Plot again some features' distributions

[gcroci2]

When PRs #368, #333 and issue #346 will be merged/solved, and after having regenerated the hdf5 files (#140) replot the distributions of the features.

• Replot features distributions in not one-hot encoded cases (2/3 features per image). Put particular attention (1 single plot per image) into:
  • vanderwalls and electric
• Evaluate which feature distribution is not normal "enough"
• For the features not normal "enough", evaluate which power transform makes more sense for making their distributions more normal (see here for ideas). Plot the results.
• add distribution per target value (one plot for 0 and one plot for 1, for each feature)

[joyceljy]

Features distributions overview

Data used in this issue are the ones described in issue #140 . More detailed description for the all the features and what they represent can be found here.

• Node features
  • One-hot encoded: polarity (4 channels), res_type (20 channels)
  • Others: bsa, hb_acceptors, hb_donors, info_content, irc_negative_negative, irc_negative_positive, irc_nonpolar_negative, irc_nonpolar_nonpolar, irc_nonpolar_polar, irc_nonpolar_positive, irc_polar_negative, irc_polar_polar, irc_polar_positive, irc_positive_positive, irc_total, res_charge, res_depth, res_mass, res_pI, res_size, sasa, hse (3 channels), pssm (20 channels)
• Edge features
  • One hot-encoded: covalent, same_chain
  • Others: distance, electrostatic, vanderwaals

Features distributions for non one-hot encoded cases

Features were placed in groups of images except for vanderwalls and electric which were plotted individually.
Replotted images can be found here.
except_onehotencoded.zip

Evaluating the feature distributions

Note: one-hot encoded features (polarity, res_type, covalent, same_chain) and pssm were excluded for now from the analysis.

• We won't normalize nor standardize one-hot encoded features. For motivation, see for example this thread (this is the common opinion among the community).
• In general, the rule of thumb for deciding when applying transformation before standardization is to have a distribution that widespreads the features values, ideally resembling a Gaussian, but not mandatorily (for example electrostatic and vanderwaals cube version is better than the original one).
• Features to which we won't apply log, but standardization directly: res_size, res_charge, hb_donors, hb_acceptors, hse, irc_ features, res_mass, res_pI, distance
• Features to which we'll apply log(x+1): res_depth, bsa, info_content
• Features to which we'll apply square root: sasa
• Features to which we'll apply cube root: electrostatic, vanderwaals
• We'll remove for now pssm since it's not correctly computed

TODOs
Considering all features distributions except for res_size, res_charge, hb_donors, hb_acceptors, hse (they're already fine in their original distributions), do:

• Only for features with values > 0 (no 0s, no negative values)
  • Replot the distributions using log(x)
  • Replot the distributions using log(x+1)
  • Replot the distributions using np.sqrt(x)
• Only for features with values >= 0 (there are 0s, but no negative values)
  • Replot the distributions using log(x+1)
  • Replot the distributions using np.sqrt(x)
• Only for features with values ><= 0 (there are 0s, negative and positive values)
  • Replot the distributions using log(exp(x)+1) (we were still getting infinite values so we gave up on this)
  • Replot the distributions using cubic root
• Only for bsa and sasa, try to plot log(log(x+1)+1)

Features considered as Gaussian-like distribution (skewed)

• electrostatic

Original	Yeo-Johnson	Cube root	Binary

• res_size

Original	Yeo-Johnson	Log	Binary

• res_charge

Original	Yeo-Johnson	Log	Binary

• vanderwaals

Original	Zoomed	Yeo-Johnson	Cube root	Binary

Features considered as Gaussian-like distribution (exponential)

