Table of Contents

Frequency Position Analysis
Velocity Analysis
Periodic Behavior in Velocity

ASCII_Analysis.ipynb

This Jupyter notebook, titled 'ASCII_Analysis.ipynb', is a comprehensive analysis tool designed for the exploration and statistical study of ASCII data related to dance movements and the associated emotional states. The script includes functionalities for data preprocessing, visualization, and the extraction of meaningful statistics from time-series data. Through various statistical and signal processing techniques such as Lomb-Scargle periodograms and Gaussian fitting, it investigates properties like the center of position evolution, average distance from center, velocity analysis, and frequency domain analysis to discern patterns correlated with different emotions in dance movements. The notebook utilizes libraries such as pandas, matplotlib, numpy, scipy, seaborn, and mplEasyAnimate for its analysis.

snippet.python

import pandas as pd
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from tqdm import tqdm
import numpy as np
from mplEasyAnimate import animation
from scipy.signal import lombscargle
import os
from scipy.optimize import curve_fit
import seaborn as sns

snippet.python

def frameToArray(frame):
    start = 1
    vecs = np.zeros(shape=(int((frame.shape[0]-1)/3), 3))
    for itr, end in enumerate(range(4, frame.shape[0]+3, 3)):
        vecs[itr] = np.array(frame[start:end])
        start = end
    return vecs

snippet.python

def CalcCenterOfPos(frame):
    vecs = frameToArray(frame)
    return vecs.mean(axis=0)

snippet.python

def CenterOfPosEvolution(df):
    COPs = np.zeros(shape=(df.shape[0], 3))
    times = df['Time'].values
    for itr, frame in tqdm(df.iterrows(), total=df.shape[0]):
        COPs[itr] = CalcCenterOfPos(frame)
    return COPs, times

snippet.python

def getAvgPosFromCenter(frame):
    COP = CalcCenterOfPos(frame)
    vecs = frameToArray(frame)
    return np.abs(vecs-COP).mean(axis=0)

snippet.python

def getAvgDistFromCenter(frame):
    COP = CalcCenterOfPos(frame)
    vecs = frameToArray(frame)
    return np.mean(np.sqrt(np.sum(np.power(np.subtract(COP, vecs), 2), axis=1)))

snippet.python

def evolveAvgPosFromCenter(df):
    SEPs = np.zeros(shape=(df.shape[0], 3))
    times = df['Time'].values
    for itr, frame in tqdm(df.iterrows(), total=df.shape[0]):
        SEPs[itr] = getAvgPosFromCenter(frame)
    return SEPs, times

snippet.python

def evolveAvgDistFromCenter(df):
    SEPs = np.zeros(shape=(df.shape[0],))
    times = df['Time'].values
    for itr, frame in tqdm(df.iterrows(), total=df.shape[0]):
        SEPs[itr] = getAvgDistFromCenter(frame)
    return SEPs, times

snippet.python

def genLSP(t, y, s=None):
    nyquist = 1/(2*(t[1]-t[0]))
    res = (t[1]-t[0])/t.shape[0]
    if not s:
        s = int(1/res)
    f = 2*np.pi*np.linspace(res/10, 0.5, s)
    pgram = lombscargle(t, y, f, normalize=True)
    return f, pgram

snippet.python

analyzedFiles = os.listdir('AnalyzedData/')
analyzedFiles = ["AnalyzedData/{}".format(x) for x in analyzedFiles if x[0] != '.']

snippet.python

emotions = [(x.split('.')[0]).split('_')[-1] for x in analyzedFiles]

snippet.python

data = list()
for file in analyzedFiles:
    analysis = np.load(file)
    data.append(analysis)

snippet.python

for i, element in enumerate(data):
    data[i][1] = (data[i][1]-np.mean(data[i][1]))/np.mean(data[i][1])

snippet.python

velocities = list()
for dance in data:
    vel = (np.roll(dance[1], -1) - np.roll(dance[1], 1)) / (np.roll(dance[0], -1) - np.roll(dance[0], 1))
    velocities.append(np.vstack([dance[0], vel]))

snippet.python

for dance in velocities:
    plt.plot(dance[0], abs(dance[1]))

snippet.python

for dance in data:
    plt.plot(dance[0], dance[1])

snippet.python

fig, ax = plt.subplots(1, 1, figsize=(10, 7))
ax.plot(data[0][0], data[0][1], 'k', linewidth=1)
ax.set_xlabel('Time [s]', fontsize=17)
ax.set_ylabel('Mean Radial Seperation [m]', fontsize=17)
ax.tick_params(axis='both', which='major', labelsize=15)
plt.savefig("Figures/MeanRadialSeperation.pdf", bbox_inches='tight')

