James
5.2 MiB
5.2 MiB
Windowed PCA and fluctuation intensity in COVID19 data¶
In [1]:
import pandas as pd import numpy as np import seaborn as sns import matplotlib.pyplot as plt from jmspack.utils import apply_scaling, JmsColors from jmspack.NLTSA import (fluctuation_intensity, distribution_uniformity, complexity_resonance, complexity_resonance_diagram, cumulative_complexity_peaks, cumulative_complexity_peaks_plot) from sklearn import decomposition from sklearn.linear_model import LinearRegression from scipy.stats import norm import time
In [2]:
start = time.time()
In [3]:
if "jms_style_sheet" in plt.style.available: plt.style.use("jms_style_sheet")
In [4]:
country_choice="Netherlands" filepath=f"../shield-complexity/data/{country_choice}_worldsurvey_nonmissing_c_of_v_since_2021-06-08_to_2022-01-18.csv" filepath2="../shield-complexity/data/MH_Netherlands_worldsurvey_nonmissing_c_of_v_since_2021-06-08_to_2022-01-18.csv"
In [5]:
df = pd.read_csv(filepath) mh_df = pd.read_csv(filepath2)
In [6]:
df["date"] = pd.to_datetime(df["date"]).dt.date mh_df["date"] = pd.to_datetime(mh_df["date"]).dt.date
In [7]:
display(df.head()); df.shape
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| date | pct_covid | pct_flu | percent_mc | percent_hf | percent_anos | pct_twodoses | pct_concerned_sideeffects | pct_community_cli | pct_activity_work_outside_home | ... | pct_want_info_children_education | pct_want_info_economic_impact | pct_want_info_mental_health | pct_want_info_relationships | pct_want_info_employment | pct_want_info_none | pct_delayed_care_cost | pct_mask_work_outside_home_1d | pct_mask_shop_1d | pct_mask_spent_time_1d | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2021-06-09 | 14.535989 | 13.195395 | 0.770978 | 3.346972 | 6.422849 | 1.337626 | 1.292528 | 4.387491 | 1.258690 | ... | 5.271337 | 4.509109 | 3.382587 | 3.528127 | 4.871057 | 1.119098 | 3.155650 | 1.074371 | 0.432519 | 3.148366 |
| 1 | 2021-06-10 | 14.773657 | 14.773657 | 0.715611 | 3.498316 | 7.144337 | 1.267841 | 1.550583 | 4.649098 | 1.376345 | ... | 4.687061 | 3.669607 | 3.150838 | 3.858300 | 5.208682 | 1.071412 | 3.435815 | 1.034580 | 0.358411 | 3.208651 |
| 2 | 2021-06-11 | 18.572413 | 18.203818 | 0.649700 | 3.456743 | 9.709611 | 1.245488 | 1.449014 | 4.170443 | 1.320875 | ... | 5.485248 | 3.985184 | 3.796074 | 3.540908 | 4.152605 | 1.011222 | 3.139859 | 0.967428 | 0.346627 | 2.720786 |
| 3 | 2021-06-13 | 17.418052 | 17.418052 | 0.703517 | 3.761218 | 10.277039 | 1.348971 | 1.526305 | 5.509964 | 1.503175 | ... | 5.254944 | 3.342272 | 3.168605 | 3.342676 | 4.585373 | 1.245500 | 3.266020 | 1.129369 | 0.294228 | 3.224900 |
| 4 | 2021-06-14 | 20.332173 | 17.400103 | 0.716563 | 3.497908 | 7.931059 | 1.214978 | 1.482273 | 5.389113 | 1.490736 | ... | 5.430036 | 3.805503 | 3.120780 | 3.441871 | 4.359385 | 1.047207 | 3.108143 | 0.911346 | 0.471995 | 3.524901 |
5 rows × 67 columns
Out[7]:
(212, 67)
In [8]:
display(mh_df.head()); mh_df.shape
