T*******x
发帖数: 8565 | 1 hyperplane has dimension one less than the original space.
I usually think of hyperplane as a plane in a 3-dimensional space.
I dare not say I understand hyperplane.
It is used in a separation thoerem (geometric Hahn-Banach Theorem).
That's one place it is used.
What |
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q**x
发帖数: 1636 | 2 recently, I had to study functional analysis by myself.
I read a definition of hyperplane, but did not get a clear picture of it. What
is the meaning of hyperplane? What is the use of it?
Thanks. |
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k*******s
发帖数: 134 | 3 And I don't see why do you need this condition "这些点两两距离都大于1".
My reasoning is there are infinite number of hyperplanes, but there are a
finite number of hyperplanes where any two points' 投影重合. So there exists
hyperplane which there are n^3 points.
By the way, I'm not math major, I am not even very clear what is a
hyperplane. Just borrow the word :) |
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B****x
发帖数: 17 | 4 ACM Paris Kanellakis Theory and Practice Award奖励对计算机应用有重大影响的理论
发现. http://awards.acm.org/kanellakis/
2008
Cortes, Corinna
Vapnik, Vladimir
Paris Kanellakis Theory and Practice Award
2008 – Vladimir Vapnik
Fellow of NEC Laboratories/Columbia University (2008)
Citation
For the development of Support Vector Machines, a highly effective
algorithm for classification and related machine learning problems.
Full Citation
In their 1995 paper titled "Support vector networks," Cortes and Vapnik
introduced ... 阅读全帖 |
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z***u
发帖数: 105 | 5 有个想法，可不可以把所有的点按找离hyperplane 的距离排序呢？ 比如说每个
hyperplane 有两个map之类。
不知道值不值的这样做，有没有更好的数据结构？
point |
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p****r
发帖数: 104 | 6 给出4个点的坐标和他们的class如下：
(0, 1)+
(0,-1)-
(1, 2)+
(1,-2)-
请给出SVM的decision hyperplane
如果现在增加一个点：(2, 0)+，请再给出SVM的decision hyperplane？
想知道面对这样类型的问题，如何解答？我虽然对SVM的算法了解，但是这样的例子题
在面试当中出现，还真不知道如何回答才好。请各位大侠支招！ |
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s**********d
发帖数: 36899 | 7 他这不是hyperplaning，是突然打轮失控的。
最常见的出事原因之一。 |
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a*******y
发帖数: 1040 | 8 1. 一个array，sorted，你知道有一个数出现的次数no less than 51%， how to get
it?
2. if it is not sorted, how do you do it?
3. if given you 95% confidence to find that element, how do you find it?
4. a pond which is irregular, you cannot measure the volumn or area, but the
fish there is uniformly distributed, how do you measure how many fish are
there?
5. why SVM does not return you the hyperplane directlY? |
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h*d
发帖数: 19309 | 9 SVM出来的hyperplane已经不好直觉了，SVD出来的东西就更无法直觉理解，前两年还是
ensemble效果最好，不知道最近两年TREC用什么的最好。 |
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w******j
发帖数: 7 | 10 我怎么看都觉得应该有人做过。哪位给说说？
What I suggested to you was a further use of GAs for dealing with SVMs.
The support vectors give an optimal classifier in the sense that they
maximize the margin of separation between classes. But they do not
provide the optimal classifier. A better classifier will be possible by
using some of the SVs and some other data points to define the
separating hyperplane. You could experiment with this using GAs and
having your starting population as the SVs obtained by a standard S |
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J*****n
发帖数: 4859 | 11 但这是reducible的阿。any divisor in P, is always of form dH(H is hyperplane
section). |
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j**p
发帖数: 53 | 12 hi friends, I was just wondering whether there is a name for the following
system of algebraic equations (must have been extensively studied I assume)
\sum_{i=1}^K n_i = N_1
\sum_{i=1}^K {n_i}^2 = N_2
essentially we are looking for integer solutions on the intersection of a
hyper-sphere and a hyperplane in K-dimensions.
Many thanks! |
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s*****s
发帖数: 1559 | 13 第一个就是subpace.
第二个是说subspace平移以后的一个东西。
也许要看行文，才能知道作者到底指哪个。 一般指第二个，但是这个词也很少出现在
数学书里，没有太大意思。数学书多用plane, hyperplane 更直观的说法。 |
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d*****u
发帖数: 17243 | 14 thanks
再问一个问题吧。
如果N维空间里有两类点，怎么知道这两类点能被一个N-1维的hyperplane分隔呢？
有没有什么直接的证明方式？ |
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c*****n
发帖数: 33 | 15 If the two convex hulls of the two kinds of point have no
intersections, then this is clear.
hyperplane分隔呢？ |
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D******g
发帖数: 125 | 16 you are smart, there must be a such hyperplane. But the point of my question
is assuming the average IQ of this board is around 90. So I propose a
weaker version . |
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a**n
发帖数: 3801 | 17 separating hyperplane theorem
V0 |
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L*******t
发帖数: 2385 | 18 以往每年都有，discrete time的，我这届居然没有。
discrete time简单很多，不用seperating hyperplane... |
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j*******2
发帖数: 309 | 19 谢大牛回答。什么是L1 svm 和L2呢？就我的理解，kernel函数把低维的feature映射到
高维，这样
的话，最后得到的hyperplane维数还是很高的，为什么是sparse feature呢？ 另外，
svm是不是
用在small sample上效果很好？
还有，svm最后的结果只和support vector有关，这是不是算法稳定的原因呢？
高。 |
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