Frequency Position Analysis

snippet.python

FTs = np.zeros(shape=(49, 2, 2000))

snippet.python

count = 0
for did, dance in tqdm(enumerate(data), total=len(data)):
    if did != 9:
        f, pgram = genLSP(dance[0], dance[1], s=2000)
        FTs[count, 0] = f
        FTs[count, 1] = pgram
        count += 1

snippet.python

for fid, FT in enumerate(FTs):
    if np.mean(FT[1]) > 0.4:
        print(fid)
    plt.plot(FT[0], FT[1])

snippet.python

fig, ax = plt.subplots(1, 1, figsize=(10, 7))
ax.plot(FTs[0][0], FTs[0][1], 'k', linewidth=1)
ax.set_xlabel(r'Frequency [s$^{-1}$]', fontsize=17)
ax.set_ylabel('Fractional Amplitude', fontsize=17)
ax.tick_params(axis='both', which='major', labelsize=15)
plt.savefig("Figures/FTExample.pdf", bbox_inches='tight')

snippet.python

len(evalEmotions)

snippet.python

stats = np.zeros(shape=(49, 3))
evalEmotions = list()
count = 0
for fid, FT in enumerate(FTs):
    stats[count] = np.array([FT[0][FT[1].argmax()], FT[1][FT[1].argmax()], np.mean(FT[1])])
    evalEmotions.append(emotions[count])
    count += 1

snippet.python

fig, axs = plt.subplots(3, 1, figsize=(10, 10))
axs[0].plot(stats[:, 0], stats[:, 1], 'o')
axs[1].plot(stats[:, 1], stats[:, 2], 'x')
axs[2].plot(stats[:, 0], stats[:, 2], 's')
 
for stat, emotion in zip(stats, evalEmotions):
    axs[2].annotate(emotion, xy=(stat[0], stat[2]))

snippet.python

gaus = lambda x, mu, sigma: 1/np.sqrt(2*np.pi*(sigma**2))*np.exp(-((x-mu)**2)/(2*(sigma**2)))
 
bimodal = lambda x, mu1, sigma1, mu2, sigma2: gaus(x, mu1, sigma1)+gaus(x, mu2, sigma2)

snippet.python

fig = plt.figure(figsize=(10, 7))
bins = plt.hist(stats[:, 0], bins=20)
centers = (bins[1][1:]+bins[1][:-1])/2
plt.xlabel('Frequencey of Max Amplitude', fontsize=20)

Text(0.5, 0, 'Frequencey of Max Amplitude')

snippet.python

fit1, covar1 = curve_fit(gaus, centers, bins[0], p0=[0.1, 0.2])
err1 = np.sqrt(np.diag(covar1))
fit2, covar2 = curve_fit(gaus, centers, bins[0], p0=[1, 0.1])
err2 = np.sqrt(np.diag(covar2))

snippet.python

fig = plt.figure(figsize=(10, 7))
x = np.linspace(0, 1.75, 1000)
bins = plt.hist(stats[:, 0], bins=20, color='grey', alpha=0.5, ec='black')
plt.plot(x, gaus(x, *fit1)+gaus(x, *fit2), color='black', linestyle='dashed')
plt.xlabel('Frequencey of Max Amplitude', fontsize=20)
 
plt.annotate(r'$\mu_{{1}}={:0.2f}\pm{:0.2f}$ Hz'.format(fit1[0], err1[0]), xy=(0.5, 6), fontsize=15)
plt.annotate(r'$\sigma_{{1}}={:0.2f}\pm{:0.2f}$ Hz'.format(fit1[1], err1[1]), xy=(0.5, 5.5), fontsize=15)
 
plt.annotate(r'$\mu_{{2}}={:0.2f}\pm{:0.2f}$ Hz'.format(fit2[0], err2[0]), xy=(1, 6), fontsize=15)
plt.annotate(r'$\sigma_{{2}}={:0.2f}\pm{:0.2f}$ Hz'.format(fit2[1], err2[1]), xy=(1, 5.5), fontsize=15)
 
plt.savefig('Figures/FrequencyDist.pdf', bbox_inches='tight')

