Earthquake_real

• 1. 데이터 정의
• 2. $f(x) = y$ 정의
• 3. 비유클리드 공간에서의 거리 정의
• 4. time 고려, 거리를 이용한 a weighted adjacency matrix $W_{i,j}$ 정의
• 5. $W_{i,j}$ 행렬을 이용한 차수 행렬 정의
• 6. Graph Laplacian matrix 정의
• 7. 고유값 분해
• 8. 주성분 분석
• 9. PCA
• $dist$를 이용한 $\theta$ = 80, $\kappa$ = 1000
• $dist$를 이용한 $\theta$ = 90, $\kappa$ = 1000
• $dist$를 이용한 $\theta$ = 100, $\kappa$ = 1000
• $haversine$ 패키지를 이용한 $\theta$ = 50000,$\kappa$ = 100000
• $haversine$ 패키지를 이용한 $\theta$ = 75000,$\kappa$ = 100000
• $haversine$ 패키지를 이용한 $\theta$ = 100000,$\kappa$ = 100000

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt 
import networkx as nx
import folium
from IPython.display import HTML

df=pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/earthquakes-23k.csv')

대지진 순위중 일부 추출

pd.read_html('https://ko.wikipedia.org/wiki/%EC%A7%80%EC%A7%84_%EB%AA%A9%EB%A1%9D',encoding='utf-8')[1].iloc[[2,3,8],:]

	순위	일자	장소	이름	규모
2	3	2004년 12월 26일	인도네시아 수마트라섬	2004년 인도양 지진 해일	9.1-9.3
3	4	2011년 3월 11일	일본 산리쿠 해역	2011년 도호쿠 지방 태평양 앞바다 지진	9.1
8	6 (공동)	2010년 2월 27일	칠레 마울레주 해역	2010년 칠레 지진	8.8

• t = Year
• x = Latitude
• y = Longitude
• f = Magnitude

1. 데이터 정의

_df = df.assign(Year=list(map(lambda x: x.split('/')[-1], df.Date))).query('Year>="2004" & Year<="2011"').reset_index().iloc[:,1:]

2. $f(x) = y$ 정의

• $y$ = Magnitude, 지진 규모로 정의

f = _df.loc[:,"Magnitude"]

3. 비유클리드 공간에서의 거리 정의

• $x$ = Latitude, 위도로 정의
• $y$ = Longitude, 경도로 정의

$$dist((x_i,y_i),(x_j,y_j)) = \sqrt{(x_j-x_i)^2+(y_j-y_i)^2}$$

4. time 고려, 거리를 이용한 a weighted adjacency matrix $W_{i,j}$ 정의

• $V_t$ : the number of countries, $|V| = n$
• $\cal{V} = \begin{bmatrix} 2004a & 2005a & 2006a & \dots \\ 2004b & 2005b & 2006b & \dots \\ \vdots & \vdots & \vdots & \vdots \\ \dots & \dots & \dots & \dots \end{bmatrix}$, $|\cal{V}| = nm$, (단, $m = t$)
• $W_t=\exp(-\frac{[dist(i,j)]^2}{2\theta^2}) $ $\quad \text{if } dist(i,j) \leq \kappa$
• $W_{u_r,v_s}=\begin{cases} W_t(u,v) & \quad \text{if } u,v \in V_t \\ \beta & \quad \text{if } u = v \wedge r=s-1 \\ 0 & \quad \text{otherwise} \end{cases}$
• $W(u,v) = \begin{bmatrix} weight(2004a,2004a) & weight(2004a,2005a) & \dots & \dots \\ weight(2004a,2004b) & weight(2005b,2005b) & \dots& \dots \\ \vdots & \vdots & \vdots & \vdots \\ \dots & \dots & \dots & \dots \end{bmatrix}$

V_2004 = np.array([_df.query('Year=="2004"').iloc[:,1:3]])

