Trying to fix cv_pls
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parent
9ccdf97d07
commit
b39e71ca2b
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@ -13,9 +13,8 @@ try:
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from symeig import symeig
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except:
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has_sym = False
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has_sym=False
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def pca(a, aopt,scale='scores',mode='normal',center_axis=-1):
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def pca(a, aopt,scale='scores',mode='normal',center_axis=0):
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""" Principal Component Analysis.
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Performs PCA on given matrix and returns results in a dictionary.
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@ -49,7 +48,8 @@ def pca(a, aopt,scale='scores',mode='normal',center_axis=-1):
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Uses kernel speed-up if m>>n or m<<n.
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If residuals turn rank deficient, a lower number of component than given
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in input will be used. The number of components used is given in results-dict.
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in input will be used. The number of components used is given in
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results-dict.
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Examples
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--------
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@ -57,7 +57,7 @@ def pca(a, aopt,scale='scores',mode='normal',center_axis=-1):
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>>> import scipy,engines
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>>> a=scipy.asarray([[1,2,3],[2,4,5]])
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>>> dat=engines.pca(a, 2)
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>>> dat['expvar']
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>>> dat['expvarx']
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array([0.,99.8561562, 100.])
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"""
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@ -76,7 +76,6 @@ def pca(a, aopt,scale='scores',mode='normal',center_axis=-1):
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aopt = minimum(aopt, eff_rank)
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T = u*s
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s = s[:aopt]
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e = e[:aopt]
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T = T[:,:aopt]
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P = v[:,:aopt]
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@ -91,7 +90,6 @@ def pca(a, aopt,scale='scores',mode='normal',center_axis=-1):
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E = empty((aopt, m, n))
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ssq = []
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lev = []
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expvarx = empty((aopt, aopt+1))
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for ai in range(aopt):
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E[ai,:,:] = a - dot(T[:,:ai+1], P[:,:ai+1].T)
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ssq.append([(E[ai,:,:]**2).sum(0), (E[ai,:,:]**2).sum(1)])
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@ -99,9 +97,6 @@ def pca(a, aopt,scale='scores',mode='normal',center_axis=-1):
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lev.append([((s*T)**2).sum(1), (P**2).sum(1)])
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else:
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lev.append([(T**2).sum(1), ((s*P)**2).sum(1)])
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expvarx[ai,:] = r_[0, 100*e.cumsum()/e.sum()]
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else:
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# residuals
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E = a - dot(T, P.T)
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@ -113,7 +108,7 @@ def pca(a, aopt,scale='scores',mode='normal',center_axis=-1):
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else:
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lev = [(1./m)+((T/s)**2).sum(1), (1./n)+(P**2).sum(1)]
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# variances
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expvarx = r_[0, 100*e.cumsum()/e.sum()]
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expvarx = r_[0, 100*e.cumsum()/e.sum()][:aopt+1]
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return {'T':T, 'P':P, 'E':E, 'expvarx':expvarx, 'levx':lev, 'ssqx':ssq, 'aopt':aopt}
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@ -143,7 +138,7 @@ def pcr(a, b, aopt, scale='scores',mode='normal',center_axis=0):
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Center along given axis. If neg.: no centering (-inf,..., matrix modes)
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:SeeAlso:
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- pcr : other blm
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- pca : other blm
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- pls : other blm
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- lpls : other blm
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@ -161,8 +156,9 @@ def pcr(a, b, aopt, scale='scores',mode='normal',center_axis=0):
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>>> import scipy,engines
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>>> a=scipy.asarray([[1,2,3],[2,4,5]])
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>>> dat=engines.pca(a, 2)
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>>> dat['expvar']
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>>> b=scipy.asarray([[1,1],[2,3]])
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>>> dat=engines.pcr(a, 2)
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>>> dat['expvarx']
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array([0.,99.8561562, 100.])
