6,469 research outputs found
Improved Approximation Algorithms for Segment Minimization in Intensity Modulated Radiation Therapy
he segment minimization problem consists of finding the smallest set of
integer matrices that sum to a given intensity matrix, such that each summand
has only one non-zero value, and the non-zeroes in each row are consecutive.
This has direct applications in intensity-modulated radiation therapy, an
effective form of cancer treatment. We develop three approximation algorithms
for matrices with arbitrarily many rows. Our first two algorithms improve the
approximation factor from the previous best of to (roughly) and , respectively, where is
the largest entry in the intensity matrix. We illustrate the limitations of the
specific approach used to obtain these two algorithms by proving a lower bound
of on the approximation
guarantee. Our third algorithm improves the approximation factor from to , where is (roughly) the largest
difference between consecutive elements of a row of the intensity matrix.
Finally, experimentation with these algorithms shows that they perform well
with respect to the optimum and outperform other approximation algorithms on
77% of the 122 test cases we consider, which include both real world and
synthetic data.Comment: 18 page
A generalized matrix profile framework with support for contextual series analysis
The Matrix Profile is a state-of-the-art time series analysis technique that can be used for motif discovery, anomaly detection, segmentation and others, in various domains such as healthcare, robotics, and audio. Where recent techniques use the Matrix Profile as a preprocessing or modeling step, we believe there is unexplored potential in generalizing the approach. We derived a framework that focuses on the implicit distance matrix calculation. We present this framework as the Series Distance Matrix (SDM). In this framework, distance measures (SDM-generators) and distance processors (SDM-consumers) can be freely combined, allowing for more flexibility and easier experimentation. In SDM, the Matrix Profile is but one specific configuration. We also introduce the Contextual Matrix Profile (CMP) as a new SDM-consumer capable of discovering repeating patterns. The CMP provides intuitive visualizations for data analysis and can find anomalies that are not discords. We demonstrate this using two real world cases. The CMP is the first of a wide variety of new techniques for series analysis that fits within SDM and can complement the Matrix Profile
Constraint-based Sequential Pattern Mining with Decision Diagrams
Constrained sequential pattern mining aims at identifying frequent patterns
on a sequential database of items while observing constraints defined over the
item attributes. We introduce novel techniques for constraint-based sequential
pattern mining that rely on a multi-valued decision diagram representation of
the database. Specifically, our representation can accommodate multiple item
attributes and various constraint types, including a number of non-monotone
constraints. To evaluate the applicability of our approach, we develop an
MDD-based prefix-projection algorithm and compare its performance against a
typical generate-and-check variant, as well as a state-of-the-art
constraint-based sequential pattern mining algorithm. Results show that our
approach is competitive with or superior to these other methods in terms of
scalability and efficiency.Comment: AAAI201
A Compact Index for Order-Preserving Pattern Matching
Order-preserving pattern matching was introduced recently but it has already
attracted much attention. Given a reference sequence and a pattern, we want to
locate all substrings of the reference sequence whose elements have the same
relative order as the pattern elements. For this problem we consider the
offline version in which we build an index for the reference sequence so that
subsequent searches can be completed very efficiently. We propose a
space-efficient index that works well in practice despite its lack of good
worst-case time bounds. Our solution is based on the new approach of
decomposing the indexed sequence into an order component, containing ordering
information, and a delta component, containing information on the absolute
values. Experiments show that this approach is viable, faster than the
available alternatives, and it is the first one offering simultaneously small
space usage and fast retrieval.Comment: 16 pages. A preliminary version appeared in the Proc. IEEE Data
Compression Conference, DCC 2017, Snowbird, UT, USA, 201
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