Robustness of dimensions - varying number of ratings threshold for characters

[jwzimmer-zz]

df_n: (800, 269) Avg min: 42.07125 Std for n: 52.91026529358461

If 10 ratings are required for each trait for each character in order for that character to be included in the matrix, then: newdf: (560, 236)

First dimension (first row of V^T)

Second dimension

Third dimension

Fourth dimension

Fifth dimension

Sixth dimension

Seventh dimension

Eighth dimension

Ninth dimension

Tenth dimension

20 rating threshold: newdf: (436, 236)

First dimension

Second dimension

Third dimension

Fourth dimension

Fifth dimension

Sixth dimension

Seventh dimension

Eighth dimension

Ninth dimension

Tenth dimension

=============================== 30 rating threshold: newdf: (323, 236)

First dimension

Second dimension

Third dimension

=============================== 40 rating threshold: newdf: (280, 236)

First dimension

Second dimension

Third dimension

=============================== 50 rating threshold: newdf: (218, 236)

First dimension

Second dimension

Third dimension

=============================== 60 rating threshold: newdf: (167, 236)

First dimension

Second dimension

Third dimension

Fourth dimension

Fifth dimension

Sixth dimension

Seventh dimension

Eighth dimension

Ninth dimension

Tenth dimension

=============================== 70 rating threshold: newdf: (140, 236)

First dimension

Second dimension

Third dimension

============================= 80 rating threshold: newdf: (132, 236) First dimension

Second dimension

Third dimension

============================= 90 rating threshold: newdf: (116, 236) First dimension

Second dimension

Third dimension

============================= 100 rating threshold: newdf: (100, 236)

First dimension

Second dimension

Third dimension

Fourth dimension

Fifth dimension

Sixth dimension

Seventh dimension

Eighth dimension

Ninth dimension

Tenth dimension

Eleventh dimension

Twelfth dimension

Thirteenth dimension

Fourteenth dimension

Fifteenth dimension

========================= Threshold 150 ratings: newdf: (40, 236)

First dimension

Second dimension

Third dimension

Fourth dimension

Fifth dimension

========================== Threshold 200 ratings: newdf: (19, 236)

First dimension

Second dimension

Third dimension

Fourth dimension

Fifth dimension

============================== Threshold 250 ratings: newdf: (12, 236)

First dimension

Second dimension

Third dimension

============================== Threshold 300 ratings: newdf: (5, 236)

First d

Second d

Third d

============================== To rerun (with e.g. 10 rating threshold):

df_min_n = get_chars_with_at_least_min_n_ratings_per_trait(df_n,df2,n=10)
df3, U3, D3, V3, Sig3, X3, remakeX3 = runSVD(df_min_n)
vector_barchart(df3.columns, V3[0,:], 10, style="by_mag", ascending=False)

Relevant code:

import pandas as pd
from pandas_ods_reader import read_ods
import json
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
from numpy import linalg
from numpy.linalg import svd
from collections import Counter
from mpl_toolkits.mplot3d import Axes3D
import random
import scipy as sp

# === === Helper functions === ===
def write_json(data, filename):
    with open(filename,"w") as f:
        json.dump(data,f)
    return None
def get_json(filename):
    with open(filename) as f:
        jsonobj = json.load(f)
    return jsonobj

def add_character_name(row,character_map):
    return tuple(character_map[character_map['ID'] == row['unnamed.1']]['Character display name'])[0]

def add_work_name(row,character_map):
    return tuple(character_map[character_map['ID'] == row['unnamed.1']]['Fictional work'])[0]

#=================================
df_bap = pd.read_json("July2021_df_bap.json")
df_traits = pd.read_json("July2021_df_traits.json")
df_std = pd.read_json("June2021_df_std_original.json")
df_n = pd.read_json("June2021_df_n_original.json")

clean_column_dict = get_json("July2021_cleaned_column_dict.json")

def runSVD(df1,dropcols=['unnamed.1','name','work'],n=None):
    if len(dropcols) > 0:
        for x in dropcols:
            if x in df1.columns:
                df1 = df1.drop(x,axis=1)
    if n==None:
        n=df1.shape[1]-1
    X = df1.to_numpy()
    #decompose
    U, D, V = np.linalg.svd(X)
    # get dim of X
    M,N = X.shape
    # Construct sigma matrix in SVD (it simply adds null row vectors to match the dim of X)
    Sig = sp.linalg.diagsvd(D,M,N)
    # Now you can get X back:
    remakeX = np.dot(U, np.dot(Sig, V))
    assert np.sum(remakeX - X) < 0.00001
    return df1, U, D, V, Sig, X, remakeX

