13,737 research outputs found
A tight lower bound instance for k-means++ in constant dimension
The k-means++ seeding algorithm is one of the most popular algorithms that is
used for finding the initial centers when using the k-means heuristic. The
algorithm is a simple sampling procedure and can be described as follows: Pick
the first center randomly from the given points. For , pick a point to
be the center with probability proportional to the square of the
Euclidean distance of this point to the closest previously chosen
centers.
The k-means++ seeding algorithm is not only simple and fast but also gives an
approximation in expectation as shown by Arthur and Vassilvitskii.
There are datasets on which this seeding algorithm gives an approximation
factor of in expectation. However, it is not clear from these
results if the algorithm achieves good approximation factor with reasonably
high probability (say ). Brunsch and R\"{o}glin gave a dataset where
the k-means++ seeding algorithm achieves an approximation ratio
with probability that is exponentially small in . However, this and all
other known lower-bound examples are high dimensional. So, an open problem was
to understand the behavior of the algorithm on low dimensional datasets. In
this work, we give a simple two dimensional dataset on which the seeding
algorithm achieves an approximation ratio with probability
exponentially small in . This solves open problems posed by Mahajan et al.
and by Brunsch and R\"{o}glin.Comment: To appear in TAMC 2014. arXiv admin note: text overlap with
arXiv:1306.420
What Statutes Mean: Interpretive Lessons from Positive Theories of Communication and Legislation
How should judges interpret statutes? For some scholars and judges, interpreting statutes requires little more than a close examination of statutory language, with perhaps a dictionary and a few interpretive canons nearby. For others, statutory interpretation must be based upon an assessment of a statute\u27s underlying purpose, an evaluation of society\u27s current norms and values, or a normative objective, such as the law\u27s integrity. With such differences squarely framed in the literature, it is reasonable to ask whether anything of value can be added. We contend that there is
Irrelevance of memory in the minority game
By means of extensive numerical simulations we show that all the distinctive
features of the minority game introduced by Challet and Zhang (1997), are
completely independent from the memory of the agents. The only crucial
requirement is that all the individuals must posses the same information,
irrespective of the fact that this information is true or false.Comment: 4 RevTeX pages, 4 figure
Multi-market minority game: breaking the symmetry of choice
Generalization of the minority game to more than one market is considered. At
each time step every agent chooses one of its strategies and acts on the market
related to this strategy. If the payoff function allows for strong fluctuation
of utility then market occupancies become inhomogeneous with preference given
to this market where the fluctuation occured first. There exists a critical
size of agent population above which agents on bigger market behave
collectively. In this regime there always exists a history of decisions for
which all agents on a bigger market react identically.Comment: 15 pages, 12 figures, Accepted to 'Advances in Complex Systems
Aquatic Feeding by Moose: Seasonal Variation in Relation to Plant Chemical Composition and Use of Mineral Licks
Activity of moose (Alces alces) was studied at aquatic feeding areas and at natural, sodium-rich licks during four periods covering late May to early September. Aquatic feeding increased from period 1 (late May and early June) to period 2 (late June and early July) and had declined by late July. Major activity at mineral licks occurred earlier in the season than aquatic feeding, especially for males. Chemical composition of aquatic plants showed no seasonal changes corresponding to the peak of aquatic feeding in period 2, although the sodium content of some species declined in period 3. We suggest that moose in the study area are attracted to sodium sources from late May to mid-July, that aquatic feeding replaces use of licks in June as the most sodium-rich aquatic plants become abundant, and that both activities decrease in midsummer because of declining attraction to sodium
Detection and Estimation Theory
Contains reports on two research projects.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 36-039-AMC-03200(E)
Statistics of the Kolkata Paise Restaurant Problem
We study the dynamics of a few stochastic learning strategies for the
'Kolkata Paise Restaurant' problem, where N agents choose among N equally
priced but differently ranked restaurants every evening such that each agent
tries get to dinner in the best restaurant (each serving only one customer and
the rest arriving there going without dinner that evening). We consider the
learning strategies to be similar for all the agents and assume that each
follow the same probabilistic or stochastic strategy dependent on the
information of the past successes in the game. We show that some 'naive'
strategies lead to much better utilization of the services than some relatively
'smarter' strategies. We also show that the service utilization fraction as
high as 0.80 can result for a stochastic strategy, where each agent sticks to
his past choice (independent of success achieved or not; with probability
decreasing inversely in the past crowd size). The numerical results for
utilization fraction of the services in some limiting cases are analytically
examined.Comment: 10 pages, 3 figs; accepted in New J Phy
Self-organized Networks of Competing Boolean Agents
A model of Boolean agents competing in a market is presented where each agent
bases his action on information obtained from a small group of other agents.
The agents play a competitive game that rewards those in the minority. After a
long time interval, the poorest player's strategy is changed randomly, and the
process is repeated. Eventually the network evolves to a stationary but
intermittent state where random mutation of the worst strategy can change the
behavior of the entire network, often causing a switch in the dynamics between
attractors of vastly different lengths.Comment: 4 pages, 3 included figures. Some text revision and one new figure
added. To appear in PR
A thermal model for adaptive competition in a market
New continuous and stochastic extensions of the minority game, devised as a
fundamental model for a market of competitive agents, are introduced and
studied in the context of statistical physics. The new formulation reproduces
the key features of the original model, without the need for some of its
special assumptions and, most importantly, it demonstrates the crucial role of
stochastic decision-making. Furthermore, this formulation provides the exact
but novel non-linear equations for the dynamics of the system.Comment: 4 RevTeX pages, 3 EPS figures. Revised versio
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