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| date | pct_covid | pct_flu | percent_mc | percent_hf | percent_anos | pct_twodoses | pct_concerned_sideeffects | pct_community_cli | pct_activity_work_outside_home | ... | pct_want_info_children_education | pct_want_info_economic_impact | pct_want_info_mental_health | pct_want_info_relationships | pct_want_info_employment | pct_want_info_none | pct_delayed_care_cost | pct_mask_work_outside_home_1d | pct_mask_shop_1d | pct_mask_spent_time_1d | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2021-06-09 | 14.535989 | 13.195395 | 0.770978 | 3.346972 | 6.422849 | 1.337626 | 1.292528 | 4.387491 | 1.258690 | ... | 5.271337 | 4.509109 | 3.382587 | 3.528127 | 4.871057 | 1.119098 | 3.155650 | 1.074371 | 0.432519 | 3.148366 |
| 1 | 2021-06-10 | 14.773657 | 14.773657 | 0.715611 | 3.498316 | 7.144337 | 1.267841 | 1.550583 | 4.649098 | 1.376345 | ... | 4.687061 | 3.669607 | 3.150838 | 3.858300 | 5.208682 | 1.071412 | 3.435815 | 1.034580 | 0.358411 | 3.208651 |
| 2 | 2021-06-11 | 18.572413 | 18.203818 | 0.649700 | 3.456743 | 9.709611 | 1.245488 | 1.449014 | 4.170443 | 1.320875 | ... | 5.485248 | 3.985184 | 3.796074 | 3.540908 | 4.152605 | 1.011222 | 3.139859 | 0.967428 | 0.346627 | 2.720786 |
| 3 | 2021-06-13 | 17.418052 | 17.418052 | 0.703517 | 3.761218 | 10.277039 | 1.348971 | 1.526305 | 5.509964 | 1.503175 | ... | 5.254944 | 3.342272 | 3.168605 | 3.342676 | 4.585373 | 1.245500 | 3.266020 | 1.129369 | 0.294228 | 3.224900 |
| 4 | 2021-06-14 | 20.332173 | 17.400103 | 0.716563 | 3.497908 | 7.931059 | 1.214978 | 1.482273 | 5.389113 | 1.490736 | ... | 5.430036 | 3.805503 | 3.120780 | 3.441871 | 4.359385 | 1.047207 | 3.108143 | 0.911346 | 0.471995 | 3.524901 |
5 rows × 67 columns
Out[8]:
(212, 67)
In [9]:
df.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 212 entries, 0 to 211 Data columns (total 67 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 date 212 non-null object 1 pct_covid 212 non-null float64 2 pct_flu 212 non-null float64 3 percent_mc 212 non-null float64 4 percent_hf 212 non-null float64 5 percent_anos 212 non-null float64 6 pct_twodoses 212 non-null float64 7 pct_concerned_sideeffects 212 non-null float64 8 pct_community_cli 212 non-null float64 9 pct_activity_work_outside_home 212 non-null float64 10 pct_activity_shop 212 non-null float64 11 pct_activity_restaurant_bar 212 non-null float64 12 pct_activity_spent_time 212 non-null float64 13 pct_activity_large_event 212 non-null float64 14 pct_activity_public_transit 212 non-null float64 15 pct_food_security 212 non-null float64 16 pct_anxious_7d 212 non-null float64 17 pct_depressed_7d 212 non-null float64 18 pct_symp_fever 212 non-null float64 19 pct_symp_cough 212 non-null float64 20 pct_symp_diff_breathing 212 non-null float64 21 pct_symp_fatigue 212 non-null float64 22 pct_symp_stuffy_nose 212 non-null float64 23 pct_symp_aches 212 non-null float64 24 pct_symp_sore_throat 212 non-null float64 25 pct_symp_chest_pain 212 non-null float64 26 pct_symp_nausea 212 non-null float64 27 pct_symp_headache 212 non-null float64 28 pct_symp_chills 212 non-null float64 29 pct_testing_rate 212 non-null float64 30 pct_avoid_contact 212 non-null float64 31 pct_worried_catch_covid 212 non-null float64 32 