Velocity Analysis

snippet.python

nonStatGaus = lambda x, mu, sigma, A: A*np.exp(-((x-mu)**2)/(2*(sigma**2)))

snippet.python

meanVels = [np.std(x[1]) for x in velocities]

snippet.python

x = np.linspace(2, 8, 1000)
bins = plt.hist(meanVels, bins=7)
centers = (bins[1][1:]+bins[1][:-1])/2
fit, covar = curve_fit(nonStatGaus, centers, bins[0], p0=[4.5, 6, 7])
plt.plot(x, nonStatGaus(x, *fit))
plt.show()

snippet.python

timeSeriseStats = np.zeros(shape=(49, 4))
count = 0
for did, dance in enumerate(velocities):
    if did != 9:
        timeSeriseStats[count, 0] = np.mean(dance[1])
        timeSeriseStats[count, 1] = np.median(dance[1])
        timeSeriseStats[count, 2] = np.max(dance[1])
        timeSeriseStats[count, 3] = np.std(dance[1])
        count += 1

snippet.python

df = pd.DataFrame(data=timeSeriseStats, columns=['Mean', 'Median', 'Max', 'Sigma'])
df['Emotion'] = pd.Series(evalEmotions, index=df.index)

snippet.python

df

<div> <style scoped>

  .dataframe tbody tr th:only-of-type {
      vertical-align: middle;
  }

  .dataframe tbody tr th {
      vertical-align: top;
  }

  .dataframe thead th {
      text-align: right;
  }

</style> <table border=“1” class=“dataframe”

