12,446 research outputs found
On Finding the Jaccard Center
We initiate the study of finding the Jaccard center of a given collection N of sets. For two sets X,Y, the Jaccard index is defined as |Xcap Y|/|Xcup Y| and the corresponding distance is 1-|Xcap Y|/|Xcup Y|. The Jaccard center is a set C minimizing the maximum distance to any set of N.
We show that the problem is NP-hard to solve exactly, and that it admits a PTAS while no FPTAS can exist unless P = NP.
Furthermore, we show that the problem is fixed parameter tractable in the maximum Hamming norm between Jaccard center and any input set. Our algorithms are based on a compression technique similar in spirit to coresets for the Euclidean 1-center problem.
In addition, we also show that, contrary to the previously studied median problem by Chierichetti et al. (SODA 2010), the continuous version of the Jaccard center problem admits a simple polynomial time algorithm
Polynomial Time Approximation Schemes for All 1-Center Problems on Metric Rational Set Similarities
In this paper, we investigate algorithms for finding centers of a given collection N of sets. In particular, we focus on metric rational set similarities, a broad class of similarity measures including Jaccard and Hamming. A rational set similarity S is called metric if D= 1 - S is a distance function. We study the 1-center problem on these metric spaces. The problem consists of finding a set C that minimizes the maximum distance of C to any set of N. We present a general framework that computes a (1 + ε) approximation for any metric rational set similarity
Predicting B Cell Receptor Substitution Profiles Using Public Repertoire Data
B cells develop high affinity receptors during the course of affinity
maturation, a cyclic process of mutation and selection. At the end of affinity
maturation, a number of cells sharing the same ancestor (i.e. in the same
"clonal family") are released from the germinal center, their amino acid
frequency profile reflects the allowed and disallowed substitutions at each
position. These clonal-family-specific frequency profiles, called "substitution
profiles", are useful for studying the course of affinity maturation as well as
for antibody engineering purposes. However, most often only a single sequence
is recovered from each clonal family in a sequencing experiment, making it
impossible to construct a clonal-family-specific substitution profile. Given
the public release of many high-quality large B cell receptor datasets, one may
ask whether it is possible to use such data in a prediction model for
clonal-family-specific substitution profiles. In this paper, we present the
method "Substitution Profiles Using Related Families" (SPURF), a penalized
tensor regression framework that integrates information from a rich assemblage
of datasets to predict the clonal-family-specific substitution profile for any
single input sequence. Using this framework, we show that substitution profiles
from similar clonal families can be leveraged together with simulated
substitution profiles and germline gene sequence information to improve
prediction. We fit this model on a large public dataset and validate the
robustness of our approach on an external dataset. Furthermore, we provide a
command-line tool in an open-source software package
(https://github.com/krdav/SPURF) implementing these ideas and providing easy
prediction using our pre-fit models.Comment: 23 page
SEED: efficient clustering of next-generation sequences.
MotivationSimilarity clustering of next-generation sequences (NGS) is an important computational problem to study the population sizes of DNA/RNA molecules and to reduce the redundancies in NGS data. Currently, most sequence clustering algorithms are limited by their speed and scalability, and thus cannot handle data with tens of millions of reads.ResultsHere, we introduce SEED-an efficient algorithm for clustering very large NGS sets. It joins sequences into clusters that can differ by up to three mismatches and three overhanging residues from their virtual center. It is based on a modified spaced seed method, called block spaced seeds. Its clustering component operates on the hash tables by first identifying virtual center sequences and then finding all their neighboring sequences that meet the similarity parameters. SEED can cluster 100 million short read sequences in <4 h with a linear time and memory performance. When using SEED as a preprocessing tool on genome/transcriptome assembly data, it was able to reduce the time and memory requirements of the Velvet/Oasis assembler for the datasets used in this study by 60-85% and 21-41%, respectively. In addition, the assemblies contained longer contigs than non-preprocessed data as indicated by 12-27% larger N50 values. Compared with other clustering tools, SEED showed the best performance in generating clusters of NGS data similar to true cluster results with a 2- to 10-fold better time performance. While most of SEED's utilities fall into the preprocessing area of NGS data, our tests also demonstrate its efficiency as stand-alone tool for discovering clusters of small RNA sequences in NGS data from unsequenced organisms.AvailabilityThe SEED software can be downloaded for free from this site: http://manuals.bioinformatics.ucr.edu/home/[email protected] informationSupplementary data are available at Bioinformatics online
Finding missing edges in networks based on their community structure
Many edge prediction methods have been proposed, based on various local or
global properties of the structure of an incomplete network. Community
structure is another significant feature of networks: Vertices in a community
are more densely connected than average. It is often true that vertices in the
same community have "similar" properties, which suggests that missing edges are
more likely to be found within communities than elsewhere. We use this insight
to propose a strategy for edge prediction that combines existing edge
prediction methods with community detection. We show that this method gives
better prediction accuracy than existing edge prediction methods alone.Comment: 7 pages, 6 figure
Improvised Salient Object Detection and Manipulation
In case of salient subject recognition, computer algorithms have been heavily
relied on scanning of images from top-left to bottom-right systematically and
apply brute-force when attempting to locate objects of interest. Thus, the
process turns out to be quite time consuming. Here a novel approach and a
simple solution to the above problem is discussed. In this paper, we implement
an approach to object manipulation and detection through segmentation map,
which would help to desaturate or, in other words, wash out the background of
the image. Evaluation for the performance is carried out using the Jaccard
index against the well-known Ground-truth target box technique.Comment: 7 page
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