9,971 research outputs found
An interior point algorithm for minimum sum-of-squares clustering
Copyright @ 2000 SIAM PublicationsAn exact algorithm is proposed for minimum sum-of-squares nonhierarchical clustering, i.e., for partitioning a given set of points from a Euclidean m-space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong. This problem is expressed as a constrained hyperbolic program in 0-1 variables. The resolution method combines an interior point algorithm, i.e., a weighted analytic center column generation method, with branch-and-bound. The auxiliary problem of determining the entering column (i.e., the oracle) is an unconstrained hyperbolic program in 0-1 variables with a quadratic numerator and linear denominator. It is solved through a sequence of unconstrained quadratic programs in 0-1 variables. To accelerate resolution, variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached. Estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region. Proved minimum sum-of-squares partitions are determined for the rst time for several fairly large data sets from the literature, including Fisher's 150 iris.This research was supported by the Fonds
National de la Recherche Scientifique Suisse, NSERC-Canada, and FCAR-Quebec
Boosting Deep Open World Recognition by Clustering
While convolutional neural networks have brought significant advances in
robot vision, their ability is often limited to closed world scenarios, where
the number of semantic concepts to be recognized is determined by the available
training set. Since it is practically impossible to capture all possible
semantic concepts present in the real world in a single training set, we need
to break the closed world assumption, equipping our robot with the capability
to act in an open world. To provide such ability, a robot vision system should
be able to (i) identify whether an instance does not belong to the set of known
categories (i.e. open set recognition), and (ii) extend its knowledge to learn
new classes over time (i.e. incremental learning). In this work, we show how we
can boost the performance of deep open world recognition algorithms by means of
a new loss formulation enforcing a global to local clustering of class-specific
features. In particular, a first loss term, i.e. global clustering, forces the
network to map samples closer to the class centroid they belong to while the
second one, local clustering, shapes the representation space in such a way
that samples of the same class get closer in the representation space while
pushing away neighbours belonging to other classes. Moreover, we propose a
strategy to learn class-specific rejection thresholds, instead of heuristically
estimating a single global threshold, as in previous works. Experiments on
RGB-D Object and Core50 datasets show the effectiveness of our approach.Comment: IROS/RAL 202
MACOC: a medoid-based ACO clustering algorithm
The application of ACO-based algorithms in data mining is growing over the last few years and several supervised and unsupervised learning algorithms have been developed using this bio-inspired approach. Most recent works concerning unsupervised learning have been focused on clustering, showing great potential of ACO-based techniques. This work presents an ACO-based clustering algorithm inspired by the ACO Clustering (ACOC) algorithm. The proposed approach restructures ACOC from a centroid-based technique to a medoid-based technique, where the properties of the search space are not necessarily known. Instead, it only relies on the information about the distances amongst data. The new algorithm, called MACOC, has been compared against well-known algorithms (K-means and Partition Around Medoids) and with ACOC. The experiments measure the accuracy of the algorithm for both synthetic datasets and real-world datasets extracted from the UCI Machine Learning Repository
LexRank: Graph-based Lexical Centrality as Salience in Text Summarization
We introduce a stochastic graph-based method for computing relative
importance of textual units for Natural Language Processing. We test the
technique on the problem of Text Summarization (TS). Extractive TS relies on
the concept of sentence salience to identify the most important sentences in a
document or set of documents. Salience is typically defined in terms of the
presence of particular important words or in terms of similarity to a centroid
pseudo-sentence. We consider a new approach, LexRank, for computing sentence
importance based on the concept of eigenvector centrality in a graph
representation of sentences. In this model, a connectivity matrix based on
intra-sentence cosine similarity is used as the adjacency matrix of the graph
representation of sentences. Our system, based on LexRank ranked in first place
in more than one task in the recent DUC 2004 evaluation. In this paper we
present a detailed analysis of our approach and apply it to a larger data set
including data from earlier DUC evaluations. We discuss several methods to
compute centrality using the similarity graph. The results show that
degree-based methods (including LexRank) outperform both centroid-based methods
and other systems participating in DUC in most of the cases. Furthermore, the
LexRank with threshold method outperforms the other degree-based techniques
including continuous LexRank. We also show that our approach is quite
insensitive to the noise in the data that may result from an imperfect topical
clustering of documents
Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs
We develop data structures for dynamic closest pair problems with arbitrary
distance functions, that do not necessarily come from any geometric structure
on the objects. Based on a technique previously used by the author for
Euclidean closest pairs, we show how to insert and delete objects from an
n-object set, maintaining the closest pair, in O(n log^2 n) time per update and
O(n) space. With quadratic space, we can instead use a quadtree-like structure
to achieve an optimal time bound, O(n) per update. We apply these data
structures to hierarchical clustering, greedy matching, and TSP heuristics, and
discuss other potential applications in machine learning, Groebner bases, and
local improvement algorithms for partition and placement problems. Experiments
show our new methods to be faster in practice than previously used heuristics.Comment: 20 pages, 9 figures. A preliminary version of this paper appeared at
the 9th ACM-SIAM Symp. on Discrete Algorithms, San Francisco, 1998, pp.
619-628. For source code and experimental results, see
http://www.ics.uci.edu/~eppstein/projects/pairs
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