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For example, financial data has in some cases strong positive and negative correlations between different stocks (feature space) and also strong positive and negative correlations between specific dates (sample space), if surprising positive or negative news was released on those dates.

What are other sources of continuous data, such as audio, visual, or data obtained by some measurement instrument or process, that display the above characteristics? See also "transposable data".

Importantly, it seems that in the sample space often negative correlations are non-sensical or non-causal, which limits the types of data sources with positive and negative correlations in both sample and feature space.

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A couple of spatio-temporal datasets are likely to exhibit this characteristic:

  • Transportation demand across different locations of a city over different hours of a day. While residential locations have high demand originating there in the morning hours, and low demand in the evening, the reverse is true of work locations. The demand pattern of these two location types will be negatively correlated, whereas that of two different residential locations (or two locations of the same type) will be positively correlated. From the point of view of hours, correlation between two morning hours will be positive, whereas between a morning and an evening hour will be negative.

  • Temperature pattern across days, for different cities across the world. Here, data for cities in the northern and southern hemisphere will be negatively correlated.

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  • $\begingroup$ Interesting. Are there any other types than spatio-temporal (as for these examples) or financial-temporal (as for the stocks example)? $\endgroup$ – baf84b4c May 7 '18 at 11:49
  • $\begingroup$ The last example with temperature patterns does not seem to work, as there are only anti-correlations and never any correlations when days are regarded as features and cities as samples. $\endgroup$ – baf84b4c May 10 '18 at 11:11
  • $\begingroup$ Do you mean no two cities have good correlation in their temperatures? What about cities which are close to each other? $\endgroup$ – raghu May 13 '18 at 5:36
  • $\begingroup$ No, the other way around, when two days are regarded as features. But I'm not so clear on it. $\endgroup$ – baf84b4c May 14 '18 at 10:24

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