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layout: post title: ‘주식 클러스터링’ tags: [Etc]
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%matplotlib inline
Visualizing the stock market structure¶
This example employs several unsupervised learning techniques to extract the stock market structure from variations in historical quotes.
The quantity that we use is the daily variation in quote price: quotes that are linked tend to cofluctuate during a day.
Learning a graph structure¶
We use sparse inverse covariance estimation to find which quotes are correlated conditionally on the others. Specifically, sparse inverse covariance gives us a graph, that is a list of connection. For each symbol, the symbols that it is connected too are those useful to explain its fluctuations.
Clustering¶
We use clustering to group together quotes that behave similarly. Here, amongst the various clustering techniques <clustering> available in the scikit-learn, we use affinity_propagation as it does not enforce equal-size clusters, and it can choose automatically the number of clusters from the data.
Note that this gives us a different indication than the graph, as the graph reflects conditional relations between variables, while the clustering reflects marginal properties: variables clustered together can be considered as having a similar impact at the level of the full stock market.
Embedding in 2D space¶
For visualization purposes, we need to lay out the different symbols on a 2D canvas. For this we use manifold techniques to retrieve 2D embedding.
Visualization¶
The output of the 3 models are combined in a 2D graph where nodes represents the stocks and edges the:
- cluster labels are used to define the color of the nodes
- the sparse covariance model is used to display the strength of the edges
- the 2D embedding is used to position the nodes in the plan
This example has a fair amount of visualization-related code, as visualization is crucial here to display the graph. One of the challenge is to position the labels minimizing overlap. For this we use an heuristic based on the direction of the nearest neighbor along each axis.
In [2]:
print(__doc__)
# Author: Gael Varoquaux gael.varoquaux@normalesup.org
# License: BSD 3 clause
from datetime import datetime
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
from six.moves.urllib.request import urlopen
from six.moves.urllib.parse import urlencode
from sklearn import cluster, covariance, manifold
# #############################################################################
# Retrieve the data from Internet
def retry(f, n_attempts=3):
"Wrapper function to retry function calls in case of exceptions"
def wrapper(*args, **kwargs):
for i in range(n_attempts):
try:
return f(*args, **kwargs)
except Exception as e:
if i == n_attempts - 1:
raise
return wrapper
def quotes_historical_google(symbol, date1, date2):
"""Get the historical data from Google finance.
Parameters
----------
symbol : str
Ticker symbol to query for, for example ``"DELL"``.
date1 : datetime.datetime
Start date.
date2 : datetime.datetime
End date.
Returns
-------
X : array
The columns are ``date`` -- datetime, ``open``, ``high``,
``low``, ``close`` and ``volume`` of type float.
"""
params = urlencode({
'q': symbol,
'startdate': date1.strftime('%b %d, %Y'),
'enddate': date2.strftime('%b %d, %Y'),
'output': 'csv'
})
url = 'http://www.google.com/finance/historical?' + params
response = urlopen(url)
dtype = {
'names': ['date', 'open', 'high', 'low', 'close', 'volume'],
'formats': ['object', 'f4', 'f4', 'f4', 'f4', 'f4']
}
converters = {0: lambda s: datetime.strptime(s.decode(), '%d-%b-%y')}
return np.genfromtxt(response, delimiter=',', skip_header=1,
dtype=dtype, converters=converters,
missing_values='-', filling_values=-1)
# Choose a time period reasonably calm (not too long ago so that we get
# high-tech firms, and before the 2008 crash)
d1 = datetime(2003, 1, 1)
d2 = datetime(2008, 1, 1)
