blocks|key|919656|text|如果维度是相关的，Principal+component+analysis可能会很有帮助。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|919657|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Principal_component_analysis^0|9|S|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@$A|M|B|N|1|O]]|C|$]]|$1|D|3|-4|5|6|7|P|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]]]

<a href="http://en.wikipedia.org/wiki/Principal_component_analysis" rel="noreferrer" title="Principal component analysis">Principal component analysis</a> could be helpful if the dimensions are correlated.

blocks|key|703271|text|Parallel+coordinates是一种用于可视化高维数据的流行方法。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|703272|哪种类型的可视化最适合您的数据，具体取决于其特征--不同维度的相关性如何？|703273|entityMap|0|LINK|mutability|MUTABLE|url|http://vis.stanford.edu/protovis/ex/cars.html^0|0|K|0|0|0^^$0|@$1|2|3|4|5|6|7|N|8|@]|9|@$A|O|B|P|1|Q]]|C|$]]|$1|D|3|E|5|6|7|R|8|@]|9|@]|C|$]]|$1|F|3|-4|5|6|7|S|8|@]|9|@]|C|$]]]|G|$H|$5|I|J|K|C|$L|M]]]]

<a href="http://vis.stanford.edu/protovis/ex/cars.html" rel="noreferrer">Parallel coordinates</a> are a popular method for visualizing high-dimensional data.

What kind of visualization is best for your data in particular will depend on its characteristics-- how correlated are the different dimensions?

blocks|key|703444|text|我搜索的流行语是multidimensional+scaling。这是一种从高维空间到低维空间(2维或3维)的投影，使得在全空间中接近的点在投影中也是接近的。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|703445|它通常用于可视化集群算法的输出(即，如果您的集群在MDS投影中是紧凑的，则它们很可能也在整个空间中)。|703446|编辑:这不一定有助于确定数据是密集的还是稀疏的，因为您在投影中丢失了比例，但它将显示数据是均匀的还是块状的(可能这就是您的意思)。|703447|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Multidimensional_scaling^0|8|O|0|0|0|0^^$0|@$1|2|3|4|5|6|7|P|8|@]|9|@$A|Q|B|R|1|S]]|C|$]]|$1|D|3|E|5|6|7|T|8|@]|9|@]|C|$]]|$1|F|3|G|5|6|7|U|8|@]|9|@]|C|$]]|$1|H|3|-4|5|6|7|V|8|@]|9|@]|C|$]]]|I|$J|$5|K|L|M|C|$N|O]]]]

The buzzword I would search for is <a href="http://en.wikipedia.org/wiki/Multidimensional_scaling" rel="nofollow">multidimensional scaling</a>. It is a technique to develop a projection from the high dimensional space to a lower space (2 or 3 dimensional) in such a way that points which are close in the full space will be close in the projection.

It is often used for visualising the output of clustering algorithms (i.e. if your clusters are compact in the MDS projection there is a good chance they are also in the full space).

Edit: This wouldn't necessarily help with determining if the data is dense or sparse, because you lose the scale in the projection, but it would show whether it is uniform or clumpy (perhaps thats what you mean).

blocks|key|919960|text|不确定您希望从数据中看到哪种模式。t-SNE及其更快的变体Barnes-Hut-SNE在可视化高维数据的相关概念组方面做得非常好。它可以通过R获得。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|919961|有一个简短的教程，介绍如何使用它来处理大约300维的高维数据。http://www.codeproject.com/Tips/788739/Visualizing-High-Dimensional-Vector-using-T-SNE-wi|offset|length|919962|entityMap|0|LINK|mutability|MUTABLE|url|http://www.codeproject.com/Tips/788739/Visualizing-High-Dimensional-Vector-using-T-SNE-wi^0|0|V|2H|0|0^^$0|@$1|2|3|4|5|6|7|N|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|O|8|@]|9|@$D|P|E|Q|1|R]]|A|$]]|$1|F|3|-4|5|6|7|S|8|@]|9|@]|A|$]]]|G|$H|$5|I|J|K|A|$L|M]]]]

Not sure what kind of patterns you would like to see from the data. t-SNE and its faster variant Barnes-Hut-SNE do a very good job in visualizing groups of related concepts for high-dimensional data. It is available through R.

