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| '''Large margin nearest neighbor (LMNN)<ref name="Weinberger05">{{cite journal
| | Your assignment is to plan your work in the right way, sticking with our guidelines:. The essay will likely be produced from a certain dilemma, and even will need a certain form, just like contrast and compare or evaluate. In writing College Application Essay, the students may also tell about themselves that will capture the attention of the readers. It will help you to become a more effective writer. After all, they aren't cheating by using an academic writing service. <br><br>The company offers all kinds of medical essay writing in all subjects of medical course for the student in all academic levels. This is looked down upon as one of the major causes of getting bad grades. The second step towards learning the fine art of writing essay is reading widely. Every good essay begins with a thought or argument called 'a thesis. On the whole, the additional description and appealing details they utilize further which will be for the readers. <br><br>For the students to acquire good grades, it is understandable for them to seek out help. You will never regret your choice of buying essay from us. Well, lucky for you several online writing service providers can help you do your homework on time. This is to ensure writers who provide you with services are qualified. The reason to write it in paper form with paper sources is that you can spread the material out on a table, and will allow you to see if one source conflicts with another, if one article states a fact better than another, etc. <br><br>This is where lessons learned will be described and the importance of the topic emphasized. People may feel that writing an essay might be extremely difficult and complicated but it is not so. Equally, most of the author's students, members in the initially indigenous online populace, favor reading virtual texts to looking at genuine books: For them, it implies that just about every college course should acknowledge the increasing online assets (from educational e-books to social book-renting web sites) offered to college students who commit extra time engaged together with the World wide web than glued into the Tv set. Consequently, we suggest you to apply Exclusive-Essays. Don't try to force your opinion but make them think over it by giving them some stats or proves. <br><br>If you enjoyed this write-up and you would like to obtain more info relating to [http://www.4gam3rs.com/profile/dashenton essay service australia] kindly visit our page. When writing your essay, be careful to avoid overusing flowery tongue. So remember, to gain top marks for your poetry essays, simply split the poem up into these chunks and they will allow you to write a clear, incisive and comprehensive essay every time. Our essay writing company offers its customers with essay custom writing services. Alternate the details from one side of the comparison or oppose the other, each time giving specific details to support both subjects of your comparison. Essay writing services have sprung up thanks to consumer demand. |
| | last = Weinberger
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| | first = K. Q.
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| | coauthors = Blitzer J. C., Saul L. K.
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| | title = Distance Metric Learning for Large Margin Nearest Neighbor Classification,
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| | journal = Advances in Neural Information Processing Systems 18 (NIPS)
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| | year=2006
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| | pages=1473–1480
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| | url=http://books.nips.cc/papers/files/nips18/NIPS2005_0265.pdf
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| }}</ref> classification''' is a statistical [[machine learning]] [[algorithm]]. It learns a [[Pseudometric]] designed for [[k-nearest neighbor]] classification. The algorithm is based on [[semidefinite programming]], a sub-class of [[convex optimization]].
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| The goal of [[supervised learning]] (more specifically classification) is to learn a decision rule that can categorize data instances into pre-defined classes. The [[k-nearest neighbor]] rule assumes a ''training'' data set of labeled instances (i.e. the classes are known). It classifies a new data instance with the class obtained from the majority vote of the k closest (labeled) training instances. Closeness is measured with a pre-defined [[Metric_(mathematics)|metric]]. Large Margin Nearest Neighbors is an algorithm that learns this global (pseudo-)metric in a supervised fashion to improve the classification accuracy of the k-nearest neighbor rule.
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| ==Setup==
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| The main intuition behind LMNN is to learn a [[pseudometric]] under which all data instances in the training set are surrounded by at least k instances that share the same class label. If this is achieved, the [[leave-one-out]] error (a special case of [[cross validation]]) is minimized. Let the training data consist of a data set <math> D=\{(\vec x_1,y_1),\dots,(\vec x_n,y_n)\}\subset R^d\times C</math>, where the set of possible class categories is <math>C=\{1,\dots,c\}</math>.
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| The algorithm learns a [[pseudometric]] of the type
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| :<math>d(\vec x_i,\vec x_j)=(\vec x_i-\vec x_j)^\top\mathbf{M}(\vec x_i-\vec x_j)</math>.
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| For <math>d(\cdot,\cdot)</math> to be well defined, the matrix <math>\mathbf{M}</math> needs to be [[positive semi-definite]]. The Euclidean metric is a special case, where <math>\mathbf{M}</math> is the identity matrix. This generalization is often (falsely) referred to as [[Mahalanobis metric]].