# Output from SVD without removing means
df1, U, D, V, Sig, X, remakeX = runSVD(df_traits)

# Remove the average of each trait
#df1_means = df1.mean().mean()
df1_means = 50
df1_normed = df1 - df1_means

# Output from SVD WITH removing means
df2, U2, D2, V2, Sig2, X2, remakeX2 = runSVD(df1_normed,dropcols=[])
# When remaking X, Sig2 and V2 are combined, then their product is combined with U2, so here is that first product
SigV2 = np.dot(Sig2,V2)
# the traits in order of columns
col2 = df2.columns

def get_chars_with_at_least_min_n_ratings_per_trait(df_n,df,
                                          n=0,
                                          verbose=True,
                                          chart=True):
    df_n = df_n.drop('unnamed.1',axis=1)
    df_n['min']=df_n.apply(lambda row: min(row), axis=1)
    if verbose:
        print("df_n: ",df_n.shape)
        #print("Avg min: ",sum(df_n['min'])/len(df_n['min']))
        #print("Std for n: ",np.std(df_n['min']))
    if chart:
        # matplotlib histogram
        plt.hist(df_n['min'], color = 'blue', edgecolor = 'black',
                  bins = 100)

        # Add labels
        plt.title('Histogram of min per trait per char')
        plt.xlabel('cells of df_n')
        plt.ylabel('number')
    #select characters in self.df who have min ratings >= n for all cols in self.coldict
    newchars = pd.DataFrame()
    for chari in range(df_n.shape[0]):
        if df_n.iloc[chari].min() >= n:
            newchars = newchars.append(df.iloc[chari])
    if verbose:
        print("newdf:  ",newchars.shape)
        print(newchars.head())
    return newchars

df_min_n = get_chars_with_at_least_min_n_ratings_per_trait(df_n,df2)

def vector_barchart(vector_names,vector,n,style="by_mag",ascending=False):
    """ vector_names should be the labels for the values in the vector
        vector should be the vector (ndarray)
        n should be the number of values you want displayed in the chart
        style should be the format of the chart
        ascending=False will be most relevant traits by magnitude,
        ascending=True will be least relevant traits by magnitude"""
    n=min(n,len(vector_names))
    vectordf = pd.DataFrame()
    vectordf["Trait"] = vector_names
    vectordf["Values"] = vector

    if style=="by_mag":
        vectordf["Magnitude"] = vectordf.apply(lambda row: abs(row["Values"]), axis = 1)
        sorteddf = vectordf.sort_values(by="Magnitude",ascending=ascending)
        #plotguy = sorteddf.iloc[-2*n:].iloc[::-1]
        plotguy = sorteddf.iloc[0:2*n]
    # if side=="half_n_half":
    #     sorteddf = lincombos3d.sort_values(by=d)
    #     top_n_top = sorteddf.iloc[0:n]
    #     top_n_bottom = sorteddf.iloc[-n:].iloc[::-1]
    #     plotguy = pd.concat([top_n_top,top_n_bottom])
    # if side=="neg":
    #     plotguy = sorteddf.iloc[0:2*n]
    # if side=="pos":
    #     plotguy = sorteddf.iloc[-2*n:].iloc[::-1]
    #print(plotguy)
    #sns.set(font_scale = 2)
    sns.barplot(plotguy["Values"],plotguy["Trait"])
    #sns.set(font_scale = 1)
    return vectordf, plotguy

[jwzimmer-zz]

Sort of related sanity checking: https://github.com/jwzimmer/tv-tropening/issues/17

If we transpose the matrix and run SVD, we see the same dimensions in terms of traits as the columns of U.

[jwzimmer-zz]

[jwzimmer-zz]

Talking with Dodds

• Number of characters vs. dot product of V^T dimension with itself at 800 characters vs at new cutoff
• Need to take absolute value because they can flip around