The purpose of this test is to show that there is correlation between modifiable argument in Vocaloid project file and quality of tuning.
What is Vocaloid? Here is a link to wiki page.
Vocaloid:
Vocaloid (ボーカロイド, Bōkaroido) is a singing voice synthesizer software product. Its signal processing part was developed through a joint research project led by Kenmochi Hideki at the Pompeu Fabra University in Barcelona, Spain, in 2000 and was not originally intended to be a full commercial project. Backed by the Yamaha Corporation, it developed the software into the commercial product “Vocaloid” which was released in 2004.
Project github repo: https://github.com/Discover304/AI-Tuner
In this part we will get a formated vsqx data in dictionary with 2 dimension infromation note and id.
# adding path to system
import sys, os
sys.path.append(os.getcwd())
# read the data index json file
import json
dataPath = os.path.join(os.getcwd(), 'VocaloidVSQXCollection')
with open(os.path.join(dataPath,"source.json"), 'r',encoding='utf-8') as f:
source = json.load(f) # source is a dictionary
fileList = [source[sourceIndex]["file"] for sourceIndex in range(len(source))]
[print(str(sourceIndex+1) + ". Thanks for the data from creator: " + source[sourceIndex]["creator"] + "\n\tSource of data: " + source[sourceIndex]["website"] + "\n") for sourceIndex in range(len(source))]
# initialise all reoslvers
from vocaloidDao import vocaloidVSQXResolver
resolverList = [vocaloidVSQXResolver(os.path.join(dataPath, fileName)) for fileName in fileList]
1. Thanks for the data from creator: 混音: リサRisa
Source of data: https://www.vsqx.top/project/vn1801
2. Thanks for the data from creator: 扒谱:星葵/混音:seedking
Source of data: https://www.vsqx.top/project/vn1743
3. Thanks for the data from creator: N/A
Source of data: https://www.vsqx.top/project/vn1784
4. Thanks for the data from creator: vsqx:DZ韦元子
Source of data: https://www.vsqx.top/project/vn1752
5. Thanks for the data from creator: N/A
Source of data: https://www.vsqx.top/project/vn1749
6. Thanks for the data from creator: 填词~超监督乌鸦,千年食谱颂vsqx~的的的的的说,制作~cocok7
Source of data: https://www.vsqx.top/project/vn1798
7. Thanks for the data from creator: 伴奏:小野道ono (https://www.dizzylab.net/albums/d/dlep02/)
Source of data: https://www.vsqx.top/project/vn1788
8. Thanks for the data from creator: 调/混:邪云 扒谱:天啦噜我的串串儿
Source of data: https://www.vsqx.top/project/vn1796
9. Thanks for the data from creator: 扒谱:磷元素P
Source of data: https://www.vsqx.top/project/vn1753
10. Thanks for the data from creator: N/A
Source of data: https://www.vsqx.top/project/vn1778
# resolve all original data in parallel way, and save them to loacl
from vocaloidDao import parallelResolve
print("It may take a while if the file are resolved for the first time.")
parallelResolve(resolverList)
It may take a while if the file are resolved for the first time.
local computer has: 16 cores
Parallal computing takes 0.00 seconds to finish.
# load saved data
VocaloidDataDfs = [resolver.loadFormatedVocaloidData() for resolver in resolverList]
# import as dataframe
import pandas as pd
VocaloidDataDf = pd.DataFrame()
for VocaloidDataDfIndex in range(len(VocaloidDataDfs)):
VocaloidDataDf = VocaloidDataDf.append(VocaloidDataDfs[VocaloidDataDfIndex])
VocaloidDataDf = VocaloidDataDf.reset_index()
VocaloidDataDf.head()
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index | D | G | W | P | S | VEL | T | OPE | DUR | |
---|---|---|---|---|---|---|---|---|---|---|
0 | 0 | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 6... | [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... | [127, 127, 127, 127, 127, 127, 127, 127, 127, ... | [90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 9... |
1 | 1 | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 6... | [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... | [127, 127, 127, 127, 127, 127, 127, 127, 127, ... | [30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 3... |
2 | 2 | [64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 6... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [2418, 2418, 2418, 2418, 2418, 2418, 2418, 241... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 6... | [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... | [127, 127, 127, 127, 127, 127, 127, 127, 127, ... | [150, 150, 150, 150, 150, 150, 150, 150, 150, ... |
3 | 3 | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 6... | [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... | [127, 127, 127, 127, 127, 127, 127, 127, 127, ... | [30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 3... |
4 | 4 | [55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 5... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | [64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 6... | [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... | [127, 127, 127, 127, 127, 127, 127, 127, 127, ... | [30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 3... |
2248*9*960
19422720
The above dataframe is scary, with 19 million data as 3 dimension. We have to reduce the data by extract the main features of each 960 vector, and join to a dataframe. So, the next challenge we face is how to extract this features.