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"""
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@ -171,12 +167,11 @@ def pcr(a, b, aopt, scale='scores',mode='normal',center_axis=0):
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b = b - expand_dims(b.mean(center_axis), center_axis)
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dat = pca(a, aopt=aopt, scale=scale, mode=mode, center_axis=center_axis)
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T = dat['T']
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weights = apply_along_axis(vnorm, 0, T)
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weights = apply_along_axis(vnorm, 0, T)**2
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if scale=='loads':
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# fixme: check weights
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Q = dot(b.T, T*weights**2)
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Q = dot(b.T, T*weights)
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else:
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Q = dot(b.T, T/weights**2)
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Q = dot(b.T, T/weights)
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if mode=='fast':
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dat.update({'Q':Q})
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@ -187,24 +182,69 @@ def pcr(a, b, aopt, scale='scores',mode='normal',center_axis=0):
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F[i,:,:] = b - dot(T[:,:i+1], Q[:,:i+1].T)
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else:
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F = b - dot(T, Q.T)
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#fixme: explained variance in Y + Y-var leverages
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dat.update({'Q':Q, 'F':F})
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expvary = r_[0, 100*((T**2).sum(0)*(Q**2).sum(0)/(b**2).sum()).cumsum()[:aopt]]
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#fixme: Y-var leverages
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dat.update({'Q':Q, 'F':F, 'expvary':expvary})
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return dat
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def pls(a, b, aopt=2, scale='scores', mode='normal', ab=None):
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def pls(a, b, aopt=2, scale='scores', mode='normal', ax_center=0, ab=None):
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"""Partial Least Squares Regression.
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Applies plsr to given matrices and returns results in a dictionary.
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Performs PLS on given matrix and returns results in a dictionary.
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:Parameters:
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a : array
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Data measurement matrix, (samples x variables)
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b : array
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Data response matrix, (samples x responses)
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aopt : int
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Number of components to use, aopt<=min(samples, variables)
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:Returns:
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results : dict
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keys -- values, T -- scores, P -- loadings, E -- residuals,
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levx -- leverages, ssqx -- sum of squares, expvarx -- cumulative
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explained variance of descriptors, expvary -- cumulative explained
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variance of responses, aopt -- number of components used
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:OtherParameters:
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mode : str
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Amount of info retained, ('fast', 'normal', 'detailed')
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center_axis : int
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Center along given axis. If neg.: no centering (-inf,..., matrix modes)
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:SeeAlso:
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- pca : other blm
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- pcr : other blm
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- lpls : other blm
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Notes
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-----
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Uses kernel speed-up if m>>n or m<<n.
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If residuals turn rank deficient, a lower number of component than given
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in input will be used. The number of components used is given in results-dict.
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Examples
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--------
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>>> import scipy,engines
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>>> a=scipy.asarray([[1,2,3],[2,4,5]])
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>>> b=scipy.asarray([[1,1],[2,3]])
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>>> dat=engines.pls(a, b, 2)
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>>> dat['expvarx']
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array([0.,99.8561562, 100.])
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Fast pls for calibration. Only inefficient for many Y-vars.
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"""
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m, n = a.shape
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m, n = m_shape(a)
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if ab!=None:
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mm, ll = m_shape(ab)
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mm, l = m_shape(ab)
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assert(m==mm)
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else:
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k, l = m_shape(b)
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assert(m==mm)
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assert(l==ll)
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W = empty((n, aopt))
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P = empty((n, aopt))
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R = empty((n, aopt))
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@ -217,13 +257,21 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', ab=None):
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for i in range(aopt):
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if ab.shape[1]==1:
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w = ab.reshape(n, l)
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w = w/vnorm(w)
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elif n<l:
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if has_sym:
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s, u = symeig(dot(ab.T, ab),range=[l,l],overwrite=True)
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else:
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u, s, vh = svd(dot(ab, ab.T))
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w = u[:,0]
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else:
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if has_sym:
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s, u = symeig(dot(ab.T, ab),range=[l,l],overwrite=True)
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else:
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u, s, vh = svd(dot(ab.T, ab))
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w = dot(ab, u[:,:1])
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w = w/vnorm(w)
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w = dot(ab, u)
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r = w.copy()
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if i>0: # recursive estimate to
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if i>0:
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for j in range(0, i, 1):
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r = r - dot(P[:,j].T, w)*R[:,j][:,newaxis]
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t = dot(a, r)
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@ -233,8 +281,6 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', ab=None):
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ab = ab - dot(p, q.T)*tt
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T[:,i] = t.ravel()
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W[:,i] = w.ravel()
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P[:,i] = p.ravel()
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R[:,i] = r.ravel()
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if mode=='fast' and i==aopt-1:
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if scale=='loads':
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@ -243,6 +289,8 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', ab=None):
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W = W*tnorm
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return {'T':T, 'W':W}
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P[:,i] = p.ravel()
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R[:,i] = r.ravel()
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Q[:,i] = q.ravel()
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B[i] = dot(R[:,:i+1], Q[:,:i+1].T)
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@ -272,14 +320,14 @@ def w_simpls(aat, b, aopt):
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"""
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bb = b.copy()
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m, m = aat.shape
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U = empty((m, aopt))
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U = empty((m, aopt)) # W
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T = empty((m, aopt))
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H = empty((m, aopt)) #just like W in simpls
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PROJ = empty((m, aopt)) #just like R in simpls
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H = empty((m, aopt)) # R
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PROJ = empty((m, aopt)) # P?