• bsa

Original	Yeo-Johnson	Square	Log(x+1)	Log(log(x+1)+1)	Binary

• hb_donors

Original	Yeo-Johnson	Log	Binary

• irc_nonpolar_negative

Original	Yeo-Johnson	Square	Log(x+1)	Binary

• irc_nonpolar_nonpolar

Original	Yeo-Johnson	Square	Log(x+1)	Binary

• irc_nonpolar_polar

Original	Yeo-Johnson	Square	Log(x+1)	Binary

• irc_nonpolar_positive

Original	Yeo-Johnson	Square	Log(x+1)	Binary

• irc_polar_polar

Original	Yeo-Johnson	Square	Log(x+1)	Binary

• irc_polar_positive

Original	Yeo-Johnson	Square	Log(x+1)	Binary

• irc_total

Original	Yeo-Johnson	Square	Log(x+1)	Binary

• irc_negative_positive

Original	Yeo-Johnson	Square	Log(x+1)	Binary

• irc_positive_positive

Original	Yeo-Johnson	Square	Log(x+1)	Binary

• irc_polar_negative

Original	Yeo-Johnson	Square	Log(x+1)	Binary

• irc_negative_negative

Original	Yeo-Johnson	Square	Log(x+1)	Binary

• res_depth

Original	Yeo-Johnson	Log	Log(x+1)	Square	Binary

• sasa

Original	Yeo-Johnson	Square	Log(x+1)	Log(log(x+1)+1)	Binary

Features that are not Gaussian-like distribution

• hb_acceptors

Original	Binary

• hse

Original	Binary(hse_0)	Binary(hse_1)	Binary(hse_2)

• info_content

Original	Log(x+1)	Square	Binary

• res_mass

Original	Log	Log(x+1)	Square	Binary

• res_pI

Original	Log	Log(x+1)	Square	Binary

• distance

Original	Log	Log(x+1)	Square	Binary

[LilySnow]

The Binary panel always have the same mean and std for binders and non-binders... is it a bug?

[gcroci2]

The Binary panel always have the same mean and std for binders and non-binders... is it a bug?

Good catch! We'll check it and in case we'll post the right plots. The distributions are right though, so in case only the mean and the std values will change.

[gcroci2]

Now means and std dev for the binary plots are correct @LilySnow

[joyceljy]

Conclusion:
Features suitable for log(x) transformation:
None

Features suitable for Yeo-Johnson transformation:
res_size,

Features suitable for log(x) transformation:
res_charge, res_depth

Features suitable for log(x+1) transformation:
bsa,

Features suitable for Square root transformation:
sasa

Features suitable for Cube root transformation:
electrostatic, vanderwaals,

Original Distribution is already good:
res_size, res_charge, hb_donors, hb_acceptors, hse, irc_nonpolar_negative, irc_nonpolar_nonpolar, irc_nonpolar_polar, irc_nonpolar_positive, irc_polar_polar, irc_polar_positive, irc_total, irc_negative_positive, irc_positive_positive, irc_polar_negative, irc_negative_negative

[gcroci2]

Conclusion: Features suitable for log(x) transformation: None

Features suitable for Yeo-Johnson transformation: res_size,

We'll keep the original distribution for res_size

Features suitable for log(x) transformation: res_charge, res_depth

We'll keep the original distribution for res_charge, while I think that log(x+1) works better for res_depth

Features suitable for log(x+1) transformation: bsa,

We'll try log(log(x+1)+1) for it

Features suitable for Square root transformation: sasa

We'll try log(log(x+1)+1) for it as well

Features suitable for Cube root transformation: electrostatic, vanderwaals,

Agree

Original Distribution is already good: res_size, res_charge, hb_donors, hb_acceptors, hse, irc_nonpolar_negative, irc_nonpolar_nonpolar, irc_nonpolar_polar, irc_nonpolar_positive, irc_polar_polar, irc_polar_positive, irc_total, irc_negative_positive, irc_positive_positive, irc_polar_negative, irc_negative_negative

Agree

[joyceljy]

Update:
I think doing log(log(x+1)) for bsa and sasa doesn't seem to have a lot of change to distribution. For sasa, log(log(x+1)) even make it having another high peak. For bsa, only the x-axis range changed. So I will suggest to keep bsa using log(x+1) and sasa using square root transformation.

Conclusion:
Features suitable for log(x) transformation:
None

Features suitable for Yeo-Johnson transformation:
None

Features suitable for log(x+1) transformation:
bsa, res_depth

Features suitable for Square root transformation:
sasa

Features suitable for Cube root transformation:
electrostatic, vanderwaals,

Original Distribution is already good:
res_size, res_charge, hb_donors, hb_acceptors, hse, irc_nonpolar_negative, irc_nonpolar_nonpolar, irc_nonpolar_polar, irc_nonpolar_positive, irc_polar_polar, irc_polar_positive, irc_total, irc_negative_positive, irc_positive_positive, irc_polar_negative, irc_negative_negative