>

<thead>
  <tr style="text-align: right;">
    <th></th>
    <th>Mean</th>
    <th>Median</th>
    <th>Max</th>
    <th>Sigma</th>
    <th>Emotion</th>
  </tr>
</thead>
<tbody>
  <tr>
    <th>0</th>
    <td>-0.001798</td>
    <td>-0.004902</td>
    <td>56.168820</td>
    <td>2.978317</td>
    <td>Miserable</td>
  </tr>
  <tr>
    <th>1</th>
    <td>-0.001649</td>
    <td>0.002063</td>
    <td>62.108348</td>
    <td>5.054398</td>
    <td>Mix</td>
  </tr>
  <tr>
    <th>2</th>
    <td>-0.004032</td>
    <td>0.006175</td>
    <td>44.446849</td>
    <td>5.329097</td>
    <td>Angry</td>
  </tr>
  <tr>
    <th>3</th>
    <td>-0.002111</td>
    <td>0.007060</td>
    <td>42.284433</td>
    <td>3.910049</td>
    <td>Tired</td>
  </tr>
  <tr>
    <th>4</th>
    <td>-0.000834</td>
    <td>0.002970</td>
    <td>46.395794</td>
    <td>4.436914</td>
    <td>Pleased</td>
  </tr>
  <tr>
    <th>5</th>
    <td>-0.001896</td>
    <td>-0.001654</td>
    <td>48.362561</td>
    <td>4.013522</td>
    <td>Sad</td>
  </tr>
  <tr>
    <th>6</th>
    <td>-0.002551</td>
    <td>0.000869</td>
    <td>59.083402</td>
    <td>3.036652</td>
    <td>Relaxed</td>
  </tr>
  <tr>
    <th>7</th>
    <td>-0.002301</td>
    <td>-0.002254</td>
    <td>48.161705</td>
    <td>5.110528</td>
    <td>Pleased</td>
  </tr>
  <tr>
    <th>8</th>
    <td>-0.002890</td>
    <td>-0.000064</td>
    <td>52.981581</td>
    <td>4.607283</td>
    <td>Afraid</td>
  </tr>
  <tr>
    <th>9</th>
    <td>0.000044</td>
    <td>0.002082</td>
    <td>48.025167</td>
    <td>3.730987</td>
    <td>Mix</td>
  </tr>
  <tr>
    <th>10</th>
    <td>-0.000073</td>
    <td>-0.000042</td>
    <td>55.873222</td>
    <td>4.402845</td>
    <td>Afraid</td>
  </tr>
  <tr>
    <th>11</th>
    <td>-0.000254</td>
    <td>-0.001653</td>
    <td>62.410698</td>
    <td>6.520325</td>
    <td>Sad</td>
  </tr>
  <tr>
    <th>12</th>
    <td>-0.001560</td>
    <td>0.000646</td>
    <td>41.603721</td>
    <td>4.267015</td>
    <td>Angry</td>
  </tr>
  <tr>
    <th>13</th>
    <td>-0.001363</td>
    <td>-0.000718</td>
    <td>32.500379</td>
    <td>3.303371</td>
    <td>Angry</td>
  </tr>
  <tr>
    <th>14</th>
    <td>-0.002550</td>
    <td>-0.001232</td>
    <td>53.745451</td>
    <td>4.533554</td>
    <td>Satisfied</td>
  </tr>
  <tr>
    <th>15</th>
    <td>-0.001855</td>
    <td>0.001056</td>
    <td>53.571594</td>
    <td>4.125465</td>
    <td>Tired</td>
  </tr>
  <tr>
    <th>16</th>
    <td>-0.002170</td>
    <td>-0.001059</td>
    <td>56.175345</td>
    <td>3.739604</td>
    <td>Annoyed</td>
  </tr>
  <tr>
    <th>17</th>
    <td>-0.000951</td>
    <td>0.001410</td>
    <td>43.203369</td>
    <td>4.116629</td>
    <td>Bored</td>
  </tr>
  <tr>
    <th>18</th>
    <td>0.000185</td>
    <td>0.000682</td>
    <td>53.907577</td>
    <td>4.237050</td>
    <td>Pleased</td>
  </tr>
  <tr>
    <th>19</th>
    <td>-0.000184</td>
    <td>-0.000246</td>
    <td>52.905508</td>
    <td>4.148395</td>
    <td>Excited</td>
  </tr>
  <tr>
    <th>20</th>
    <td>-0.001560</td>
    <td>-0.001905</td>
    <td>55.523178</td>
    <td>4.340211</td>
    <td>Happy</td>
  </tr>
  <tr>
    <th>21</th>
    <td>-0.001759</td>
    <td>0.000900</td>
    <td>45.436848</td>
    <td>4.257791</td>
    <td>Angry</td>
  </tr>
  <tr>
    <th>22</th>
    <td>-0.000372</td>
    <td>0.002558</td>
    <td>57.722183</td>
    <td>4.424116</td>
    <td>Miserable</td>
  </tr>
  <tr>
    <th>23</th>
    <td>0.000884</td>
    <td>0.004534</td>
    <td>31.542905</td>
    <td>3.119212</td>
    <td>Miserable</td>
  </tr>
  <tr>
    <th>24</th>
    <td>-0.002209</td>
    <td>-0.000254</td>
    <td>62.365436</td>
    <td>6.278034</td>
    <td>Relaxed</td>
  </tr>
  <tr>
    <th>25</th>
    <td>-0.003495</td>
    <td>0.002474</td>
    <td>62.691057</td>
    <td>6.775984</td>
    <td>Annoyed</td>
  </tr>
  <tr>
    <th>26</th>
    <td>-0.000142</td>
    <td>-0.009252</td>
    <td>52.386723</td>
    <td>6.254499</td>
    <td>Afraid</td>
  </tr>
  <tr>
    <th>27</th>
    <td>-0.000601</td>
    <td>-0.002673</td>
    <td>45.750873</td>
    <td>5.537992</td>
    <td>Excited</td>
  </tr>
  <tr>
    <th>28</th>
    <td>-0.002934</td>
    <td>0.005929</td>
    <td>35.486262</td>
    <td>4.347244</td>
    <td>Excited</td>
  </tr>
  <tr>
    <th>29</th>
    <td>-0.002131</td>
    <td>0.002095</td>
    <td>49.055195</td>
    <td>5.256263</td>
    <td>Happy</td>
  </tr>
  <tr>
    <th>30</th>
    <td>0.004173</td>
    <td>-0.001804</td>
    <td>51.143077</td>
    <td>5.439556</td>
    <td>Bored</td>
  </tr>
  <tr>
    <th>31</th>
    <td>-0.000224</td>
    <td>-0.006051</td>
    <td>40.074855</td>
    <td>3.727305</td>
    <td>Happy</td>
  </tr>
  <tr>
    <th>32</th>
    <td>-0.002232</td>
    <td>0.004002</td>
    <td>47.220204</td>
    <td>5.129865</td>
    <td>Afraid</td>
  </tr>
  <tr>
    <th>33</th>
    <td>-0.003202</td>
    <td>0.001654</td>
    <td>27.594398</td>
    <td>3.238834</td>
    <td>Annoyed</td>
  </tr>
  <tr>
    <th>34</th>
    <td>-0.002317</td>
    <td>0.000272</td>
    <td>63.977990</td>
    <td>4.435240</td>
    <td>Bored</td>
  </tr>
  <tr>
    <th>35</th>
    <td>-0.002719</td>
    <td>0.004786</td>
    <td>43.860434</td>
    <td>4.161989</td>
    <td>Annoyed</td>
  </tr>
  <tr>
    <th>36</th>
    <td>-0.000957</td>
    <td>0.000309</td>
    <td>41.176874</td>
    <td>2.883719</td>
    <td>Sad</td>
  </tr>
  <tr>
    <th>37</th>
    <td>-0.001290</td>
    <td>-0.000089</td>
    <td>55.583615</td>
    <td>5.272462</td>
    <td>Tired</td>
  </tr>
  <tr>
    <th>38</th>
    <td>-0.000217</td>
    <td>-0.004358</td>
    <td>49.607502</td>
    <td>6.279034</td>
    <td>Relaxed</td>
  </tr>
  <tr>
    <th>39</th>
    <td>-0.000071</td>
    <td>-0.002206</td>
    <td>38.600903</td>
    <td>5.021533</td>
    <td>Satisfied</td>
  </tr>
  <tr>
    <th>40</th>
    <td>-0.001090</td>
    <td>-0.001596</td>
    <td>68.660583</td>
    <td>4.984018</td>
    <td>Satisfied</td>
  </tr>
  <tr>
    <th>41</th>
    <td>-0.000999</td>
    <td>0.000668</td>
    <td>77.463016</td>
    <td>5.703841</td>
    <td>Mix</td>
  </tr>
  <tr>
    <th>42</th>
    <td>-0.001357</td>
    <td>0.000859</td>
    <td>54.578165</td>
    <td>4.464673</td>
    <td>Happy</td>
  </tr>
  <tr>
    <th>43</th>
    <td>0.003839</td>
    <td>0.004214</td>
    <td>42.680804</td>
    <td>4.096789</td>
    <td>Excited</td>
  </tr>
  <tr>
    <th>44</th>
    <td>-0.002007</td>
    <td>-0.000875</td>
    <td>55.284132</td>
    <td>4.743275</td>
    <td>Sad</td>
  </tr>
  <tr>
    <th>45</th>
    <td>0.004543</td>
    <td>0.002699</td>
    <td>44.558832</td>
    <td>4.904963</td>
    <td>Bored</td>
  </tr>
  <tr>
    <th>46</th>
    <td>0.000246</td>
    <td>0.000620</td>
    <td>34.547461</td>
    <td>3.294687</td>
    <td>Relaxed</td>
  </tr>
  <tr>
    <th>47</th>
    <td>-0.000669</td>
    <td>0.007457</td>
    <td>47.166044</td>
    <td>5.101586</td>
    <td>Pleased</td>
  </tr>
  <tr>
    <th>48</th>
    <td>-0.000959</td>
    <td>-0.000093</td>
    <td>48.413527</td>
    <td>4.118721</td>
    <td>Mix</td>
  </tr>
</tbody>

