522 research outputs found
Improvements on the k-center problem for uncertain data
In real applications, there are situations where we need to model some
problems based on uncertain data. This leads us to define an uncertain model
for some classical geometric optimization problems and propose algorithms to
solve them. In this paper, we study the -center problem, for uncertain
input. In our setting, each uncertain point is located independently from
other points in one of several possible locations in a metric space with metric , with specified probabilities
and the goal is to compute -centers that minimize the
following expected cost here
is the probability space of all realizations of given uncertain points and
In restricted assigned version of this problem, an assignment is given for any choice of centers and the
goal is to minimize In unrestricted version, the
assignment is not specified and the goal is to compute centers
and an assignment that minimize the above expected
cost.
We give several improved constant approximation factor algorithms for the
assigned versions of this problem in a Euclidean space and in a general metric
space. Our results significantly improve the results of \cite{guh} and
generalize the results of \cite{wang} to any dimension. Our approach is to
replace a certain center point for each uncertain point and study the
properties of these certain points. The proposed algorithms are efficient and
simple to implement
Sequentially Cohen-Macaulay matroidal ideals
Let be the polynomial ring in variables over a field
and let be a matroidal ideal of degree in . In this paper, we
study the class of sequentially Cohen-Macaulay matroidal ideals. In particular,
all sequentially Cohen-Macaulay matroidal ideals of degree are classified.
Furthermore, we give a classification of sequentially Cohen-Macaulay matroidal
ideals of degree in some special cases.Comment: 12 pages, Comments are welcome
A Deep Learning Anomaly Detection Method in Textual Data
In this article, we propose using deep learning and transformer architectures
combined with classical machine learning algorithms to detect and identify text
anomalies in texts. Deep learning model provides a very crucial context
information about the textual data which all textual context are converted to a
numerical representation. We used multiple machine learning methods such as
Sentence Transformers, Auto Encoders, Logistic Regression and Distance
calculation methods to predict anomalies. The method are tested on the texts
data and we used syntactic data from different source injected into the
original text as anomalies or use them as target. Different methods and
algorithm are explained in the field of outlier detection and the results of
the best technique is presented. These results suggest that our algorithm could
potentially reduce false positive rates compared with other anomaly detection
methods that we are testing.Comment: 8 Pages, 4 Figure
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