We decide to take following data:
Continuous
means one note one value, Discrete
means one time stamp one valueSee more: https://www.cnblogs.com/xingshansi/p/6815217.html
def zcr(dataArray):
pass
# get discrete args fearure
discreteArgsDf = VocaloidDataDf[["VEL","OPE","DUR"]].applymap(lambda x : x[0])
discreteArgsDf.columns = discreteArgsDf.columns.map(lambda x : x+("-SINGLE"))
discreteArgsDf.head()
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VEL-SINGLE | OPE-SINGLE | DUR-SINGLE | |
---|---|---|---|
0 | 64 | 127 | 90 |
1 | 64 | 127 | 30 |
2 | 64 | 127 | 150 |
3 | 64 | 127 | 30 |
4 | 64 | 127 | 30 |
# get continuous args feature
import numpy as np
## mean
continuousArgsDf = pd.DataFrame()
continuousArgsDf = VocaloidDataDf[["D","G","W","P","S"]].applymap(lambda x : np.mean([i for i in x if i!=0]+[0]))
continuousArgsDf.columns = continuousArgsDf.columns.map(lambda x : x+("-MEAN"))
# without 0s
from scipy import stats
## list all function we need
aspectDict = {"-MID": np.median, "-SD": np.std, "-MOD": lambda x : stats.mode(x)[0][0]}
## prepare a mapping function
def appendAspect(dict, continuousArgsDf):
for key in dict.keys():
continuousArgsDfTemp = VocaloidDataDf[["D","G","W","P","S"]].applymap(lambda x : dict[key]([i for i in x if i!=0]+[0]))
continuousArgsDfTemp.columns = continuousArgsDfTemp.columns.map(lambda x : x+(key))
continuousArgsDf = continuousArgsDf.join(continuousArgsDfTemp,on=continuousArgsDf.index)
return continuousArgsDf
## apply mapping function to our data set
continuousArgsDf = appendAspect(aspectDict,continuousArgsDf)
continuousArgsDf.head()
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D-MEAN | G-MEAN | W-MEAN | P-MEAN | S-MEAN | D-MID | G-MID | W-MID | P-MID | S-MID | D-SD | G-SD | W-SD | P-SD | S-SD | D-MOD | G-MOD | W-MOD | P-MOD | S-MOD | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0 | 0 | 0 | 0 | 0 |
1 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0 | 0 | 0 | 0 | 0 |
2 | 63.576159 | 0.0 | 0.0 | 2401.986755 | 0.0 | 64.0 | 0.0 | 0.0 | 2418.0 | 0.0 | 5.190972 | 0.0 | 0.0 | 196.121397 | 0.0 | 64 | 0 | 0 | 2418 | 0 |
3 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0 | 0 | 0 | 0 | 0 |
4 | 53.225806 | 0.0 | 0.0 | 0.000000 | 0.0 | 55.0 | 0.0 | 0.0 | 0.0 | 0.0 | 9.717658 | 0.0 | 0.0 | 0.000000 | 0.0 | 55 | 0 | 0 | 0 | 0 |
# join both discrete and continuous args dataframe
argsDf = pd.DataFrame.join(discreteArgsDf, continuousArgsDf, on=discreteArgsDf.index)
argsDf.head()
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VEL-SINGLE | OPE-SINGLE | DUR-SINGLE | D-MEAN | G-MEAN | W-MEAN | P-MEAN | S-MEAN | D-MID | G-MID | ... | D-SD | G-SD | W-SD | P-SD | S-SD | D-MOD | G-MOD | W-MOD | P-MOD | S-MOD | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 64 | 127 | 90 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.0 | ... | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0 | 0 | 0 | 0 | 0 |
