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def __init__(self, X, Ncomp=10):
## define color palette to use for plotting
self.__palette = 'YlGn'
numerical_data, categorical_data, scaled_values = col_cat(X)
self.catdata = list(categorical_data.columns)
## input matrix
self.__x = pd.DataFrame(scaled_values)
self._varnames = X.columns
self._rownames = X.index
## set the number of components to compute and fit the model
self.__ncp = Ncomp
M = PCA(n_components = self.__ncp)
M.fit(self.__x)
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######## results ########
# Explained variability
self.__pcnames = [f'PC{i+1}({100 * M.explained_variance_ratio_[i].round(2)}%)' for i in range(self.__ncp)]
self._Qexp_ratio = pd.DataFrame(100 * M.explained_variance_ratio_, columns = ["Qexp"], index= [f'PC{i+1}' for i in range(self.__ncp)])
# Loadings and scores
#scores
s = M.transform(self.__x)
self.__t = s
self._t = s
self._r = pd.DataFrame(2*(s-s.min(axis=0))/(s.max(axis=0)-s.min(axis=0)) -1, index= self._rownames)
self._r.columns = self.__pcnames
# Normalize each loading vector to have unit length
self._p = (M.components_ / np.linalg.norm(M.components_, axis=0)).T
# Matrix reconstruction or prediction making
#
self.res = pd.DataFrame()
for i in range(self.__ncp):
self._xp = np.dot(self.__t[:,i].reshape((-1,1)), self._p[:,i].reshape((1,-1)))
# residuals
self._e = self.__x - self._xp
self.res[self.__pcnames[i]] = np.diag(self._e@self._e.T)
#self._res = pd.DataFrame( self._e, columns = self._varnames, index = self._rownames )
self._xp = self.__t @ self._p.T
# Compute the cosine similarity between the normalized loading vectors
self.lev = {}
## Laverage: leverage values range between 0 and 1
for i in range(self._t.shape[1]):
ti = self._t[:,i].reshape((-1,1))
Hat = ti @ np.linalg.pinv(np.transpose(ti) @ ti) @ np.transpose(ti)
self.lev[self._r.columns[i]] = ti.ravel()
self.leverage = pd.DataFrame(self.lev)
## Hotelling t2
#self.eigvals = M.singular_values_**2
#self.Lambda = np.diag(self.eigvals)
#self.T2 = self.__t @ np.linalg.inv(self.Lambda) @self.__t.T
@property
def scores_(self):
return pd.DataFrame(self._r)
@property
def loadings_(self):
return pd.DataFrame(self._p, columns=self.__pcnames, index=self._varnames)
@property
def leverage_(self):
return self.leverage
@property
def residuals(self):
return self.res