28,699 research outputs found
Pattern Recognition for Conditionally Independent Data
In this work we consider the task of relaxing the i.i.d assumption in pattern
recognition (or classification), aiming to make existing learning algorithms
applicable to a wider range of tasks. Pattern recognition is guessing a
discrete label of some object based on a set of given examples (pairs of
objects and labels). We consider the case of deterministically defined labels.
Traditionally, this task is studied under the assumption that examples are
independent and identically distributed. However, it turns out that many
results of pattern recognition theory carry over a weaker assumption. Namely,
under the assumption of conditional independence and identical distribution of
objects, while the only assumption on the distribution of labels is that the
rate of occurrence of each label should be above some positive threshold.
We find a broad class of learning algorithms for which estimations of the
probability of a classification error achieved under the classical i.i.d.
assumption can be generalised to the similar estimates for the case of
conditionally i.i.d. examples.Comment: parts of results published at ALT'04 and ICML'0
On Recursive Edit Distance Kernels with Application to Time Series Classification
This paper proposes some extensions to the work on kernels dedicated to
string or time series global alignment based on the aggregation of scores
obtained by local alignments. The extensions we propose allow to construct,
from classical recursive definition of elastic distances, recursive edit
distance (or time-warp) kernels that are positive definite if some sufficient
conditions are satisfied. The sufficient conditions we end-up with are original
and weaker than those proposed in earlier works, although a recursive
regularizing term is required to get the proof of the positive definiteness as
a direct consequence of the Haussler's convolution theorem. The classification
experiment we conducted on three classical time warp distances (two of which
being metrics), using Support Vector Machine classifier, leads to conclude
that, when the pairwise distance matrix obtained from the training data is
\textit{far} from definiteness, the positive definite recursive elastic kernels
outperform in general the distance substituting kernels for the classical
elastic distances we have tested.Comment: 14 page
Expanding the Family of Grassmannian Kernels: An Embedding Perspective
Modeling videos and image-sets as linear subspaces has proven beneficial for
many visual recognition tasks. However, it also incurs challenges arising from
the fact that linear subspaces do not obey Euclidean geometry, but lie on a
special type of Riemannian manifolds known as Grassmannian. To leverage the
techniques developed for Euclidean spaces (e.g, support vector machines) with
subspaces, several recent studies have proposed to embed the Grassmannian into
a Hilbert space by making use of a positive definite kernel. Unfortunately,
only two Grassmannian kernels are known, none of which -as we will show- is
universal, which limits their ability to approximate a target function
arbitrarily well. Here, we introduce several positive definite Grassmannian
kernels, including universal ones, and demonstrate their superiority over
previously-known kernels in various tasks, such as classification, clustering,
sparse coding and hashing
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