1 | 64 | 127 | 30 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.0 | ... | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0 | 0 | 0 | 0 | 0 |
2 | 64 | 127 | 150 | 63.576159 | 0.0 | 0.0 | 2401.986755 | 0.0 | 64.0 | 0.0 | ... | 5.190972 | 0.0 | 0.0 | 196.121397 | 0.0 | 64 | 0 | 0 | 2418 | 0 |
3 | 64 | 127 | 30 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.0 | ... | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0 | 0 | 0 | 0 | 0 |
4 | 64 | 127 | 30 | 53.225806 | 0.0 | 0.0 | 0.000000 | 0.0 | 55.0 | 0.0 | ... | 9.717658 | 0.0 | 0.0 | 0.000000 | 0.0 | 55 | 0 | 0 | 0 | 0 |
5 rows × 23 columns
# get the rank list from our data list file (we has already import as json)
rankList = []
for resolverIndex in range(len(resolverList)):
noteNum = resolverList[resolverIndex].noteNum
rank = source[resolverIndex]["rank"]
for i in range(noteNum):
rankList+=[rank]
## format to data frame
rankDf = pd.DataFrame({"RANK":rankList})
rankDf.head()
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RANK | |
---|---|
0 | 6 |
1 | 6 |
2 | 6 |
3 | 6 |
4 | 6 |
# join our args rank dataframe together
dataDf = argsDf.join(rankDf, on=rankDf.index)
dataDf.head()
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VEL-SINGLE | OPE-SINGLE | DUR-SINGLE | D-MEAN | G-MEAN | W-MEAN | P-MEAN | S-MEAN | D-MID | G-MID | ... | G-SD | W-SD | P-SD | S-SD | D-MOD | G-MOD | W-MOD | P-MOD | S-MOD | RANK | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 64 | 127 | 90 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.0 | ... | 0.0 | 0.0 | 0.000000 | 0.0 | 0 | 0 | 0 | 0 | 0 | 6 |
1 | 64 | 127 | 30 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.0 | ... | 0.0 | 0.0 | 0.000000 | 0.0 | 0 | 0 | 0 | 0 | 0 | 6 |
2 | 64 | 127 | 150 | 63.576159 | 0.0 | 0.0 | 2401.986755 | 0.0 | 64.0 | 0.0 | ... | 0.0 | 0.0 | 196.121397 | 0.0 | 64 | 0 | 0 | 2418 | 0 | 6 |
3 | 64 | 127 | 30 | 0.000000 | 0.0 | 0.0 | 0.000000 | 0.0 | 0.0 | 0.0 | ... | 0.0 | 0.0 | 0.000000 | 0.0 | 0 | 0 | 0 | 0 | 0 | 6 |
4 | 64 | 127 | 30 | 53.225806 | 0.0 | 0.0 | 0.000000 | 0.0 | 55.0 | 0.0 | ... | 0.0 | 0.0 | 0.000000 | 0.0 | 55 | 0 | 0 | 0 | 0 | 6 |
5 rows × 24 columns
Notice: any other cleaning process should be done in this step
l = np.quantile(dataDf['DUR-SINGLE'],0.25)
h = np.quantile(dataDf['DUR-SINGLE'],0.75)
IQR = h+1.5*(h-l)
dataDf = dataDf[dataDf['DUR-SINGLE']<=IQR].reset_index()
dataDf = dataDf.drop(columns=["index"])
dataDf = dataDf.transpose()[dataDf.any().values].transpose()
Perform the following steps:
If the MSE is reasonaly small, we can accept this result.