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| Figure 1 illustrates the effect of the metric under varying <math>\mathbf{M}</math>. The two circles show the set of points with equal distance to the center <math>\vec x_i</math>. In the Euclidean case this set is a circle, whereas under the modified (Mahalanobis) metric it becomes an [[ellipsoid]].
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| [[File:Lmnn.png|thumb|300px|Figure 1: Schematic illustration of LMNN.]]
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| The algorithm distinguishes between two types of special data points: ''target neighbors'' and ''impostors''.
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| ===Target Neighbors===
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| Target neighbors are selected before learning. Each instance <math>\vec x_i</math> has exactly <math>k</math> different target neighbors within <math>D</math>, which all share the same class label <math>y_i</math>. The target neighbors are the data points that ''should become'' nearest neighbors ''under the learned metric''. Let us denote the set of target neighbors for a data point <math>\vec x_i</math> as <math>N_i</math>.
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| ===Impostors===
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| An impostor of a data point <math>\vec x_i</math> is another data point <math>\vec x_j</math> with a different class label (i.e. <math>y_i\neq y_j</math>) which is one of the <math>k</math> nearest neighbors of <math>\vec x_i</math>. During learning the algorithm tries to minimize the number of impostors for all data instances in the training set.
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| ==Algorithm==
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| Large Margin Nearest Neighbors optimizes the matrix <math>\mathbf{M}</math> with the help of [[semidefinite programming]]. The objective is twofold: For every data point <math>\vec x_i</math>, the ''target neighbors'' should be ''close'' and the ''impostors'' should be ''far away''. Figure 1 shows the effect of such an optimization on an illustrative example. The learned metric causes the input vector <math>\vec x_i</math> to be surrounded by training instances of the same class. If it was a test point, it would be classified correctly under the <math>k=3</math> nearest neighbor rule.
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| The first optimization goal is achieved by minimizing the average distance between instances and their target neighbors
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| :<math>\sum_{i,j\in N_i} d(\vec x_i,\vec x_j)</math>.
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| The second goal is achieved by constraining impostors <math>\vec x_l</math> to be one unit further away than target neighbors <math>\vec x_j</math> (and therefore pushing them out of the local neighborhood of <math>\vec x_i</math>). The resulting inequality constraint can be stated as:
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| :<math>\forall_{i,j \in N_i,l, y_l\neq y_i} d(\vec x_i,\vec x_j)+1\leq d(\vec x_i,\vec x_l)</math>
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| The margin of exactly one unit fixes the scale of the matrix <math>M</math>. Any alternative choice <math>c>0</math> would result in a rescaling of <math>M</math> by a factor of <math>1/c</math>.
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| The final optimization problem becomes:
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| :<math> \min_{\mathbf{M}} \sum_{i,j\in N_i} d(\vec x_i,\vec x_j) + \sum_{i,j,l} \xi_{ijl}</math>
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| :<math>\forall_{i,j \in N_i,l, y_l\neq y_i} </math> | |
| :<math> d(\vec x_i,\vec x_j)+1\leq d(\vec x_i,\vec x_l)+\xi_{ijl}</math>
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| :<math> \xi_{ijl}\geq 0</math>
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| :<math> \mathbf{M}\succeq 0</math>
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| Here the [[slack variable]]s <math>\xi_{ijl}</math> absorb the amount of violations of the impostor constraints. Their overall sum is minimized. The last constraint ensures that <math>\mathbf{M}</math> is [[positive semi-definite]]. The optimization problem is an instance of [[semidefinite programming]] (SDP). Although SDPs tend to suffer from high computational complexity, this particular SDP instance can be solved very efficiently due to the underlying geometric properties of the problem. In particular, most impostor constraints are naturally satisfied and do not need to be enforced during runtime. A particularly well suited solver technique is the [[working set]] method, which keeps a small set of constraints that are actively enforced and monitors the remaining (likely satisfied) constraints only occasionally to ensure correctness.
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| ==Extensions and efficient solvers==
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| LMNN was extended to multiple local metrics in the 2008 paper.<ref name="Weinberger08">{{cite journal
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| | last = Weinberger
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| | first = K. Q.
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| | coauthors = Saul L. K.