symbol_dict = {
'TOT': 'Total',
'XOM': 'Exxon',
'CVX': 'Chevron',
'COP': 'ConocoPhillips',
'VLO': 'Valero Energy',
'MSFT': 'Microsoft',
'IBM': 'IBM',
'TWX': 'Time Warner',
'CMCSA': 'Comcast',
'CVC': 'Cablevision',
'YHOO': 'Yahoo',
'DELL': 'Dell',
'HPQ': 'HP',
'AMZN': 'Amazon',
'TM': 'Toyota',
'CAJ': 'Canon',
'SNE': 'Sony',
'F': 'Ford',
'HMC': 'Honda',
'NAV': 'Navistar',
'NOC': 'Northrop Grumman',
'BA': 'Boeing',
'KO': 'Coca Cola',
'MMM': '3M',
'MCD': 'McDonald\'s',
'PEP': 'Pepsi',
'K': 'Kellogg',
'UN': 'Unilever',
'MAR': 'Marriott',
'PG': 'Procter Gamble',
'CL': 'Colgate-Palmolive',
'GE': 'General Electrics',
'WFC': 'Wells Fargo',
'JPM': 'JPMorgan Chase',
'AIG': 'AIG',
'AXP': 'American express',
'BAC': 'Bank of America',
'GS': 'Goldman Sachs',
'AAPL': 'Apple',
'SAP': 'SAP',
'CSCO': 'Cisco',
'TXN': 'Texas Instruments',
'XRX': 'Xerox',
'WMT': 'Wal-Mart',
'HD': 'Home Depot',
'GSK': 'GlaxoSmithKline',
'PFE': 'Pfizer',
'SNY': 'Sanofi-Aventis',
'NVS': 'Novartis',
'KMB': 'Kimberly-Clark',
'R': 'Ryder',
'GD': 'General Dynamics',
'RTN': 'Raytheon',
'CVS': 'CVS',
'CAT': 'Caterpillar',
'DD': 'DuPont de Nemours'}
symbols, names = np.array(list(symbol_dict.items())).T
# retry is used because quotes_historical_google can temporarily fail
# for various reasons (e.g. empty result from Google API).
quotes = [
retry(quotes_historical_google)(symbol, d1, d2) for symbol in symbols
]
close_prices = np.vstack([q['close'] for q in quotes])
open_prices = np.vstack([q['open'] for q in quotes])
# The daily variations of the quotes are what carry most information
variation = close_prices - open_prices
# #############################################################################
# Learn a graphical structure from the correlations
edge_model = covariance.GraphLassoCV()
# standardize the time series: using correlations rather than covariance
# is more efficient for structure recovery
X = variation.copy().T
X /= X.std(axis=0)
edge_model.fit(X)
# #############################################################################
# Cluster using affinity propagation
_, labels = cluster.affinity_propagation(edge_model.covariance_)
n_labels = labels.max()
for i in range(n_labels + 1):
print('Cluster %i: %s' % ((i + 1), ', '.join(names[labels == i])))
# #############################################################################
# Find a low-dimension embedding for visualization: find the best position of
# the nodes (the stocks) on a 2D plane
# We use a dense eigen_solver to achieve reproducibility (arpack is
# initiated with random vectors that we don't control). In addition, we
# use a large number of neighbors to capture the large-scale structure.
node_position_model = manifold.LocallyLinearEmbedding(
n_components=2, eigen_solver='dense', n_neighbors=6)
embedding = node_position_model.fit_transform(X.T).T
# #############################################################################
# Visualization
plt.figure(1, facecolor='w', figsize=(10, 8))
plt.clf()
ax = plt.axes([0., 0., 1., 1.])
plt.axis('off')
# Display a graph of the partial correlations
partial_correlations = edge_model.precision_.copy()
d = 1 / np.sqrt(np.diag(partial_correlations))
partial_correlations *= d
partial_correlations *= d[:, np.newaxis]
non_zero = (np.abs(np.triu(partial_correlations, k=1)) > 0.02)
# Plot the nodes using the coordinates of our embedding
plt.scatter(embedding[0], embedding[1], s=100 * d ** 2, c=labels,
cmap=plt.cm.spectral)
# Plot the edges
start_idx, end_idx = np.where(non_zero)
# a sequence of (*line0*, *line1*, *line2*), where::
# linen = (x0, y0), (x1, y1), ... (xm, ym)
segments = [[embedding[:, start], embedding[:, stop]]
for start, stop in zip(start_idx, end_idx)]
values = np.abs(partial_correlations[non_zero])
lc = LineCollection(segments,
zorder=0, cmap=plt.cm.hot_r,
norm=plt.Normalize(0, .7 * values.max()))
lc.set_array(values)
lc.set_linewidths(15 * values)
ax.add_collection(lc)
# Add a label to each node. The challenge here is that we want to
# position the labels to avoid overlap with other labels
for index, (name, label, (x, y)) in enumerate(
zip(names, labels, embedding.T)):
dx = x - embedding[0]
dx[index] = 1
dy = y - embedding[1]
dy[index] = 1
this_dx = dx[np.argmin(np.abs(dy))]
this_dy = dy[np.argmin(np.abs(dx))]
if this_dx > 0:
horizontalalignment = 'left'
x = x + .002
else:
horizontalalignment = 'right'
x = x - .002
if this_dy > 0:
verticalalignment = 'bottom'
y = y + .002
else:
verticalalignment = 'top'
y = y - .002
plt.text(x, y, name, size=10,
horizontalalignment=horizontalalignment,
verticalalignment=verticalalignment,
bbox=dict(facecolor='w',
edgecolor=plt.cm.spectral(label / float(n_labels)),
alpha=.6))
plt.xlim(embedding[0].min() - .15 * embedding[0].ptp(),
embedding[0].max() + .10 * embedding[0].ptp(),)
plt.ylim(embedding[1].min() - .03 * embedding[1].ptp(),
embedding[1].max() + .03 * embedding[1].ptp())
plt.show()
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!jupyter nbconvert --to html --template basic *.ipynb