V_2004

array([[[ -21.476,  169.859],
        [  -8.31 ,  115.788],
        [  17.488, -101.303],
        ...,
        [   7.636,   93.947],
        [   6.204,   92.913],
        [   4.73 ,   95.14 ]]])

V_2005 = np.array([_df.query('Year=="2005"').iloc[:,1:3]])

V_2005.shape

(1, 533, 2)

np.hstack([V_2004,V_2005])

array([[[ -21.476,  169.859],
        [  -8.31 ,  115.788],
        [  17.488, -101.303],
        ...,
        [  -1.386,  -77.517],
        [  26.822,  140.646],
        [   7.529,  -82.266]]])

def dist(i,j):
    a1=abs(_df.Latitude[j] - _df.Latitude[i])
    a2=abs(_df.Latitude[j] + _df.Latitude[i])
    b1=abs(_df.Longitude[j] - _df.Longitude[i])
    b2=abs(_df.Longitude[j] + _df.Longitude[i])
    a= np.min([a1,a2])
    b= np.min([b1,b2])
    return np.sqrt(a**2+b**2)

def weight1(i,j,theta=80,kappa=1000, beta=1):
    if i == j :
        return beta   
    if i == j+1:
        return beta 
    elif dist(i,j) <= kappa :
        return np.exp( -np.abs(dist(i,j))**2 / (2*theta**2) )
    else:
        return 0

def weight2(i,j,theta=90,kappa=1000, beta=1):
    if i == j :
        return beta   
    if i == j+1:
        return beta 
    elif dist(i,j) <= kappa :
        return np.exp( -np.abs(dist(i,j))**2 / (2*theta**2) )
    else:
        return 0

def weight3(i,j,theta=100,kappa=1000, beta=1):
    if i == j :
        return beta   
    if i == j+1:
        return beta 
    elif dist(i,j) <= kappa :
        return np.exp( -np.abs(dist(i,j))**2 / (2*theta**2) )
    else:
        return 0

---

하버사인haversine 공식 사용

from haversine import haversine

def dist2(i,j):
    return haversine((_df.Latitude[i],_df.Longitude[i]),(_df.Latitude[j],_df.Longitude[j]))

def weight4(i,j,theta=50000,kappa=100000):
    if i == j :
        return beta   
    if i == j+1:
        return beta 
    elif dist2(i,j) <= kappa :
        return np.exp( -np.abs(dist2(i,j))**2 / (2*theta**2) )
    else:
        return 0

def weight5(i,j,theta=75000,kappa=100000):
    if i == j :
        return beta   
    if i == j+1:
        return beta 
    elif dist2(i,j) <= kappa :
        return np.exp( -np.abs(dist2(i,j))**2 / (2*theta**2) )
    else:
        return 0

def weight6(i,j,theta=100000,kappa=100000):
    if i == j :
        return beta   
    if i == j+1:
        return beta 
    elif dist2(i,j) <= kappa :
        return np.exp( -np.abs(dist2(i,j))**2 / (2*theta**2) )
    else:
        return 0

---

W1 = np.array([[weight1(i,j) for i in range(len(_df.query('Year=="2004"')))] for j in range(len(_df.query('Year=="2004"')))])

W1

plt.hist(W.reshape(-1))

W2 = np.array([[weight2(i,j) for i in range(len(_df))] for j in range(len(_df))])

W3 = np.array([[weight3(i,j) for i in range(len(_df))] for j in range(len(_df))])

W4 = np.array([[weight4(i,j) for i in range(len(_df))] for j in range(len(_df))])

W5 = np.array([[weight5(i,j) for i in range(len(_df))] for j in range(len(_df))])

W6 = np.array([[weight6(i,j) for i in range(len(_df))] for j in range(len(_df))])

5. $W_{i,j}$ 행렬을 이용한 차수 행렬 정의

• $D$ = Degree Matrix

D1 = np.diag(W1.sum(axis=1))

D2 = np.diag(W2.sum(axis=1))

D3 = np.diag(W3.sum(axis=1))

