Actually there is something close: clusters of regression models. You can fit *latent class regression*, or *cluster-wise regression*, to your data, or it's extension *mixture of generalized linear models*. The model is a [finite mixture model][1]

$$f(x, \vartheta) = \sum^K_{k=1} \pi_k f_k(x, \vartheta_k)$$ 

where $f_k$ are mixture components parametrized by $\vartheta_k$ parameters, that in this case are regression components that appear in the data with latent proportions $\pi_k$. So the idea is that the distribution of your data is a mixture of $K$ components, each that can be described by a regression model $f_k$ appearing with probability $\pi_k$. This can be extended to other forms and mixtures of other classes of models and generally the approach is very flexible in the choice of $f_k$ components (e.g. mixtures of factor analyzers).

Below you can see example of such model from [`flexmix` library][2] (Leisch, 2004; Grun and Leisch, 2008) vignette fitting mixture of two regression models to made-up data.

<!-- language-all: lang-r -->

    library("flexmix")
    data("NPreg")
    m1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2)
    parameters(m1, component = 1)
    ##                      Comp.1
    ## coef.(Intercept) 14.7171662
    ## coef.x            9.8458171
    ## coef.I(x^2)      -0.9682602
    ## sigma             3.4808332
    parameters(m1, component = 2)
    ##                       Comp.2
    ## coef.(Intercept) -0.20910955
    ## coef.x            4.81646040
    ## coef.I(x^2)       0.03629501
    ## sigma             3.47505076

It is visualized on the following plots (points shapes are the true classes, colors are the classifications).

[![Example of latent class regression][3]][3]

For further details you can check the following papers:

> Wedel, M. and DeSarbo, W.S. (1995). [A Mixture Likelihood Approach for
> Generalized Linear Models.][4] *Journal of Classification , 12*,
> 21–55.
> 
> Wedel, M. and Kamakura, W.A. (2001). *Market Segmentation – Conceptual
> and Methodological Foundations.* Kluwer Academic Publishers.
> 
> Leisch, F. (2004). [Flexmix: A general framework for finite mixture
> models and latent glass regression in R.][5] *Journal of Statistical
> Software, 11(8)*, 1-18.
> 
> Grun, B. and Leisch, F. (2008). [FlexMix version 2: finite mixtures
> with concomitant variables and varying and constant parameters.][6]
> *Journal of Statistical Software, 28(1), 1-35.
> 
> McLachlan, G. and Peel, D. (2000). *Finite Mixture Models.* John Wiley & Sons.


  [1]: http://stats.stackexchange.com/questions/130805/are-there-any-non-distance-based-clustering-algorithms/130810#130810
  [2]: https://cran.r-project.org/package=flexmix
  [3]: https://i.sstatic.net/ntC6i.png
  [4]: https://www.researchgate.net/profile/Wayne_Desarbo/publication/226342466_A_mixture_likelihood_approach_for_generalized_linear_models/links/0deec51a7c223876e0000000.pdf
  [5]: https://www.jstatsoft.org/article/view/v011i08
  [6]: https://www.jstatsoft.org/article/view/v028i04