57,002 research outputs found
Data clustering using a model granular magnet
We present a new approach to clustering, based on the physical properties of
an inhomogeneous ferromagnet. No assumption is made regarding the underlying
distribution of the data. We assign a Potts spin to each data point and
introduce an interaction between neighboring points, whose strength is a
decreasing function of the distance between the neighbors. This magnetic system
exhibits three phases. At very low temperatures it is completely ordered; all
spins are aligned. At very high temperatures the system does not exhibit any
ordering and in an intermediate regime clusters of relatively strongly coupled
spins become ordered, whereas different clusters remain uncorrelated. This
intermediate phase is identified by a jump in the order parameters. The
spin-spin correlation function is used to partition the spins and the
corresponding data points into clusters. We demonstrate on three synthetic and
three real data sets how the method works. Detailed comparison to the
performance of other techniques clearly indicates the relative success of our
method.Comment: 46 pages, postscript, 15 ps figures include
Kernel methods in machine learning
We review machine learning methods employing positive definite kernels. These
methods formulate learning and estimation problems in a reproducing kernel
Hilbert space (RKHS) of functions defined on the data domain, expanded in terms
of a kernel. Working in linear spaces of function has the benefit of
facilitating the construction and analysis of learning algorithms while at the
same time allowing large classes of functions. The latter include nonlinear
functions as well as functions defined on nonvectorial data. We cover a wide
range of methods, ranging from binary classifiers to sophisticated methods for
estimation with structured data.Comment: Published in at http://dx.doi.org/10.1214/009053607000000677 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Change blindness: eradication of gestalt strategies
Arrays of eight, texture-defined rectangles were used as stimuli in a one-shot change blindness (CB) task where there was a 50% chance that one rectangle would change orientation between two successive presentations separated by an interval. CB was eliminated by cueing the target rectangle in the first stimulus, reduced by cueing in the interval and unaffected by cueing in the second presentation. This supports the idea that a representation was formed that persisted through the interval before being 'overwritten' by the second presentation (Landman et al, 2003 Vision Research 43149–164]. Another possibility is that participants used some kind of grouping or Gestalt strategy. To test this we changed the spatial position of the rectangles in the second presentation by shifting them along imaginary spokes (by ±1 degree) emanating from the central fixation point. There was no significant difference seen in performance between this and the standard task [F(1,4)=2.565, p=0.185]. This may suggest two things: (i) Gestalt grouping is not used as a strategy in these tasks, and (ii) it gives further weight to the argument that objects may be stored and retrieved from a pre-attentional store during this task
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