pct_belief_distancing_effective 212 non-null float64 33 pct_belief_masking_effective 212 non-null float64 34 pct_others_distanced_public 212 non-null float64 35 pct_others_masked_public 212 non-null float64 36 pct_belief_children_immune 212 non-null float64 37 pct_belief_no_spread_hot_humid 212 non-null float64 38 pct_received_news_local_health 212 non-null float64 39 pct_received_news_experts 212 non-null float64 40 pct_received_news_who 212 non-null float64 41 pct_received_news_govt_health 212 non-null float64 42 pct_received_news_politicians 212 non-null float64 43 pct_received_news_journalists 212 non-null float64 44 pct_received_news_friends 212 non-null float64 45 pct_received_news_religious 212 non-null float64 46 pct_received_news_none 212 non-null float64 47 pct_trust_covid_info_local_health 212 non-null float64 48 pct_trust_covid_info_experts 212 non-null float64 49 pct_trust_covid_info_who 212 non-null float64 50 pct_trust_covid_info_govt_health 212 non-null float64 51 pct_trust_covid_info_politicians 212 non-null float64 52 pct_trust_covid_info_journalists 212 non-null float64 53 pct_trust_covid_info_friends 212 non-null float64 54 pct_trust_covid_info_religious 212 non-null float64 55 pct_want_info_covid_treatment 212 non-null float64 56 pct_want_info_covid_variants 212 non-null float64 57 pct_want_info_children_education 212 non-null float64 58 pct_want_info_economic_impact 212 non-null float64 59 pct_want_info_mental_health 212 non-null float64 60 pct_want_info_relationships 212 non-null float64 61 pct_want_info_employment 212 non-null float64 62 pct_want_info_none 212 non-null float64 63 pct_delayed_care_cost 212 non-null float64 64 pct_mask_work_outside_home_1d 212 non-null float64 65 pct_mask_shop_1d 212 non-null float64 66 pct_mask_spent_time_1d 212 non-null float64 dtypes: float64(66), object(1) memory usage: 111.1+ KB
In [10]:
set(mh_df.columns.tolist()) - set(df.columns.tolist())
Out[10]:
set()
In [11]:
df = mh_df
In [12]:
shuffle_data=False if shuffle_data: df = df.set_index("date").sample(frac=1, random_state=69420).set_index(df["date"]) else: df = df.set_index("date")
In [13]:
_ = plt.figure(figsize=(20, 10)) _ = sns.heatmap(df .reindex(pd.date_range(df.index.min(), df.index.max())) # .set_index("date") .T )
In [14]:
_ = plt.figure(figsize=(20, 10)) _ = sns.heatmap(df .reindex(pd.date_range(df.index.min(), df.index.max())) # .set_index("date") .pipe(apply_scaling, method="Standard") .T )
In [15]:
df_melt = (df # .set_index("date") .pipe(apply_scaling, method="Standard") .reset_index() .melt(id_vars="date"))
In [16]:
_ = plt.figure(figsize=(30, 7)) _ = sns.lineplot(data=df_melt, x="date", y="value", hue="variable", legend=False) _ = sns.scatterplot(data=df_melt, x="date", y="value", hue="variable", legend=False)
In [17]:
g = sns.FacetGrid(df_melt, col="variable", col_wrap=3, aspect=2) _ = g.map(sns.lineplot, "date", "value") # _ = g.map(sns.scatterplot, "date", "value")
In [18]:
# def summary_window_FUN(x: pd.DataFrame, window_size: int = 7, user_func=decomposition.PCA, kwargs: dict = {}): # window_range = np.arange(0, len(x)-window_size, window_size) # cp_df = pd.DataFrame() # for window_begin in window_range: # current_cp_df = pd.DataFrame(user_func(n_components=None, **kwargs) # .fit_transform(x.iloc[window_begin: window_begin + window_size])).iloc[:, 0] # cp_df = pd.concat([cp_df, current_cp_df]) # return cp_df.rename(columns={0: f"windowed_{user_func.__name__}"}).reset_index(drop=True)
In [19]:
def window_PCA(x: pd.DataFrame, window_size: int = 7, user_func=decomposition.PCA, kwargs: dict = {}): window_range = np.arange(0, len(x)-window_size) pca_list = list() for window_begin in window_range: current_pca = user_func(n_components=None, svd_solver="full", **kwargs).fit(x.iloc[window_begin: window_begin + window_size]).explained_variance_ratio_[0] pca_list.append(current_pca) pca_df = pd.DataFrame({f"windowed_{user_func.__name__}": pca_list}) return pca_df
In [20]:
full_pca_df = pd.Series(decomposition.PCA(n_components=None, svd_solver="full").fit(df).explained_variance_ratio_).to_frame(name="explained_variance") full_pca_df
Out[20]:
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| explained_variance | |
|---|---|
| 0 | 0.463228 |
| 1 | 0.154618 |
| 2 | 0.121967 |
| 3 | 0.048974 |
| 4 | 0.030503 |
| ... | ... |
| 61 | 0.000034 |
| 62 | 0.000030 |
| 63 | 0.000024 |
| 64 | 0.000022 |
| 65 | 0.000018 |
66 rows × 1 columns
In [21]:
full_pca_df.sum()
Out[21]:
explained_variance 1.0 dtype: float64
In [22]:
window=28 pca_df = window_PCA(x=df, window_size=window).set_index(df.reset_index().loc[:df.shape[0]-window-1, "date"])
In [23]:
pca_df.head()
Out[23]:
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| windowed_PCA | |
|---|---|
| date | |
| 2021-06-09 | 0.525278 |
| 2021-06-10 | 0.532991 |
| 2021-06-11 | 0.549793 |
| 2021-06-13 | 0.539949 |
| 2021-06-14 | 0.543639 |
In [24]:
_ = plt.figure(figsize=(15, 5)) _ = sns.lineplot(data=pca_df.reset_index(), x="date", y="windowed_PCA", legend=True) _ = plt.title(f"Windowed PCA: {country_choice}") _ = plt.ylabel("Explained Variance of\nfirst principal component")
In [25]:
tmp = apply_scaling(pca_df, method="Standard")
In [26]:
significance_level=0.1 sig_plot_df = tmp.mask( tmp > norm.ppf(1 - significance_level), 1 ).mask(tmp <= norm.ppf(1 - significance_level), 0)
In [27]:
norm.ppf(1 - significance_level) norm.ppf(1 - significance_level)
Out[27]:
1.2815515655446004
In [28]:
# _ = sns.heatmap(sig_plot_df.T)
In [29]:
_ = plt.figure(figsize=(15, 5)) _ = plt.plot(tmp) _ = plt.title(f"Windowed PCA: {country_choice} (significant peaks in yellow based on z-test)") _ = plt.ylabel("Scaled explained variance of\nfirst principal component") for sig_date in sig_plot_df[sig_plot_df==True].dropna().index: _ = plt.axvline(sig_date, ls="--", c=JmsColors.YELLOW)
In [30]:
window_size=7 window_range = np.arange(0, len(tmp)-window_size, window_size) coefs_list = [] for window_begin in window_range: win_df = tmp.iloc[window_begin: window_begin + window_size].iloc[:, 0] mod = LinearRegression() _ = mod.fit(X=win_df.reset_index().index.to_numpy().reshape(-1, 1), y=win_df) coefs_list.append(mod.coef_[0])
In [31]:
_ = plt.plot(pd.Series(coefs_list))
In [32]:
