From 55dfb616dd5a7035f99109ca7d7ce623f822ae98 Mon Sep 17 00:00:00 2001 From: Andy Jones Date: Thu, 17 Dec 2020 09:56:47 -0500 Subject: [PATCH] expanded example --- README.md | 31 ++++++++++++++++++++++++++++++- plots/simulated/toydata_W.png | Bin 0 -> 77325 bytes 2 files changed, 30 insertions(+), 1 deletion(-) create mode 100644 plots/simulated/toydata_W.png diff --git a/README.md b/README.md index 286d9d7..733b7e1 100644 --- a/README.md +++ b/README.md @@ -55,10 +55,39 @@ Now we'll instantiate and fit the model with maximum likelihood estimation. ```python from pcpca import PCPCA -pcpca = PCPCA(gamma=0.7, n_components=2) +pcpca = PCPCA(gamma=0.7, n_components=1) pcpca.fit(X, Y) ``` +We can then visualize the line defined by W. (In general, this will be a hyperplane, but here we set n_components=1 for simplicity.) + +```python +import numpy as np +def abline(slope, intercept): + """Plot a line from slope and intercept""" + axes = plt.gca() + x_vals = np.array(axes.get_xlim()) + y_vals = intercept + slope * x_vals + plt.plot(x_vals, y_vals, '--') + +# Re-plot data +plt.scatter(X[0, :n//2], X[1, :n//2], alpha=0.5, label="Foreground group 1", s=80, color="green") +plt.scatter(X[0, n//2:], X[1, n//2:], alpha=0.5, label="Foreground group 2", s=80, color="orange") +plt.scatter(Y[0, :], Y[1, :], alpha=0.5, label="Background", s=80, color="gray") +plt.legend() +plt.xlim([-7, 7]) +plt.ylim([-7, 7]) + +# Plot line defined by W +origin = np.array([[0], [0]]) # origin point +abline(slope=pcpca.W_mle[1, 0] / pcpca.W_mle[0, 0], intercept=0) +plt.show() +``` + +We can see that W finds the axis that splits the two foreground groups: + +![toydata_W](./plots/simulated/toydata_W.png) + Once the model is fit, samples can be projected onto the components by calling `transform`: ```python diff --git a/plots/simulated/toydata_W.png b/plots/simulated/toydata_W.png new file mode 100644 index 0000000000000000000000000000000000000000..4b7df47fcae8bb0a70a8d4d95db4e9b6d62c6604 GIT binary patch literal 77325 zcmeFZcRbba|35CJ$Vz0dBxG+glTq1wkB~i%y+^V_sD$hgLN>=fR>-Ck2M5O<9ea<1 z-=){<{r-G^zuWiw@9(c~H{CkcInQ%FAJ^l$uSZeps?P{-Q{TqI!XkX}Tuu`U3;Q(| z*0ovOo8T)#BU6jupT{2Z`W{*kYY%U8H!Ca^a}O6sh=-${1*4aho4XyvS%6!Bn~#&x z*2BZaU5tmv>Ayd~4RN#KnV!b%fhWOpd2Zm2g+*+B_4nF0=>j{fYgkw>q>ioxe{x&42aH>9QkYRYX^p z?Z1HkR?#_o@hjhazRP)1!IfINFiX^VT~tbL;?u*n${QnOous$$UQ)DL#7{VQ*({$} z^2%}&-EESeKRd+d`4}@X!NB!1VQeOcb^Grl zN5232=>M+48^-_r8ax#_#S#&STi_KCkmXO2)A&RaNc*>%ghS8`pZcs$&(1VPOAPQy zuleBg_xJPi^19^4-@mG{b}L><$$`NPamYTOGcFTW+3Q#Qcs|lk=;-J~js^cIy$H?1 zAFZuVwxwYANWc>uJE7v@h)7;vebXhOBC)#`YQ11|Rl7IL@gHET|MMv3{{OF!NE$|N z{e9uN*eELlvfDV0NCmjyuQkDjQq-y?p5C>8u9vaeJe5UDOG{Z*)gqN8ZsAK2dxSZ! zpx}?$S;h$Ssa4C{darSx{9QWi-4h8*OUuPQUyBOL6y=*bIUQg@q&R 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