Computing Maximum-Scoring Segments in Almost Linear Time

Bengtsson, Fredrik; Chen, Jingsen

doi:10.1007/11809678_28

Cited by 5 publications

(12 citation statements)

References 14 publications

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“…When searching for the subarray with maximal sum, these negative entries will never occur at the beginning/end of the anomaly interval [3]. If they would be at the beginning/end, one could easily shorten the interval to obtain a new one with higher sum.…”

Section: Non-uniform Gaps Between Timestampsmentioning

confidence: 98%

Detecting anomalies in dynamic rating data

Günnemann

Faloutsos

2014

Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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Rating data is ubiquitous on websites such as Amazon, TripAdvisor, or Yelp. Since ratings are not static but given at various points in time, a temporal analysis of rating data provides deeper insights into the evolution of a product's quality. In this work, we tackle the following question: Given the time stamped rating data for a product or service, how can we detect the general rating behavior of users as well as time intervals where the ratings behave anomalous?We propose a Bayesian model that represents the rating data as sequence of categorical mixture models. In contrast to existing methods, our method does not require any aggregation of the input but it operates on the original time stamped data. To capture the dynamic effects of the ratings, the categorical mixtures are temporally constrained: Anomalies can occur in specific time intervals only and the general rating behavior should evolve smoothly over time. Our method automatically determines the intervals where anomalies occur, and it captures the temporal effects of the general behavior by using a state space model on the natural parameters of the categorical distributions. For learning our model, we propose an efficient algorithm combining principles from variational inference and dynamic programming. In our experimental study we show the effectiveness of our method and we present interesting discoveries on multiple real world datasets.

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Section: Non-uniform Gaps Between Timestampsmentioning

confidence: 98%

Detecting anomalies in dynamic rating data

Günnemann

Faloutsos

2014

Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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“…Also note that if the range A[i, j] contains only non-positive numbers, we return an empty range as the solution: we discuss alternatives in Appendix A, but suggest reading on to Section 4 first. Min 1 10 5 7 3 11 9 13 2 6 8 12 2 3 4 5 6 7 9 8 10 11 (3,4), (1,6), (1,8), (9,10), (9,11), (9,12).…”

Section: Notation and Definitionsmentioning

confidence: 99%

“…This problem was first studied by Csurös [7], who was motivated by an application in bioinformatics, and constructed an O(n log n) time algorithm. Later, an optimal O(n) time solution was found by Bengtsson and Chen [4]. We provide an alternative O(n) time solution, which is an almost immediate consequence of any constant time maximum-sum segment data structure that can be constructed in linear time.…”

Section: Introductionmentioning

confidence: 96%

Encodings of Range Maximum-Sum Segment Queries and Applications

Gawrychowski

Nicholson

2015

Combinatorial Pattern Matching

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Abstract. Given an array A containing arbitrary (positive and negative) numbers, we consider the problem of supporting range maximumsum segment queries on A: i.e., given an arbitrary range [i, j]Chen and Chao [Disc. App. Math. 2007] presented a data structure for this problem that occupies Θ(n) words, can be constructed in Θ(n) time, and supports queries in Θ(1) time. Our first result is that if only the indices [i , j ] are desired (rather than the maximum sum achieved in that subrange), then it is possible to reduce the space to Θ(n) bits, regardless the numbers stored in A, while retaining the same construction and query time. Our second result is to improve the trivial space lower bound for any encoding data structure that supports range maximum-sum segment queries from n bits to 1.89113n − Θ(lg n), for sufficiently large values of n. Finally, we also provide a new application of this data structure which simplifies a previously known linear time algorithm for finding k-covers: given an array A of n numbers and a number k, find k disjoint subranges [i1, j1], ..., [i k , j k ], such that the total sum of all the numbers in the subranges is maximized. As observed by Csürös [IEEE/ACM TCBB 2004], k-covers can be used to identify regions in genomes.

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“…Very recently, a linear-time algorithm has been reported in [2,4] for the k-cover problem, which is to determine k disjoint segments with maximum total score, in a sequence of n positive and negative numbers called scores. The problem is motivated from bioinformatics [10], and an earlier version of the algorithm using union-find was slightly slower [3].…”

mentioning

confidence: 99%

“…The problem is motivated from bioinformatics [10], and an earlier version of the algorithm using union-find was slightly slower [3]. However, it turns out that some reformulations reduce that problem in linear time to an instance of SME-Binary with n runs and 2k +1 segments, so that a linear-time algorithm for SME-Binary also implies the result for k-covers.…”

mentioning

confidence: 99%

Homogeneous String Segmentation using Trees and Weighted Independent Sets

Damaschke

2008

Algorithmica

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We divide a string into k segments, each with only one sort of symbols, so as to minimize the total number of exceptions. Motivations come from machine learning and data mining. For binary strings we develop a linear-time algorithm for any k. Key to efficiency is a special-purpose data structure, called W-tree, which reflects relations between repetition lengths of symbols. For non-binary strings we give a nontrivial dynamic programming algorithm. Our problem is equivalent to finding weighted independent sets with certain size constraints, either in paths (binary case) or special interval graphs (general case). We also show that this problem is FPT in bounded-degree graphs.

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Computing Maximum-Scoring Segments in Almost Linear Time

Cited by 5 publications

References 14 publications

Detecting anomalies in dynamic rating data

Detecting anomalies in dynamic rating data

Encodings of Range Maximum-Sum Segment Queries and Applications

Homogeneous String Segmentation using Trees and Weighted Independent Sets

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