Related papers: Geometric Aspects of Biological Sequence Compariso…
We propose a new segmentation evaluation metric, called segmentation similarity (S), that quantifies the similarity between two segmentations as the proportion of boundaries that are not transformed when comparing them using edit distance,…
We prove several criteria for quasi-isometry between non-locally-finite graphs and their structure trees. Results of M\"oller in \cite{moeller92ends2} for locally finite and transitive graphs are generalized. We also give a criterion which…
Ancestral sequence reconstruction is a key task in computational biology. It consists in inferring a molecular sequence at an ancestral species of a known phylogeny, given descendant sequences at the tip of the tree. In addition to its many…
Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as…
We present a variation of quasi-isometry to approach the problem of defining a geometric notion equivalent to commensurability. In short, this variation can be summarized as "quasi-isometry with uniform parameters for a large enough family…
Gene annotation has traditionally required direct comparison of DNA sequences between an unknown gene and a database of known ones using string comparison methods. However, these methods do not provide useful information when a gene does…
Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional…
The gapped local alignment score of two random sequences follows a Gumbel distribution. If computers could estimate the parameters of the Gumbel distribution within one second, the use of arbitrary alignment scoring schemes could increase…
This work briefly explores the possibility of approximating spatial distance (alternatively, similarity) between data points using the Isolation Forest method envisioned for outlier detection. The logic is similar to that of isolation: the…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
While there has been substantial progress in learning suitable distance metrics, these techniques in general lack transparency and decision reasoning, i.e., explaining why the input set of images is similar or dissimilar. In this work, we…
We initiate the rigorous study of classification in quasi-metric spaces. These are point sets endowed with a distance function that is non-negative and also satisfies the triangle inequality, but is asymmetric. We develop and refine a…
The evolutionary edit distance between two individuals in a population, i.e., the amount of applications of any genetic operator it would take the evolutionary process to generate one individual starting from the other, seems like a…
This paper proposes some extensions to the work on kernels dedicated to string or time series global alignment based on the aggregation of scores obtained by local alignments. The extensions we propose allow to construct, from classical…
We extend several recent results providing symmetry-based guarantees for variational inference (VI) with location-scale families. VI approximates a target density $p$ by the best match $q^*$ in a family $Q$ of tractable distributions that…
Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…
The complexity quasi-metric of Schellekens is a topological framework in which the asymmetry of computational comparisons -- ``$A$ is at most as fast as $B$'' carrying different information than ``$B$ is at most as slow as $A$'' -- is built…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
We introduce GSimCNN (Graph Similarity Computation via Convolutional Neural Networks) for predicting the similarity score between two graphs. As the core operation of graph similarity search, pairwise graph similarity computation is a…
Quasi-isometries are mappings on graphs, with distance-distortions parameterized by a multiplicative factor and an additive constant. The distance-distortions of quasi-isometries are in a general form that captures a wide range of…