def _compute(self):
''' Perform all the steps required for a PCA. '''
# Center the dataframe
self.df -= self.df.mean()
# If specified, reduce the dataframe
if self.reduced is True:
self.df /= self.df.std()
# Apply the SVD
self.U, self.W, self.V = util.svd(self.df, k=self.components)
# Compute eigenvectors
self.eigenvectors = np.asmatrix(self.V)
# Compute eigenvalues
self.eigenvalues = self.W ** 2
# Sort the eigenvalues from high to low
self.eigenvalues = sorted(self.eigenvalues, reverse=True)
# Compute the row projections
self._compute_row_projections()
# Compute the variable correlations towards the eigenvectors
self._compute_variable_correlations()
# Compute the cumulative explained variance
self._compute_explained_variance()
# Compute the rowsum inertia
self._compute_row_inertia()
# Compute the total inertia
self._compute_total_inertia()
def _compute(self):
''' Perform all the steps required for a CA. '''
data = np.matrix(self.df, float)
N = np.sum(data)
# Stochastic matrix
self.stochastic_matrix = data / N
# Row sums
self.row_sums = np.sum(self.stochastic_matrix, 1)
# Row weights
self.row_weights = (1 / self.row_sums).reshape(1, -1).tolist()[0]
# Column sums
self.col_sums = np.sum(self.stochastic_matrix, 0)
# Column weights
self.col_weights = (1 / self.col_sums).tolist()[0]
# Expected values
self.expected_values = np.prod((
np.diag(np.sqrt(self.row_weights)),
self.stochastic_matrix - self.row_sums * self.col_sums,
np.diag(np.sqrt(self.col_weights))
))
# Singular Value Decomposition
self.U, self.W, self.V = util.svd(self.df, k=self.components)
# Singular values
d = np.diag(self.W.tolist())
columns = ['Component {}'.format(i) for i in range(self.p)]
# Row projections
N = np.diag(np.sqrt(self.row_sums.reshape(1, -1).tolist()[0])) * self.U
projections = np.diag(self.row_weights) * N * d
self.row_projections = pd.DataFrame(
projections,
index=self.df.index,
columns=columns
)
# Column projections
M = np.diag(np.sqrt(self.col_sums.tolist()[0])) * np.transpose(self.V)
projections = np.diag(self.col_weights) * M * d.T
self.column_projections = pd.DataFrame(
projections,
index=self.df.columns,
columns=columns
)
# Compute eigenvalues
self.eigenvalues = self.W ** 2
# Compute total inertia
self.total_inertia = sum(self.eigenvalues)
# Sort the eigenvalues from high to low
self.eigenvalues = sorted(self.eigenvalues, reverse=True)
self._compute_explained_variance()
