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In [[machine learning]] and [[data mining]], a '''string kernel''' is a [[Positive-definite kernel|kernel function]] that operates on [[String (computer science)|strings]], i.e. finite sequences of symbols that need not be of the same length. String kernels can be intuitively understood as functions measuring the similarity of pairs of strings: the more similar two strings ''a'' and ''b'' are, the higher the value of a string kernel ''K''(''a'', ''b'') will be.
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Using string kernels with [[Kernel trick|kernelized]] learning algorithms such as [[support vector machine]]s allow such algorithms to work with strings, without having to translate these to fixed-length, real-valued [[feature vector]]s.<ref name="Lodhi"/> String kernels are used in domains where sequence data are to be [[Cluster analysis|clustered]] or [[statistical classification|classified]], e.g. in [[text mining]] and [[bioinformatics|gene analysis]].<ref>
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{{Citation
  | title = The spectrum kernel: A string kernel for SVM protein classification
  | last = Leslie
  | first = C.
  | last2 = Eskin
  | first2 = E.
  | last3 = Noble
  | first3 = W.S.
  | booktitle = Proceedings of the Pacific Symposium on Biocomputing
  | volume = 7
  | pages = 566–575
  | year = 2002
}}</ref>
 
==Informal introduction==
 
Suppose one wants to compare some text passages automatically and indicate their relative similarity.
For many applications, it might be sufficient to find some keywords which match exactly.
One example where exact matching is not always enough is found in [[Spam (electronic)|spam]] detection.<ref>
{{Citation
  | title = Improved Online Support Vector Machines Spam Filtering Using String Kernels
  | last = Amayri
  | first = O.
}}</ref>
Another would be in computational gene analysis, where [[Homology (biology)|homologous]] [[genes]] have [[mutated]], resulting in common subsequences along with deleted, inserted or replaced symbols.
<!--- TODO insert a picture here --->
 
==Motivation==
 
Since several well-proven data clustering, classification and information retrieval
<!--- and other ... see manifold learning --->
methods (for example support vector machines) are designed to work on vectors
(i.e. data are elements of a vector space), using a string kernel allows the extension of these methods to handle sequence data.
 
The string kernel method is to be contrasted with earlier approaches for text classification where feature vectors only indicated
the presence or absence of a word.
Not only does it improve on these approaches, but it is an example for a whole class of kernels adapted to data structures, which
began to appear at the turn of the 21st century. A survey of such methods has been compiled by Gärtner.<ref>
{{Citation
  | last = Gärtner
  | first = T.
  | title = A survey of kernels for structured data
  | journal = CM SIGKDD Explorations Newsletter
  | publisher = [[Association for Computing Machinery|ACM]]
  | year = 2003
  | volume = 5
  | number = 1
  | page = 58}}
</ref>
 
==Definition==
 
A [[Kernel trick|kernel]] on a domain <math>D</math> is a function <math>K: D \times D \rightarrow \mathbb{R}</math>
satisfying some conditions (being [[symmetric]] in the arguments, [[continuous function|continuous]] and [[Positive-semidefinite function|positive semidefinite]] in a certain sense).
 
[[Mercer's theorem]] asserts that <math>K</math> can then be expressed as <math>K(x,y)=\varphi(x)\cdot \varphi(y)</math> with <math>\varphi</math> mapping the arguments into an [[inner product space]].
 