# define a normaliser
def normalizer(dataArray):
if dataArray.max() - dataArray.min() == 0:
return dataArray
return (dataArray-dataArray.min())/(dataArray.max() - dataArray.min())
# define a standardizer
def standardizer(dataArray):
if dataArray.max() - dataArray.min() == 0:
return dataArray
return (dataArray-dataArray.mean())/dataArray.std()
dataDfNormalized = dataDf.apply(normalizer)
dataDfNormalized.head()
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VEL-SINGLE | OPE-SINGLE | DUR-SINGLE | D-MEAN | G-MEAN | P-MEAN | S-MEAN | D-MID | G-MID | P-MID | S-MID | D-SD | G-SD | P-SD | S-SD | D-MOD | G-MOD | P-MOD | S-MOD | RANK | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0.503937 | 1.0 | 0.198614 | 0.000000 | 0.0 | 0.500042 | 0.0 | 0.000000 | 0.0 | 0.499785 | 0.0 | 0.000000 | 0.0 | 0.000000 | 0.0 | 0.000000 | 0.0 | 0.499785 | 0.0 | 0.0 |
1 | 0.503937 | 1.0 | 0.060046 | 0.000000 | 0.0 | 0.500042 | 0.0 | 0.000000 | 0.0 | 0.499785 | 0.0 | 0.000000 | 0.0 | 0.000000 | 0.0 | 0.000000 | 0.0 | 0.499785 | 0.0 | 0.0 |
2 | 0.503937 | 1.0 | 0.337182 | 0.503959 | 0.0 | 0.648399 | 0.0 | 0.503937 | 0.0 | 0.648429 | 0.0 | 0.151537 | 0.0 | 0.083406 | 0.0 | 0.503937 | 0.0 | 0.648429 | 0.0 | 0.0 |
3 | 0.503937 | 1.0 | 0.060046 | 0.000000 | 0.0 | 0.500042 | 0.0 | 0.000000 | 0.0 | 0.499785 | 0.0 | 0.000000 | 0.0 | 0.000000 | 0.0 | 0.000000 | 0.0 | 0.499785 | 0.0 | 0.0 |
4 | 0.503937 | 1.0 | 0.060046 | 0.421914 | 0.0 | 0.500042 | 0.0 | 0.433071 | 0.0 | 0.499785 | 0.0 | 0.283683 | 0.0 | 0.000000 | 0.0 | 0.433071 | 0.0 | 0.499785 | 0.0 | 0.0 |
# prepare for evaluation tool
import seaborn as sns
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
from scipy.spatial import Voronoi, voronoi_plot_2d
def noiser(df):
return df.applymap(lambda x : x+np.random.random()*0.001)
def distributionPlot(columnName0, columnName1, hueColumn, dataDfNormalized):
# getting data
dataPoints = dataDfNormalized[[columnName0, columnName1]]
# adding noise
dataPointsWithNoise = noiser(dataDfNormalized)
# plot the overview of the data
fig, ax = plt.subplots(1, sharey=True)
sns.scatterplot(x = columnName0 ,y = columnName1, data = dataPointsWithNoise, hue=hueColumn, marker = "o", ax=ax)
plt.xlim([-0.01,1.01]), plt.ylim([-0.01,1.01])
"""
https://stackoverflow.com/questions/20515554/colorize-voronoi-diagram/20678647#20678647
https://ipython-books.github.io/145-computing-the-voronoi-diagram-of-a-set-of-points/
"""
# add 4 distant dummy points to fix coloring problem
dataPoints = np.append((dataDfNormalized)[['P-MEAN', 'RANK']], [[2,2], [-2,2], [2,-2], [-2,-2]], axis = 0)
# plot Voronoi diagrame
## since it the function in scipy return a figure rather an ax,
## we can not plot both figure in the same figure by normal way,
## this can be improved later
vor = Voronoi(dataPoints)
voronoi_plot_2d(vor, show_vertices = True, point_size = 0.5)
# color list
colorList = []
for regionIndex in range(len(vor.regions)):
if not -1 in vor.regions[regionIndex]:
polygon = [vor.vertices[i] for i in vor.regions[regionIndex]]
if len(polygon) == 0:
colorList += colorList[-1:]
continue
colorList += [np.array(polygon).transpose().min()]
colorList += colorList[-1:]
colorList = normalizer(np.array(colorList))
# colorize by the distance from 0 point
for regionIndex in range(len(vor.regions)):
if not -1 in vor.regions[regionIndex]:
polygon = [vor.vertices[i] for i in vor.regions[regionIndex]]
plt.fill(*zip(*polygon),color=np.repeat(colorList[regionIndex],3))
# fix the range of axes
plt.xlim([-0.2,1.2]), plt.ylim([-0.2,1.2])
plt.xlabel(columnName0)
plt.ylabel(columnName1)
plt.show()
def comparisionPlot(columnName0, columnName1, dataDfNormalized):
# Plotting
fig = plt.figure(figsize=(12,10))
gs1 = gridspec.GridSpec(nrows=2, ncols=2)
ax1 = fig.add_subplot(gs1[:, 0])
ax2 = fig.add_subplot(gs1[0, 1])
ax3 = fig.add_subplot(gs1[1, 1])
dataPointsWithNoise = noiser(dataDfNormalized)
sns.scatterplot(x = columnName0 ,y = columnName1, data = dataPointsWithNoise, hue="RANK", marker = "o", ax = ax1)
# noise half version high
dataPointsWithNoise = noiser(dataDfNormalized[dataDfNormalized["RANK"]<0.5])
sns.scatterplot(x = columnName0 ,y = columnName1, data = dataPointsWithNoise, hue="RANK", marker = "o", ax = ax2)
# noise half version low
dataPointsWithNoise = noiser(dataDfNormalized[dataDfNormalized["RANK"]>0.5])
sns.scatterplot(x = columnName0 ,y = columnName1, data = dataPointsWithNoise, hue="RANK", marker = "o", ax = ax3)
ax1.set_xlim([0,1.01]), ax1.set_ylim([0,1.01])
ax2.set_xlim([0,1.01]), ax2.set_ylim([0,1.01])
ax3.set_xlim([0,1.01]), ax3.set_ylim([0,1.01])
ax1.set_title("Plot of " +columnName0+ " v.s. " +columnName1)
ax2.set_title("Seperate Plot of Higher Rank Notes")
ax3.set_title("Seperate Plot of Lower Rank Notes")
plt.show()
print(len(dataDfNormalized.columns))
dataDfNormalized.columns
20
Index(['VEL-SINGLE', 'OPE-SINGLE', 'DUR-SINGLE', 'D-MEAN', 'G-MEAN', 'P-MEAN',
'S-MEAN', 'D-MID', 'G-MID', 'P-MID', 'S-MID', 'D-SD', 'G-SD', 'P-SD',
'S-SD', 'D-MOD', 'G-MOD', 'P-MOD', 'S-MOD', 'RANK'],
dtype='object')
# distributionPlot('DUR-SINGLE','P-SD',"RANK",dataDfNormalized)
comparisionPlot('DUR-SINGLE','P-SD',dataDfNormalized)
tempDf = dataDfNormalized[dataDfNormalized['P-SD']!=0]
fig = plt.figure(figsize=(3,4))
plt.bar(["High rank","Low rank"],[tempDf[tempDf['RANK']<0.5]['P-SD'].mean(), tempDf[tempDf['RANK']>0.5]['P-SD'].mean()])
plt.ylabel("Mean P-SD")
plt.show()
dataDfNormalized.columns
Index(['VEL-SINGLE', 'OPE-SINGLE', 'DUR-SINGLE', 'D-MEAN', 'G-MEAN', 'P-MEAN',
'S-MEAN', 'D-MID', 'G-MID', 'P-MID', 'S-MID', 'D-SD', 'G-SD', 'P-SD',
'S-SD', 'D-MOD', 'G-MOD', 'P-MOD', 'S-MOD', 'RANK'],
dtype='object')
from sklearn.decomposition import PCA
pca = PCA(n_components=(len(dataDfNormalized.columns[:-1])))
pca.fit(dataDfNormalized[dataDfNormalized.columns[:-1]].values)
pca_result = pca.transform(dataDfNormalized[dataDfNormalized.columns[:-1]].values)
