-the-art in overlap removal through an extensive comparative evaluation considering multiple different metrics while it is 2 or 3 orders of magnitude faster for large datasets.Comment: 11 pages and 9 figure

On the Greedy Algorithm for the Shortest Common Superstring Problem with Reversals

We study a variation of the classical Shortest Common Superstring (SCS) problem in which a shortest superstring of a finite set of strings $S$ is sought containing as a factor every string of $S$ or its reversal. We call this problem Shortest Common Superstring with Reversals (SCS-R). This problem has been introduced by Jiang et al., who designed a greedy-like algorithm with length approximation ratio $4$. In this paper, we show that a natural adaptation of the classical greedy algorithm for SCS has (optimal) compression ratio $\frac12$, i.e., the sum of the overlaps in the output string is at least half the sum of the overlaps in an optimal solution. We also provide a linear-time implementation of our algorithm.Comment: Published in Information Processing Letter

Separating Overlapping Tissue Layers from Microscopy Images

Manual preparation of tissue slices for microscopy imaging can introduce tissue tears and overlaps. Typically, further digital processing algorithms such as registration and 3D reconstruction from tissue image stacks cannot handle images with tissue tear/overlap artifacts, and so such images are usually discarded. In this paper, we propose an imaging model and an algorithm to digitally separate overlapping tissue data of mouse brain images into two layers. We show the correctness of our model and the algorithm by comparing our results with the ground truth

Pattern reconstruction and sequence processing in feed-forward layered neural networks near saturation

The dynamics and the stationary states for the competition between pattern reconstruction and asymmetric sequence processing are studied here in an exactly solvable feed-forward layered neural network model of binary units and patterns near saturation. Earlier work by Coolen and Sherrington on a parallel dynamics far from saturation is extended here to account for finite stochastic noise due to a Hebbian and a sequential learning rule. Phase diagrams are obtained with stationary states and quasi-periodic non-stationary solutions. The relevant dependence of these diagrams and of the quasi-periodic solutions on the stochastic noise and on initial inputs for the overlaps is explicitly discussed.Comment: 9 pages, 7 figure

Better Summarization Evaluation with Word Embeddings for ROUGE

ROUGE is a widely adopted, automatic evaluation measure for text summarization. While it has been shown to correlate well with human judgements, it is biased towards surface lexical similarities. This makes it unsuitable for the evaluation of abstractive summarization, or summaries with substantial paraphrasing. We study the effectiveness of word embeddings to overcome this disadvantage of ROUGE. Specifically, instead of measuring lexical overlaps, word embeddings are used to compute the semantic similarity of the words used in summaries instead. Our experimental results show that our proposal is able to achieve better correlations with human judgements when measured with the Spearman and Kendall rank coefficients.Comment: Pre-print - To appear in proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP

The Relativistic Hopfield network: rigorous results

The relativistic Hopfield model constitutes a generalization of the standard Hopfield model that is derived by the formal analogy between the statistical-mechanic framework embedding neural networks and the Lagrangian mechanics describing a fictitious single-particle motion in the space of the tuneable parameters of the network itself. In this analogy the cost-function of the Hopfield model plays as the standard kinetic-energy term and its related Mattis overlap (naturally bounded by one) plays as the velocity. The Hamiltonian of the relativisitc model, once Taylor-expanded, results in a P-spin series with alternate signs: the attractive contributions enhance the information-storage capabilities of the network, while the repulsive contributions allow for an easier unlearning of spurious states, conferring overall more robustness to the system as a whole. Here we do not deepen the information processing skills of this generalized Hopfield network, rather we focus on its statistical mechanical foundation. In particular, relying on Guerra's interpolation techniques, we prove the existence of the infinite volume limit for the model free-energy and we give its explicit expression in terms of the Mattis overlaps. By extremizing the free energy over the latter we get the generalized self-consistent equations for these overlaps, as well as a picture of criticality that is further corroborated by a fluctuation analysis. These findings are in full agreement with the available previous results.Comment: 11 pages, 1 figur