How do you do supplementary Figure 5 ?

[eddgeag]

In supplementary figure 5, what do you mean by log rho(data) and Y and z axis ( in color map) what does it mean ?

[martingerlach]

Looking at the positions of all respondents in the 5D-trait space (i.e. their factor scores), I am sampling the density rho(x) for points x in the 2D-hyperplane spanned by the vectors of 3 of the types. Specifically, I am sampling this hyperplane along 2 orthonormal unitvectors (x and y axis).
The left plot shows the logarithm of the density measured in the original data.
The right plot shows the difference between log rho of the original data and log rho of the randomized data.
I added a notebook which performs all the steps and with which you generate the figure ("analysis_density-01_Supplementary-Figure-5.ipynb").

I hope this clarifies; otherwise let me know.
Best,
Martin

[martingerlach]

I also added another notebook which gives a complimentary view of the density around each type which is not included in the paper/supplementary("analysis_density-02_Number-of-respondents-around-types.ipynb").
Here I simply count the number of respondents that are located within a 5D-sphere of radius x of each type (increasing the radius x) and compare with the number obtained in a randomized dataset.

[eddgeag]

Thank you very much Martin

[eddgeag]

When you say the covariance matrix for each cluster is projected. I interpret is projected from the 5-D to the 2-D plane. So what you do is the next: cov(5x5) (dot product) Orthonormal Normal base ( 5x2)
This projection gives the list_sigma_coords_x?

[martingerlach]

If you have two unit-vectors e1 and e2 and SIgma is the covariance matrix, the product e1x Sigma x e2 gives a scalar, the covariance between those two dimensions. Thus if you calculate e1 x Sigma x e1 you get the variance in dimension e1.

[eddgeag]

If you have two unit-vectors e1 and e2 and SIgma is the covariance matrix, the product e1x Sigma x e2 gives a scalar, the covariance between those two dimensions. Thus if you calculate e1 x Sigma x e1 you get the variance in dimension e1.

So, once you have the variance in dimension e1 and dimension e2, you just draw the ellipse right?

[martingerlach]

For each unit vector e_u in the 2D-hyperplane I calculate the variance v_u = e_u Sigma e_u and from this the standard deviation s_u = sqrt(v_u). The ellipse is then defined by x_0 + s_u x e_u over all possible unit vectors in the plane (x_0 is the cluster-center).

[eddgeag]

For each unit vector e_u in the 2D-hyperplane I calculate the variance v_u = e_u Sigma e_u and from this the standard deviation s_u = sqrt(v_u). The ellipse is then defined by x_0 + s_u x e_u over all possible unit vectors in the plane (x_0 is the cluster-center).

Could you provide the code for the ellipses please ?

[martingerlach]

This is the code I use to get the coordinates of the ellipse in the plane

list_sigma_coords_x = []
list_sigma_coords_y = []

for i_n in list_inds:
x_cov = list_arr_cov[i_n,:] ## this is the covariance-matrix
list_coords_x_tmp = []
list_coords_y_tmp = []
for phi in np.linspace(0,2*np.pi,100):
## create the unit vector in the hyperplane
x1_ = np.cos(phi)
x2_ = np.sin(phi)
x_2d_ = x1_e_s1 + x2_e_s2
## project the covariance onto the unit vector
sigma = np.sqrt(np.sum(np.dot(x_2d_,x_cov)x_2d_))
## get position in hyperplane space
x_sigma = arr_cd_dom[i_n] + sigmax_2d_
## project onto hyperplane coordinates
x_sigma2d_1 = np.sum(e_s1x_sigma)
x_sigma2d_2 = np.sum(e_s2x_sigma)
list_coords_x_tmp += [x_sigma2d_1]
list_coords_y_tmp += [x_sigma2d_2]
list_sigma_coords_x += [list_coords_x_tmp]
list_sigma_coords_y += [list_coords_y_tmp]

Then plot via

contours for projected sigma\n",

try to plot the projected sigma\n",

x = list_sigma_coords_x[0]
y = list_sigma_coords_y[0]
ax.plot(x,y,ls='-',lw=1,color='black')

x = list_sigma_coords_x[1]
y = list_sigma_coords_y[1]
ax.plot(x,y,ls='-',lw=1,color='black')
x = list_sigma_coords_x[2]
y = list_sigma_coords_y[2]
ax.plot(x,y,ls='-',lw=1,color='black')

[eddgeag]

Thank you Best, El vie., 19 oct. 2018 20:50, Martin Gerlach <notifications@github.com> escribió:

…

This is the code I use to get the coordinates of the ellipse in the plane list_sigma_coords_x = [] list_sigma_coords_y = [] for i_n in list_inds: x_cov = list_arr_cov[i_n,:] ## this is the covariance-matrix list_coords_x_tmp = [] list_coords_y_tmp = [] for phi in np.linspace(0,2*np.pi,100): ## create the unit vector in the hyperplane x1_ = np.cos(phi) x2_ = np.sin(phi) x_2d_ = x1_ *e_s1 + x2_e_s2 ## project the covariance onto the unit vector sigma = np.sqrt(np.sum(np.dot(x_2d_,x_cov)x_2d_)) ## get position in hyperplane space x_sigma = arr_cd_dom[i_n] + sigmax_2d_ ## project onto hyperplane coordinates x_sigma2d_1 = np.sum(e_s1x_sigma) x_sigma2d_2 = np.sum(e_s2* x_sigma) list_coords_x_tmp += [x_sigma2d_1] list_coords_y_tmp += [x_sigma2d_2] list_sigma_coords_x += [list_coords_x_tmp] list_sigma_coords_y += [list_coords_y_tmp] Then plot via contours for projected sigma\n", try to plot the projected sigma\n", x = list_sigma_coords_x[0] y = list_sigma_coords_y[0] ax.plot(x,y,ls='-',lw=1,color='black') x = list_sigma_coords_x[1] y = list_sigma_coords_y[1] ax.plot(x,y,ls='-',lw=1,color='black') x = list_sigma_coords_x[2] y = list_sigma_coords_y[2] ax.plot(x,y,ls='-',lw=1,color='black') — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <#3 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AeiMo56ufDHs_XOajX1SPuPs4zjIL8nmks5umh4SgaJpZM4XVAy7> .

[eddgeag]

I cannot understand the code, is not indented and some variables are not declare, or they are declared but with a different name in the code it's published
could you use the same variables you published in here please ? because I can't understand what are you doing.
Thank you

[lamaral1968]

Dear Edmond, thank you so much for your interest on our research and code. We are sorry that you are having some trouble with understanding the code. I think that at some point there is very little else that we can do, and it becomes important that you take the necessary time and the required effort to understand what is going on. Warm regards, luis On Oct 24, 2018, at 10:08 AM, Edmond Geraud <notifications@github.com<mailto:notifications@github.com>> wrote: I cannot understand the code, is not indented and some variables are not declare, or they are declared but with a different name in the code it's published could you use the same variables you published in here please ? because I can't understand what are you doing. Thank you — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub<https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_amarallab_personality-2Dtypes_issues_3-23issuecomment-2D432697752&d=DwMFaQ&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=r70BoSP4G390dVfqgxfB7WNZazZh6tBD05iqdNiVxIc&m=vgy4v3aNaeSZtRCnE61sn56M17E7c2kqc3v_3G_3t6g&s=8P_MMounRuHWN0NMKqhgM3JQm3eIqM8cE-3OkeiecGs&e=>, or mute the thread<https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_notifications_unsubscribe-2Dauth_ANdTRx49DAyyOlGj46CfvH4cGfhtJ5Uaks5uoIJ9gaJpZM4XVAy7&d=DwMFaQ&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=r70BoSP4G390dVfqgxfB7WNZazZh6tBD05iqdNiVxIc&m=vgy4v3aNaeSZtRCnE61sn56M17E7c2kqc3v_3G_3t6g&s=0oLsqjerd47cRs-iwL0F8xcKjgiKjmK15PGNuOXU6FA&e=>.

…

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________________________________ For appointments, invitations, and other administrative matters, please contact: Ms. Justyna Gutowska (jgutowska@gmail.com<mailto:jgutowska@gmail.com>)

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[eddgeag]

`centers=np.array([[x0_es1,x0_es2],[x1_es1,x1_es2],[x2_es1,x2_es2]])
centersT=centers.T ## column vectors
phi=np.linspace(0,2*np.pi,100)

project covariance matrix to x and y axes

first=list_arr_cov[0,:] ## first cluster
sigma_x=np.sqrt(e_s1 @ first @ e_s1)
sigma_y=np.sqrt(e_s2 @ first @ e_s2)
x_position=centersT[0,0]
y_position=centersT[1,0]

plot acording parametric equations

ax.plot(x_position+sigma_xnp.cos(phi),y_position+sigma_ynp.sin(phi))

##############################
second=list_arr_cov[1,:] ## first cluster
sigma_x=np.sqrt(e_s1 @ second @ e_s1)
sigma_y=np.sqrt(e_s2 @ second @ e_s2)
x_position=centersT[0,1]
y_position=centersT[1,1]

plot acording parametric equations

ax.plot(x_position+sigma_xnp.cos(phi),y_position+sigma_ynp.sin(phi))
########################
third=list_arr_cov[2,:] ## first cluster
sigma_x=np.sqrt(e_s1 @ third @ e_s1)
sigma_y=np.sqrt(e_s2 @ third @ e_s2)
x_position=centersT[0,2]
y_position=centersT[1,2]

plot acording parametric equations

ax.plot(x_position+sigma_xnp.cos(phi),y_position+sigma_ynp.sin(phi))`
Yes, thank you, just here you have a clearer code with parametric equations.