D4 = np.diag(W4.sum(axis=1))

D5 = np.diag(W5.sum(axis=1))

D6 = np.diag(W6.sum(axis=1))

6. Graph Laplacian matrix 정의

• $L = D - W$

L1 = D1 - W1

L2 = D2 - W2

L3 = D3 - W3

L4 = D4 - W4

L5 = D5 - W5

L6 = D6 - W6

7. 고유값 분해

• ${\bf L} = {\boldsymbol\Psi} {\boldsymbol\Lambda} {\boldsymbol\Psi}^\top$

λ1, Ψ1 = np.linalg.eig(L1)

Λ1 = np.diag(λ1)

λ2, Ψ2 = np.linalg.eig(L2)

Λ2 = np.diag(λ2)

λ3, Ψ3 = np.linalg.eig(L3)

Λ3 = np.diag(λ3)

λ4, Ψ4 = np.linalg.eig(L4)

Λ4 = np.diag(λ4)

λ5, Ψ5 = np.linalg.eig(L5)

Λ5 = np.diag(λ5)

λ6, Ψ6 = np.linalg.eig(L6)

Λ6 = np.diag(λ6)

8. 주성분 분석

• $comp_k = f @ np.outer(Ψ[:,k], Ψ[:,k]) $
  • $k = 1, 2, 3, 8000$
    • $f = n \times 1 , np.outer(Ψ[:,k], Ψ[:,k]) = n \times n, \\ \therefore comp_k = n \times 1$
• $p = \sum_{1}^{n} comp_{1}^{2},\sum_{1}^{n} comp_{2}^{2},…,\sum_{1}^{n} comp_{n}^{2}$
• $p = \frac{p}{\sum(p)}$

def p1(i):
    return sum((f @ np.outer( Ψ1[:,i], Ψ1[:,i]))**2)

array_11 = np.array([p1(i) for i in range(1,len(_df))])

varprop1 = array_11/array_11.sum()

_index1 = pd.DataFrame({'index':range(1,len(_df)),'varprop':varprop1}).sort_values('varprop',ascending=False)
_indexlst1 = _index1.iloc[:25,0].tolist()

def p2(i):
    return sum((f @ np.outer( Ψ2[:,i], Ψ2[:,i]))**2)

array_12 = np.array([p2(i) for i in range(1,len(_df))])

varprop12 = array_12/array_12.sum()

_index2 = pd.DataFrame({'index':range(1,len(_df)),'varprop':varprop2}).sort_values('varprop',ascending=False)
_indexlst2 = _index2.iloc[:25,0].tolist()

def p3(i):
    return sum((f @ np.outer( Ψ3[:,i], Ψ3[:,i]))**2)

array_13 = np.array([p3(i) for i in range(1,len(_df))])

varprop3 = array_13/array_13.sum()

_index3 = pd.DataFrame({'index':range(1,len(_df)),'varprop':varprop3}).sort_values('varprop',ascending=False)
_indexlst3 = _index3.iloc[:25,0].tolist()

def p4(i):
    return sum((f @ np.outer( Ψ4[:,i], Ψ4[:,i]))**2)

array_14 = np.array([p4(i) for i in range(1,len(_df))])

varprop4 = array_14/array_14.sum()

_index4 = pd.DataFrame({'index':range(1,len(_df)),'varprop':varprop4}).sort_values('varprop',ascending=False)
_indexlst4 = _index4.iloc[:25,0].tolist()

def p5(i):
    return sum((f @ np.outer( Ψ5[:,i], Ψ5[:,i]))**2)

array_15 = np.array([p5(i) for i in range(1,len(_df))])

varprop5 = array_15/array_15.sum()

_index5 = pd.DataFrame({'index':range(1,len(_df)),'varprop':varprop5}).sort_values('varprop',ascending=False)
_indexlst5 = _index5.iloc[:25,0].tolist()

def p6(i):
    return sum((f @ np.outer( Ψ6[:,i], Ψ6[:,i]))**2)

array_16 = np.array([p6(i) for i in range(1,len(_df))])

varprop6 = array_16/array_16.sum()