fi_df = fluctuation_intensity(df.pipe(apply_scaling, method="Standard"), win=28, xmin=0, xmax=1, col_first=1, col_last=df.shape[1])
In [33]:
_ = complexity_resonance_diagram(fi_df, plot_title=f"Fluctuation Intensity Plot: {country_choice}", figsize = (20, 15))
In [34]:
ccp_df, sig_ccps_df = cumulative_complexity_peaks(df=fi_df, significant_level_item=0.05, significant_level_time=0.05)
In [35]:
_ = cumulative_complexity_peaks_plot(cumulative_complexity_peaks_df=ccp_df, significant_peaks_df=sig_ccps_df, plot_title=f"Cumulative Fluctuation Peaks Plot: {country_choice}", figsize = (20, 15))
In [36]:
_ = plt.figure(figsize=(15, 5)) _ = plt.plot(fi_df.sum(axis=1).replace(0, np.nan)) _ = plt.title(f"Sum of Fluctuation Intensity: {country_choice} (significant fluctuation peaks in yellow)") for sig_date in sig_ccps_df[sig_ccps_df==True].dropna().index: _ = plt.axvline(sig_date, ls="--", c=JmsColors.YELLOW)
In [37]:
print(f"time elapsed: {time.time()-start} seconds")
time elapsed: 136.54502606391907 seconds
In [38]:
rand_df = pd.concat([pd.Series(np.random.normal(size=df.shape[0]), name=f"feat_{x}") for x in range(0, df.shape[1])], axis=1) rand_df.head()
Out[38]:
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| feat_0 | feat_1 | feat_2 | feat_3 | feat_4 | feat_5 | feat_6 | feat_7 | feat_8 | feat_9 | ... | feat_56 | feat_57 | feat_58 | feat_59 | feat_60 | feat_61 | feat_62 | feat_63 | feat_64 | feat_65 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.166357 | 1.281349 | 0.253245 | -0.073998 | -2.485926 | -0.064818 | -1.728892 | 0.371097 | 1.832092 | 0.264241 | ... | -1.838798 | -1.196438 | -0.221904 | 0.177480 | 1.363301 | 1.082475 | -0.305459 | 0.668112 | -0.495329 | 0.736386 |
| 1 | 0.391213 | -0.110830 | 0.908489 | -0.665412 | -0.408234 | -0.083400 | 0.216866 | 0.048175 | -0.808516 | -1.673827 | ... | 0.551120 | 0.111760 | 0.366372 | -0.847674 | -0.713806 | -0.388091 | 1.416200 | 1.018845 | 0.402667 | 0.991774 |
| 2 | 1.200608 | 0.017200 | 1.109845 | -0.038292 | 0.398869 | 0.584483 | -0.591980 | -0.240569 | -0.214665 | 1.184046 | ... | -1.746783 | 0.609429 | 0.180562 | 1.597279 | -1.210122 | -0.723964 | -1.850715 | 0.406502 | -1.583945 | 0.142445 |
| 3 | -1.209785 | -0.375880 | -0.203059 | -0.738056 | -0.085013 | 0.048623 | 0.106745 | 0.611865 | -0.799256 | 0.499482 | ... | 1.009325 | -1.267732 | -0.935199 | 1.556323 | 0.734132 | 0.797713 | 0.293905 | -0.643621 | 0.744608 | -0.895474 |
| 4 | 0.781443 | -1.011730 | -0.899702 | 0.014832 | 0.831888 | 0.316644 | -0.223536 | 0.921638 | -1.677197 | 0.485227 | ... | 0.449124 | -1.317042 | 0.262365 | -0.535261 | 0.622562 | 0.948584 | -1.064754 | 0.490696 | 0.033285 | -0.259228 |
5 rows × 66 columns
In [39]:
pca_df = window_PCA(x=rand_df, window_size=window)
In [40]:
pca_df.head()
Out[40]:
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| windowed_PCA | |
|---|---|
| 0 | 0.086379 |
| 1 | 0.087345 |
| 2 | 0.089653 |
| 3 | 0.088032 |
| 4 | 0.091690 |
In [41]:
_ = plt.figure(figsize=(15, 5)) _ = sns.lineplot(data=pca_df.reset_index(), x="index", y="windowed_PCA", legend=True) _ = plt.title("Windowed PCA: random data") _ = plt.ylabel("Explained Variance of\nfirst principal component")
