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https://github.com/naturale0/clusterpath.jl
Julia implementation of *l*_1-norm clusterpath (Hocking et al., 2011, Radchenko & Mukerjee, 2017)
https://github.com/naturale0/clusterpath.jl
clustering julia
Last synced: 6 days ago
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Julia implementation of *l*_1-norm clusterpath (Hocking et al., 2011, Radchenko & Mukerjee, 2017)
- Host: GitHub
- URL: https://github.com/naturale0/clusterpath.jl
- Owner: naturale0
- License: mit
- Created: 2020-12-08T13:01:25.000Z (about 4 years ago)
- Default Branch: main
- Last Pushed: 2020-12-13T16:27:52.000Z (about 4 years ago)
- Last Synced: 2024-04-26T08:02:19.689Z (8 months ago)
- Topics: clustering, julia
- Language: Julia
- Homepage:
- Size: 216 KB
- Stars: 1
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
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README
# Clusterpath.jl
Julia implementation of $\ell_1$ Clusterpath, described in the paper[^1].
## installation
```julia
import Pkg
Pkg.add("Clusterpath")
```
## Quick Start
### Sample procedure (with Big Merge Tracker)
* `generate_mixture_normal()`
* generate `n` observations from mixture of univariate normals each with standard deviation $1$ and mean parameters `m` and proportion `p`.
```julia
Random.seed!(0)
x1 = generate_mixture_normal(1000, [-4.5, 4.5], [0.35, 0.65])
```
* `clusterpath()`
* inputs:
- `x`: observation vector
- `alpha`: Big Merge Tracker threshold
```julia
cc = clusterpath(x1, α=0., return_split=true)["splits"][end]
```
-1.3447486506416237
* Another toy data
```julia
N = 100
Random.seed!(1)
xx = [randn(N, 2) .* .5; (randn(N, 2) .* 0.3 .+ 3)]
gt = repeat([1, 2], inner=N);
```
* `plot_path()`
* plot clusterpath with the data(`x`) and the solution path casted by `cast_solution()`.
* If the dimension of `x` is greater than 4, only plot combinations of first four dimensions.
***`Gaston.jl` and `gnuplot` should be installed and on the PATH of your system. Install gnuplot [here](https://sourceforge.net/projects/gnuplot/files/gnuplot/).***
* `x`: data
* `solution`: solution path dataframe from `cast_solution()`
* `gt`: ground truth labels
* `savefig`: whether to save the figure as a PNG file. (default: `false`)
* `fname`: image file name to be used when `savefig` is `true`. (default: `"path_plot"`)
* `show`: whether to show the plot in the notebook. **Highly recommended not to show if the number of samples is large.** (default: `true`)
```julia
plot_path(xx[:, 1], α=0., gt=gt, show=true)
```
```julia
plot_path(xx; α=0., gt=gt, show=true)
```
* `plot_cluster()`
* Plots the scatter plot of the data `x` colored according to the cluster assigned by clusterpath algorithm.
* If the dimension of `x` is greater than 2, perform PCA and plot two PCs.
***`Gaston.jl` and `gnuplot` should be installed and on the PATH of your system. Install gnuplot [here](https://sourceforge.net/projects/gnuplot/files/gnuplot/). ***
* `x`: data
* `α`: threshold for BMT-clusterpath
* `n_node`: if greater than `1`, will assign clusters from previous merge status. (default: `1`)
* `show`: whether to show the figure.
* `savefig`: whether to save the figure as a png file. (default: `false`)
* `fname`: file name to save if `savefig` is true. (default: `"plot_clst"`)
* `verbose`: print out current iteration. (default: `false`)
```julia
plot_cluster(xx, α=0.2; show=true, savefig=false)
```
* `assign_clusters()`
* assign cluster to each of the observations in `x`.
* returns an array of length=size(x, 1) of cluster indices.
* `x`: data
* `α`: threshold for BMT-clusterpath
* `n_node`: if greater than `1`, will assign clusters from previous merge status. (default: `1`)
```julia
assign_cluster(xx, α=.2)'
```
1×200 Adjoint{Int64,Array{Int64,1}}:
1 1 1 1 1 1 1 1 1 1 1 1 1 … 2 2 2 2 2 2 2 2 2 2 2 2
### Population Procedure
```julia
include("PopulationSplit.jl");
```
* `cond_mean_on_LR()`
* Conditional mean on $(L, R)$, defined as $\mu_{L,R} = \big(\int_L^R f(x) dx\big)^{-1} \cdot \int_L^R x f(x) dx$
* `find_split()`
* Find a split point if `find_split=true`, or $\delta_1, \delta_2$ for truncation point searching if `find_deltas=true`.
* `find_truncation()`
* Find the population split points.
* `clusterpath_pop()`
* population-equivalent version of sample `clusterpath()` procedure.
```julia
splits = Array{Float64, 1}()
Lstars = Array{Float64, 1}()
Rstars = Array{Float64, 1}()
for p=0.5:0.05:0.9
cp = clusterpath_pop(p, 4.5)
push!(splits, cp["s"])
push!(Lstars, cp["L*"])
push!(Rstars, cp["R*"])
end
println([round(s, digits=2) for s in splits]')
println([round(l, digits=2) for l in Lstars]')
println([round(r, digits=2) for r in Rstars]')
```
[0.0 -0.45 -0.9 -1.36 -1.82 -2.31 -2.89 -3.82 NaN]
[-8.98 -8.54 -8.09 -7.63 -7.17 -6.67 -6.09 -5.18 NaN]
[8.98 9.44 9.89 10.34 10.79 11.24 11.7 12.17 NaN]
```julia
splits = Array{Float64, 1}()
for p=0.5:0.05:0.9
push!(splits, clusterpath_pop(p, 4.5)["s"])
end
splits'
```
1×9 Adjoint{Float64,Array{Float64,1}}:
0.0 -0.4495 -0.9005 -1.355 -1.8195 -2.314 -2.8935 -3.816 NaN
: exactly the same results as in the paper (supp. p.29 Table 1).
---
[^1]: Radchenko, P. and Mukherjee, G. (2017), Convex clustering via l1 fusion penalization. J. R. Stat. Soc. B, 79: 1527-1546. https://doi.org/10.1111/rssb.12226