_index6 = pd.DataFrame({'index':range(1,len(_df)),'varprop':varprop6}).sort_values('varprop',ascending=False)
_indexlst6 = _index6.iloc[:25,0].tolist()

9. PCA

comp11 = f @ np.outer( Ψ1[:,0], Ψ1[:,0])

comp21 = f @ np.outer( Ψ1[:,_indexlst1[0]], Ψ1[:,_indexlst1[0]])

comp31 = f @ np.outer( Ψ1[:,_indexlst1[1]], Ψ1[:,_indexlst1[1]])

comp41 = f @ np.outer( Ψ1[:,_indexlst1[2]], Ψ1[:,_indexlst1[2]])

comp51 = f @ np.outer( Ψ1[:,_indexlst1[3]], Ψ1[:,_indexlst1[3]])

_df["comp1"] = comp11

_df["comp2"] = comp21

_df["comp3"] = comp31

_df["comp4"] = comp41

_df["comp5"] = comp51

comp12 = f @ np.outer( Ψ2[:,0], Ψ2[:,0])

comp22 = f @ np.outer( Ψ2[:,_indexlst2[0]], Ψ2[:,_indexlst2[0]])

comp32 = f @ np.outer( Ψ2[:,_indexlst2[1]], Ψ2[:,_indexlst2[1]])

comp42 = f @ np.outer( Ψ2[:,_indexlst2[2]], Ψ2[:,_indexlst2[2]])

comp52 = f @ np.outer( Ψ2[:,_indexlst2[3]], Ψ2[:,_indexlst2[3]])

_df["comp1"] = comp12

_df["comp2"] = comp22

_df["comp3"] = comp32

_df["comp4"] = comp42

_df["comp5"] = comp52

---

$dist$를 이용한 $\theta$ = 80, $\kappa$ = 1000

_G1 = nx.Graph(W1-np.identity(len(f)))

_pos1 = nx.spring_layout(_G1,iterations=20)

m_pos1 = list(zip(_df.Longitude,_df.Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.comp1,node_size = abs(_df.comp1)*10, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.comp2,node_size = np.abs(_df.comp2)*100,ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Japan Sanriku", xy=(141.81051675491926,39.138785036804705), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.comp3,node_size = np.abs(_df.comp3)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Indonesia Sumatra", xy=( 101.28817388446576,-0.26014368149947664), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.comp4,node_size = np.abs(_df.comp4)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.comp5,node_size = abs(_df.comp5)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Chile Maule", xy=(-72.41179564292405,-35.301421198712724), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

---

$dist$를 이용한 $\theta$ = 90, $\kappa$ = 1000

_G2 = nx.Graph(W2-np.identity(len(f)))

_pos2 = nx.spring_layout(_G2,iterations=20)

m_pos2 = list(zip(_df.Longitude,_df.Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.comp1,node_size = abs(_df.comp1)*10, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.comp2,node_size = np.abs(_df.comp2)*100,ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Indonesia Sumatra", xy=( 101.28817388446576,-0.26014368149947664), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.comp3,node_size = np.abs(_df.comp3)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Indonesia Sumatra", xy=( 101.28817388446576,-0.26014368149947664), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.comp4,node_size = np.abs(_df.comp4)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Japan Sanriku", xy=(141.81051675491926,39.138785036804705), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.comp5,node_size = abs(_df.comp5)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Chile Maule", xy=(-72.41179564292405,-35.301421198712724), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

---

$dist$를 이용한 $\theta$ = 100, $\kappa$ = 1000

_G = nx.Graph(W-np.identity(len(f)))