There is a short tutorial on using it against high-dimensional data with about 300 dimensions.
<a href="http://www.codeproject.com/Tips/788739/Visualizing-High-Dimensional-Vector-using-T-SNE-wi" rel="nofollow">http://www.codeproject.com/Tips/788739/Visualizing-High-Dimensional-Vector-using-T-SNE-wi</a>

blocks|key|920152|text|我一直在寻找可视化高维数据的方法，发现这个t-SNE+technique已经得到了有效的使用。也可以帮助其他人。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|920153|entityMap|0|LINK|mutability|MUTABLE|url|http://lvdmaaten.github.io/tsne/^0|L|F|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@$A|M|B|N|1|O]]|C|$]]|$1|D|3|-4|5|6|7|P|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]]]

I was looking for ways to visualize high dimensional data and found this <a href="http://lvdmaaten.github.io/tsne/" rel="nofollow noreferrer">t-SNE technique</a> that has been used effectively. Might help others as well.

blocks|key|703730|text|看看http://www.ggobi.org+(巡游，平行坐标，散点图矩阵)可以用于实值变量。也可以通过http://cranvas.org获取更新的信息。R中的tourr包。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|703731|entityMap|0|LINK|mutability|MUTABLE|url|http://www.ggobi.org/|1|http://cranvas.org/^0|2|K|0|1G|I|1|0^^$0|@$1|2|3|4|5|6|7|N|8|@]|9|@$A|O|B|P|1|Q]|$A|R|B|S|1|T]]|C|$]]|$1|D|3|-4|5|6|7|U|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]|L|$5|G|H|I|C|$J|M]]]]

Take a look at <a href="http://www.ggobi.org" rel="nofollow">http://www.ggobi.org</a> (tours, parallel coordinates, scatterplot matrices) can be used for real-valued variables. Also <a href="http://cranvas.org" rel="nofollow">http://cranvas.org</a> for more recent. The tourr package in R.

blocks|key|920207|text|尝试使用http://hypertools.readthedocs.io/en/latest/。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|920208|HyperTools是一个用Python语言可视化和操作高维数据的库。|920209|entityMap|0|LINK|mutability|MUTABLE|url|http://hypertools.readthedocs.io/en/latest/^0|4|17|0|0|0^^$0|@$1|2|3|4|5|6|7|N|8|@]|9|@$A|O|B|P|1|Q]]|C|$]]|$1|D|3|E|5|6|7|R|8|@]|9|@]|C|$]]|$1|F|3|-4|5|6|7|S|8|@]|9|@]|C|$]]]|G|$H|$5|I|J|K|C|$L|M]]]]

Try using <a href="http://hypertools.readthedocs.io/en/latest/" rel="nofollow noreferrer">http://hypertools.readthedocs.io/en/latest/</a>. 

HyperTools is a library for visualizing and manipulating high-dimensional data in Python.

blocks|key|703361|text|星型架构。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|703362|http://en.wikipedia.org/wiki/Star_schema|offset|length|703363|适用于高维数据。|703364|如果事实表的基数接近维度大小的乘积，那么您拥有密集的数据。|703365|如果事实表的基数小于维度大小的乘积，则数据稀疏。|703366|在中间，你有一个判断电话。|703367|entityMap|0|LINK|mutability|MUTABLE|url^0|0|0|14|0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|U|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|V|8|@]|9|@$D|W|E|X|1|Y]]|A|$]]|$1|F|3|G|5|6|7|Z|8|@]|9|@]|A|$]]|$1|H|3|I|5|6|7|10|8|@]|9|@]|A|$]]|$1|J|3|K|5|6|7|11|8|@]|9|@]|A|$]]|$1|L|3|M|5|6|7|12|8|@]|9|@]|A|$]]|$1|N|3|-4|5|6|7|13|8|@]|9|@]|A|$]]]|O|$P|$5|Q|R|S|A|$T|C]]]]

Star Schema.

<a href="http://en.wikipedia.org/wiki/Star_schema" rel="nofollow">http://en.wikipedia.org/wiki/Star_schema</a>

Works well for high-dimensional data.

If the cardinality of your fact table is close to the product of your dimension sizes, you have dense data.

If the cardinality of your fact table is smaller than the product of your dimension sizes, you have sparse data.

In the middle you have a judgement call.

blocks|key|919866|text|curios.IT数据探索软件专为高维数据可视化而设计:数据显示为3D对象的集合(每个数据组一个)，可同时显示多达13个变量。数据变量和视觉特征之间的关系比使用其他技术(如平行坐标)更容易记忆。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|919867|entityMap|0|LINK|mutability|MUTABLE|url|http://www.kanohi.ch/index.php?id=9^0|0|9|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@$A|M|B|N|1|O]]|C|$]]|$1|D|3|-4|5|6|7|P|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]]]

The <a href="http://www.kanohi.ch/index.php?id=9" rel="nofollow">curios.IT</a> data exploration software is designed for the visualization of high dimensional data: data is shown as a collection of 3D objects (one for each data group) which can show up to 13 variables at the same time. The relationships between data variables and visual features are much easier to remember than with other techniques (like parallel coordinates).

Can someone please tell me if there is a good (easy) way to visualize high dimensional data? My data is currently 21 dimensions but I would like to see how whether it is dense or sparse. Are there techniques to achieve this?

Is there a good and easy way to visualize high dimensional data?

数据可视化

Python

有没有人能告诉我有没有一个好的(简单的)方法来可视化高维数据？我的数据目前是21维，但我想看看它是密集的还是稀疏的。有没有技术可以做到这一点？

问有没有一种既好又简单的方法来可视化高维数据？
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问有没有一种既好又简单的方法来可视化高维数据？
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