We can now reproduce the definition of a '''string subsequence kernel'''<ref name="Lodhi">{{Cite journal
  | last = Lodhi
  | first = Huma
  | last2 = Saunders
  | first2 = Craig
  | last3 = Shawe-Taylor
  | first3 = John
  | last4 = Cristianini
  | first4 = Nello
  | last5 = Watkins
  | first5 = Chris
  | title = Text classification using string kernels
  | journal = [[Journal of Machine Learning Research]]
  | year = 2002
  | pages = 419–444}}</ref>
on strings over an [[Alphabet (computer science)|alphabet]] <math>\Sigma</math>. Coordinate-wise, the mapping is defined as follows:
 
:<math>\varphi_u :
\left\{
\begin{array}{l}
\Sigma^n \rightarrow \mathbb{R}^{\Sigma^n} \\
s \mapsto \sum_{\mathbf{i} : u=s_{\mathbf{i}}} \lambda^{l(\mathbf{i})}
\end{array}
\right.
</math>
 
The <math>\mathbf{i}</math> are [[multiindices]] and <math>u</math> is a string of length <math>n</math>:
subsequences can occur in a non-contiguous manner, but gaps are penalized.
The parameter <math>\lambda</math> may be set to any value between <math>0</math> (gaps are not allowed) and <math>1</math>
(even widely-spread "occurrences" are weighted the same as appearances as a contiguous substring).
 
<!--- TODO put an example here !!! --->
 
For several relevant algorithms, data enters into the algorithm only in expressions involving an inner product of feature vectors,
hence the name [[kernel methods]]. A desirable consequence of this is that one does not need to explicitly calculate the transformation <math>\phi(x)</math>, only the inner product via the kernel, which may be a lot quicker, especially when [[approximation|approximated]].<ref name=Lodhi/>
<!--- ==Efficitent Computation== --->
<!--- == See also == --->
 
==References==
<!--- cite "alignment kernels", precursor --->
{{Reflist}}
 
[[Category:Algorithms on strings]]
[[Category:Kernel methods for machine learning]]
[[Category:Natural language processing]]
[[Category:String similarity measures]]

Latest revision as of 17:14, 16 May 2014

Making sure you have the correct size is very important; a poor fitting helmet can be uncomfortable and unsafe. Therefore, you ought to verify the fork, the wheels and the suspensions together with two or three particulars. While a well trained dolphin is not as intimidating as a close encounter with a 230 kg wild animal is a totally different experience. Are you in search of a comfort bike, a mountain bike, or a bike that is designed just for cruising and do you prefer a standard road bike or are you looking for an hybrid. That attitude completely misses what is important about Papago Park.

You can choose from many different suspensions on your bike, make sure the suspension you choose is going to fit the type of cycling you intend for it. 750 the Ribble Winter Trainer provides fantastic features with a fantastic price tag. From free shipping on all the bikes across the US, the Road Bike Outlet makes consumers happy anywhere within 1 to 6 days. Ten miles back to the truck is a long walk when pushing 200 pounds of meat on a bike. Titanium is very light and gives you an advantage and is usually used in racing bicycles.

They are electricity assisted, meaning electric power is used in response to the rider's pedaling power, with pedaling staying the key driver. Never miss the chance to experience mountain biking. Buy a bike that has a top quality body made outside of steel, aluminum, carbon fiber or titanium. If you have any issues with regards to where by and how to use Cannondale mountain bike sizing., you can get in touch with us at the web-site. Hence, having the bicycle that suits you perfectly is much easier now. If you really want a quality bike which will hold up to the rough terrain with out costing a fortune, this is a great choice.

Consequently, they became like villains in the eyes of the NBA fans outside Miami. Cold and long winters at high altitude are perfect conditions for winter recreation. If the metal tubing below the paint has become exposed, then touch this up with a dab of enamel paint, using a very fine brush. With the tips given, I am sure that you and your new bike will work together for that ultimate mountain biking adventure. The biker will encounter numerous obstacles along the way which will make his trajectory an extreme adventure.

If you can afford it, a full suspension mountain bike is always worth the purchase. The tires are wider that are designed for diverse terrains. This is the major basis of differentiation between a road bike and a mountain bike. The price range of lightweight bicycles prices vary from $200. Some switchbacks can be technically challenging and the narrow, winding trails can make for a few surprises when encountering other riders, but much of the system is gentle, rolling and easily managed by novices.

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