Jms for loop
In [42]:
window_size=28 window_range = np.arange(0, len(df)-window_size) window_range = np.arange(0, 3) for window_begin in window_range: print(f"window_begin: {window_begin}, window_end: {window_begin + window_size}") # display(df.iloc[window_begin: window_begin + window_size, :].head()) print(df.iloc[window_begin: window_begin + window_size, :].index.min()) print(df.iloc[window_begin: window_begin + window_size, :].index.max())
window_begin: 0, window_end: 28 2021-06-09 2021-07-11 window_begin: 1, window_end: 29 2021-06-10 2021-07-12 window_begin: 2, window_end: 30 2021-06-11 2021-07-13
Matti for loop
In [43]:
# for(i in (win:nrow(mattidata_withdate))){ # res.pca <- prcomp( # mattidata_withdate %>% # # For e.g. window of 28, keep observations 1-28, 2-29, 3-30 etc. # dplyr::filter(row_number() >= i-win+1 & # row_number() <= i) %>% # dplyr::select(-all_of(omitted_from_pca)), # scale = TRUE)
In [44]:
win = 28 for i in range(win, len(df)): print(f"window_begin: {i-win+1}, window_end: {i}")
window_begin: 1, window_end: 28 window_begin: 2, window_end: 29 window_begin: 3, window_end: 30 window_begin: 4, window_end: 31 window_begin: 5, window_end: 32 window_begin: 6, window_end: 33 window_begin: 7, window_end: 34 window_begin: 8, window_end: 35 window_begin: 9, window_end: 36 window_begin: 10, window_end: 37 window_begin: 11, window_end: 38 window_begin: 12, window_end: 39 window_begin: 13, window_end: 40 window_begin: 14, window_end: 41 window_begin: 15, window_end: 42 window_begin: 16, window_end: 43 window_begin: 17, window_end: 44 window_begin: 18, window_end: 45 window_begin: 19, window_end: 46 window_begin: 20, window_end: 47 window_begin: 21, window_end: 48 window_begin: 22, window_end: 49 window_begin: 23, window_end: 50 window_begin: 24, window_end: 51 window_begin: 25, window_end: 52 window_begin: 26, window_end: 53 window_begin: 27, window_end: 54 window_begin: 28, window_end: 55 window_begin: 29, window_end: 56 window_begin: 30, window_end: 57 window_begin: 31, window_end: 58 window_begin: 32, window_end: 59 window_begin: 33, window_end: 60 window_begin: 34, window_end: 61 window_begin: 35, window_end: 62 window_begin: 36, window_end: 63 window_begin: 37, window_end: 64 window_begin: 38, window_end: 65 window_begin: 39, window_end: 66 window_begin: 40, window_end: 67 window_begin: 41, window_end: 68 window_begin: 42, window_end: 69 window_begin: 43, window_end: 70 window_begin: 44, window_end: 71 window_begin: 45, window_end: 72 window_begin: 46, window_end: 73 window_begin: 47, window_end: 74 window_begin: 48, window_end: 75 window_begin: 49, window_end: 76 window_begin: 50, window_end: 77 window_begin: 51, window_end: 78 window_begin: 52, window_end: 79 window_begin: 53, window_end: 80 window_begin: 54, window_end: 81 window_begin: 55, window_end: 82 window_begin: 56, window_end: 83 window_begin: 57, window_end: 84 window_begin: 58, window_end: 85 window_begin: 59, window_end: 86 window_begin: 60, window_end: 87 window_begin: 61, 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