</table>

<

/div>

snippet.python

with sns.axes_style("ticks"):
    sns.pairplot(df, hue='Emotion')
 
plt.savefig('Figures/PairPlot.pdf', bbox_inches='tight')

/home/tboudreaux/anaconda3/envs/general/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval

Periodic Behavior in Velocity

snippet.python

FTs_V = np.zeros(shape=(49, 2, 2000))

snippet.python

count = 0
for did, dance in tqdm(enumerate(velocities), total=len(velocities)):
    if did != 9:
        f, pgram = genLSP(dance[0], dance[1], s=2000)
        FTs_V[count, 0] = f
        FTs_V[count, 1] = pgram
        count += 1

snippet.python

for fid, FT in enumerate(FTs_V):
    plt.plot(FT[0], FT[1])

snippet.python

stats_V = np.zeros(shape=(49, 3))
count = 0
for fid, FT in enumerate(FTs_V):
    stats_V[count] = np.array([FT[0][FT[1].argmax()], FT[1][FT[1].argmax()], np.mean(FT[1])])
    count += 1

snippet.python

fig, axs = plt.subplots(3, 1, figsize=(10, 10))
axs[0].plot(stats_V[:, 0], stats_V[:, 1], 'o')
axs[1].plot(stats_V[:, 1], stats_V[:, 2], 'x')
axs[2].plot(stats_V[:, 0], stats_V[:, 2], 's')

[<matplotlib.lines.Line2D at 0x7fed82866c88>]

snippet.python

df = pd.DataFrame(data=stats_V, columns=['Max Frequency', 'Max Amplitude', 'Standard Deviation'])
df['Emotion'] = pd.Series(evalEmotions, index=df.index)

snippet.python

sns.pairplot(df, hue="Emotion")

/home/tboudreaux/anaconda3/envs/general/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval





<seaborn.axisgrid.PairGrid at 0x7fed80383ba8>

python