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| | title = Fast solvers and efficient implementations for distance metric learning
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| | journal = [[Proceedings of International Conference on Machine Learning]]
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| | year=2008
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| | pages = 1160–1167
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| | url=http://research.yahoo.net/files/icml2008a.pdf
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| }}</ref>
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| This extension significantly improves the classification error, but involves a more expensive optimization problem. In their 2009 publication in the Journal of Machine Learning Research,<ref name="Weinberger09">{{cite journal
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| | last = Weinberger
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| | first = K. Q.
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| | coauthors = Saul L. K.
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| | title = Distance Metric Learning for Large Margin Classification
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| | journal = [[Journal of Machine Learning Research]]
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| | year=2009
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| | volume = 10 | pages = 207–244
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| | url=http://www.jmlr.org/papers/volume10/weinberger09a/weinberger09a.pdf
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| }}</ref> Weinberger and Saul derive an efficient solver for the semi-definite program. It can learn a metric for the [http://yann.lecun.com/exdb/mnist/ MNIST handwritten digit data set] in several hours, involving billions of pairwise constraints. An [[open source]] [[Matlab]] implementation is freely available at the [http://www.cse.wustl.edu/~kilian/code/code.html authors web page].
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| Kumal et al.<ref name="kumar07">{{cite journal
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| | last = Kumar
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| | first= M.P.
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| | coauthors= Torr P.H.S., Zisserman A.
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| | title =An invariant large margin nearest neighbour classifier
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| | journal= IEEE 11th International Conference on Computer Vision (ICCV), 2007
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| | year=2007
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| | pages= 1–8
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| | url=http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4409041
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| }}</ref> extended the algorithm to incorporate local invariances to multivariate polynomial transformations and improved regularization.
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| ==See also==
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| * [[Similarity learning]]
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| * [[Linear discriminant analysis]]
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| * [[Learning Vector Quantization]]
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| * [[Pseudometric]]
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| * [[Nearest neighbor search]]
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| * [[Cluster analysis]]
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| * [[Data classification]]
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| * [[Data mining]]
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| * [[Machine learning]]
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| * [[Pattern recognition]]
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| * [[Predictive analytics]]
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| * [[Dimension reduction]]
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| * [[Neighbourhood components analysis]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| * [http://www.cse.wustl.edu/~kilian/code/code.html Matlab Implementation]
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| * [http://compscicenter.ru/sites/default/files/materials/2012_05_03_MachineLearning_lecture_09.pdf ICML 2010 Tutorial on Metric Learning]
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| [[Category:Classification algorithms]]
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| [[Category:Machine learning]]
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Your assignment is to plan your work in the right way, sticking with our guidelines:. The essay will likely be produced from a certain dilemma, and even will need a certain form, just like contrast and compare or evaluate. In writing College Application Essay, the students may also tell about themselves that will capture the attention of the readers. It will help you to become a more effective writer. After all, they aren't cheating by using an academic writing service.
The company offers all kinds of medical essay writing in all subjects of medical course for the student in all academic levels. This is looked down upon as one of the major causes of getting bad grades. The second step towards learning the fine art of writing essay is reading widely. Every good essay begins with a thought or argument called 'a thesis. On the whole, the additional description and appealing details they utilize further which will be for the readers.
For the students to acquire good grades, it is understandable for them to seek out help. You will never regret your choice of buying essay from us. Well, lucky for you several online writing service providers can help you do your homework on time. This is to ensure writers who provide you with services are qualified. The reason to write it in paper form with paper sources is that you can spread the material out on a table, and will allow you to see if one source conflicts with another, if one article states a fact better than another, etc.
This is where lessons learned will be described and the importance of the topic emphasized. People may feel that writing an essay might be extremely difficult and complicated but it is not so. Equally, most of the author's students, members in the initially indigenous online populace, favor reading virtual texts to looking at genuine books: For them, it implies that just about every college course should acknowledge the increasing online assets (from educational e-books to social book-renting web sites) offered to college students who commit extra time engaged together with the World wide web than glued into the Tv set. Consequently, we suggest you to apply Exclusive-Essays. Don't try to force your opinion but make them think over it by giving them some stats or proves.
If you enjoyed this write-up and you would like to obtain more info relating to essay service australia kindly visit our page. When writing your essay, be careful to avoid overusing flowery tongue. So remember, to gain top marks for your poetry essays, simply split the poem up into these chunks and they will allow you to write a clear, incisive and comprehensive essay every time. Our essay writing company offers its customers with essay custom writing services. Alternate the details from one side of the comparison or oppose the other, each time giving specific details to support both subjects of your comparison. Essay writing services have sprung up thanks to consumer demand.