sns.scatterplot(x=pca_result[:,0], y=pca_result[:,1], hue=dataDfNormalized["RANK"])
plt.xlabel("PC1"), plt.ylabel("PC2")
plt.show()
sns.pointplot(y = [np.sum(pca.explained_variance_ratio_[:i]) for i in range(20)], x = [i for i in range(20)])
plt.xlabel("PCs"), plt.ylabel("Explain")
plt.show()
import statsmodels.formula.api as smf
pcs = dataDfNormalized[["RANK"]].join(pd.DataFrame({"PC1":pca_result[:,0]}),on=dataDfNormalized.index)
for i in range(1,9): # we take first 8 value
pcs = pcs.join(pd.DataFrame({"PC"+str(i+1):pca_result[:,i]}),on=dataDfNormalized.index)
model = smf.ols('RANK ~ PC1 + PC2 + PC3 + PC4', data=pcs)
result = model.fit()
result.summary()
Dep. Variable: | RANK | R-squared: | 0.131 |
---|---|---|---|
Model: | OLS | Adj. R-squared: | 0.130 |
Method: | Least Squares | F-statistic: | 106.3 |
Date: | Mon, 11 Jan 2021 | Prob (F-statistic): | 1.68e-84 |
Time: | 21:21:21 | Log-Likelihood: | 71.223 |
No. Observations: | 2832 | AIC: | -132.4 |
Df Residuals: | 2827 | BIC: | -102.7 |
Df Model: | 4 | ||
Covariance Type: | nonrobust |
coef | std err | t | P>|t| | [0.025 | 0.975] | |
---|---|---|---|---|---|---|
Intercept | 0.5392 | 0.004 | 121.492 | 0.000 | 0.530 | 0.548 |
PC1 | -0.3301 | 0.018 | -18.183 | 0.000 | -0.366 | -0.295 |
PC2 | 0.1395 | 0.020 | 6.862 | 0.000 | 0.100 | 0.179 |
PC3 | -0.1090 | 0.027 | -4.036 | 0.000 | -0.162 | -0.056 |
PC4 | -0.1681 | 0.030 | -5.599 | 0.000 | -0.227 | -0.109 |
Omnibus: | 28.744 | Durbin-Watson: | 0.186 |
---|---|---|---|
Prob(Omnibus): | 0.000 | Jarque-Bera (JB): | 19.880 |
Skew: | -0.076 | Prob(JB): | 4.82e-05 |
Kurtosis: | 2.619 | Cond. No. | 6.77 |
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
pcs = pcs.join(pd.DataFrame({"RANK-PREDICT":result.fittedvalues}), on=pcs.index)
# the square error
np.sum(np.power(pcs["RANK"]-pcs["RANK-PREDICT"],2))
157.6792358196176
fig = plt.figure(figsize=(10,10))
sns.scatterplot(x="PC1", y="RANK", data=pcs, marker="o")
sns.scatterplot(x="PC1", y="RANK-PREDICT", data=pcs, hue=np.abs(pcs["RANK"]-pcs["RANK-PREDICT"]), marker="o")
plt.show()
fig = plt.figure(figsize=(10,10))
ax = plt.subplot(111, projection="3d")
ax.scatter(pcs.PC1, pcs.PC2, pcs.RANK, c=pcs.RANK)
# ax.scatter(pcs.PC1, pcs.PC2, pcs[["RANK-PREDICT"]], c=np.abs(pcs["RANK"]-pcs["RANK-PREDICT"]), marker="x")
# pcssample = pcs.sample(10).sort_values(by="RANK")
# ax.plot_surface(pcssample.PC1, pcssample.PC2, pcssample[["RANK-PREDICT"]], rstride=1, cstride=1, cmap='rainbow')
ax.set_xlabel("PC1")
ax.set_ylabel("PC2")
ax.set_zlabel("RANK")
ax.view_init(20,10)
plt.show()
There is a really low value of R2R^2R2, less than 0.2, means the regression equation is not good enough to predict the Rank of a note from the properties we extracted from the 960 length vector. That might because of wrong choices of property, so, more research should be taken to varify the result we get in this notebook.
Next we can try to use the trend of a note to get a regression equation of it.