_pos = nx.spring_layout(_G,iterations=20)

m_pos = list(zip(_df.Longitude,_df.Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp1,node_size = abs(_df.comp1)*10, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp2,node_size = np.abs(_df.comp2)*100,ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Chile Maule", xy=(-72.41179564292405,-35.301421198712724), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp3,node_size = np.abs(_df.comp3)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Indonesia Sumatra", xy=( 101.28817388446576,-0.26014368149947664), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp4,node_size = np.abs(_df.comp4)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Japan Sanriku", xy=(141.81051675491926,39.138785036804705), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp5,node_size = abs(_df.comp5)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Indonesia Sumatra", xy=( 101.28817388446576,-0.26014368149947664), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

---

$haversine$ 패키지를 이용한 $\theta$ = 50000,$\kappa$ = 100000

_G = nx.Graph(W-np.identity(len(f)))

_pos = nx.spring_layout(_G,iterations=20)

m_pos = list(zip(_df.Longitude,_df.Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp1,node_size = abs(_df.comp1)*10, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp2,node_size = np.abs(_df.comp2)*100,ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Chile Maule", xy=(-72.41179564292405,-35.301421198712724), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp3,node_size = np.abs(_df.comp3)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Japan Sanriku", xy=(141.81051675491926,39.138785036804705), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp4,node_size = np.abs(_df.comp4)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Indonesia Sumatra", xy=( 101.28817388446576,-0.26014368149947664), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp5,node_size = abs(_df.comp5)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    # ax.annotate("Tasman Sea", xy=(160.4313,-40.8581), xycoords="data",
    #               va="center", ha="center",
    #               bbox=dict(boxstyle="circle, pad=3", alpha = 0.1,fc="w",lw=1, ec='r'))
    ax.annotate("Indonesia Sumatra", xy=( 101.28817388446576,-0.26014368149947664), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

---

$haversine$ 패키지를 이용한 $\theta$ = 75000,$\kappa$ = 100000

_G = nx.Graph(W-np.identity(len(f)))

_pos = nx.spring_layout(_G,iterations=20)

m_pos = list(zip(_df.Longitude,_df.Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp1,node_size = abs(_df.comp1)*10, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp2,node_size = np.abs(_df.comp2)*100,ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Japan Sanriku", xy=(141.81051675491926,39.138785036804705), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp3,node_size = np.abs(_df.comp3)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

    ax.annotate("Chile Maule", xy=(-72.41179564292405,-35.301421198712724), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp4,node_size = np.abs(_df.comp4)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Indonesia Sumatra", xy=( 101.28817388446576,-0.26014368149947664), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp5,node_size = abs(_df.comp5)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    # ax.annotate("Tasman Sea", xy=(160.4313,-40.8581), xycoords="data",
    #               va="center", ha="center",
    #               bbox=dict(boxstyle="circle, pad=3", alpha = 0.1,fc="w",lw=1, ec='r'))
    ax.annotate("Japan Sanriku", xy=(141.81051675491926,39.138785036804705), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

---

$haversine$ 패키지를 이용한 $\theta$ = 100000,$\kappa$ = 100000

_G = nx.Graph(W-np.identity(len(f)))

_pos = nx.spring_layout(_G,iterations=20)

m_pos = list(zip(_df.Longitude,_df.Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp1,node_size = abs(_df.comp1)*10, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp2,node_size = np.abs(_df.comp2)*100,ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Indonesia Sumatra", xy=( 101.28817388446576,-0.26014368149947664), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=3", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp3,node_size = np.abs(_df.comp3)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Japan Sanriku", xy=(141.81051675491926,39.138785036804705), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp4,node_size = np.abs(_df.comp4)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Chile Maule", xy=(-72.41179564292405,-35.301421198712724), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=5", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G,m_pos,node_color=_df.comp5,node_size = abs(_df.comp5)*100, ax=ax)
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
    ax.annotate("Indonesia Sumatra", xy=( 101.28817388446576,-0.26014368149947664), xycoords="data",
                  va="center", ha="center",
                  bbox=dict(boxstyle="circle, pad=3", alpha = 0.1,fc="w",lw=1, ec='r'))
plt.show()

---