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for i in range(aopt):
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u, s, vh = svd(dot(dot(b.T, aat), b), full_matrices=0)
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u = dot(b, u[:,:1]) #y-factor scores
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q, s, vh = svd(dot(dot(b.T, aat), b), full_matrices=0)
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u = dot(b, q[:,:1]) #y-factor scores
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U[:,i] = u.ravel()
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t = dot(aat, u)
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t = t/vnorm(t)
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@ -293,6 +341,38 @@ def w_simpls(aat, b, aopt):
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return {'T':T, 'U':U, 'Q':C, 'H':H}
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def w_pls(aat, b, aopt):
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""" Pls for wide matrices.
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Fast pls for crossval, used in calc rmsep for wide X
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There is no P or W. T is normalised
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"""
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bb = b.copy()
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m, m = aat.shape
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U = empty((m, aopt)) # W
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T = empty((m, aopt))
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R = empty((m, aopt)) # R
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PROJ = empty((m, aopt)) # P?
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for i in range(aopt):
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if has_sym:
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pass
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else:
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q, s, vh = svd(dot(dot(b.T, aat), b), full_matrices=0)
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q = q[:,:1]
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u = dot(b , q) #y-factor scores
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U[:,i] = u.ravel()
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t = dot(aat, u)
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t = t/vnorm(t)
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T[:,i] = t.ravel()
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r = dot(aat, t) #score-weights
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R[:,i] = r.ravel()
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PROJ[:,: i+1] = dot(T[:,:i+1], inv(dot(T[:,:i+1].T, R[:,:i+1])) )
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if i<aopt:
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b = b - dot(PROJ[:,:i+1], dot(R[:,:i+1].T,b) )
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C = dot(bb.T, T)
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return {'T':T, 'U':U, 'Q':C, 'H':H}
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def bridge(a, b, aopt, scale='scores', mode='normal', r=0):
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"""Undeflated Ridged svd(X'Y)
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"""
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@ -18,6 +18,7 @@ def w_pls_gen(aat,b,n_blocks=None,center=True,index_out=False):
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"""
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m, n = aat.shape
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index = randperm(m)
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if n_blocks==None: n_blocks = m
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nValuesInBlock = m/n_blocks
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if n_blocks==m:
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index = arange(m)
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@ -31,7 +32,7 @@ def w_pls_gen(aat,b,n_blocks=None,center=True,index_out=False):
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b_out = b[out,:]
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if center:
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aat_in, mn = outerprod_centering(aat_in)
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aat_out = aat_out - mn
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b_in = b_in - b_in.mean(0) # b_in + b_out/(b_in.shape[0])
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if index_out:
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yield aat_in,aat_out,b_in,b_out,out
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else:
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@ -217,7 +218,7 @@ def outerprod_centering(aat, ret_mn=True):
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mn_a = h + h.T # beauty of broadcasting
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aatc = aat - mn_a
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if ret_mn:
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return aatc, mn_a
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return aatc, h
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return aatc
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@ -61,7 +61,6 @@ def w_pls_cv_val(X, Y, amax, n_blocks=None, algo='simpls'):
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V = w_pls_gen(XXt, Y, n_blocks=n_blocks, center=True)
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for Din, Doi, Yin, Yout in V:
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ym = -sum(Yout, 0)[newaxis]/(1.0*Yin.shape[0])
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Yin = Yin - ym
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PRESS[:,0] = PRESS[:,0] + ((Yout - ym)**2).sum(0)
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if algo=='simpls':
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dat = w_simpls(Din, Yin, amax)
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@ -76,13 +75,12 @@ def w_pls_cv_val(X, Y, amax, n_blocks=None, algo='simpls'):
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E = Yout[:,j][:,newaxis] - TQ
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E = E + sum(E, 0)/Din.shape[0]
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PRESS[j,1:] = PRESS[j,1:] + sum(E**2, 0)
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Yhat = Y - dot(That,Q.T)
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rmsep = sqrt(PRESS/Y.shape[0])
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aopt = find_aopt_from_sep(rmsep)
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return rmsep, Yhat, aopt
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#Yhat = Yin - dot(That,Q.T)
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msep = PRESS/(Y.shape[0])
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aopt = find_aopt_from_sep(msep)
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return sqrt(msep)
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def pls_val(X, Y, amax=2, n_blocks=10, algo='pls', metric=None):
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k, l = m_shape(Y)
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PRESS = zeros((l, amax+1), dtype='<f8')
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EE = zeros((amax, k, l), dtype='<f8')
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@ -105,9 +103,10 @@ def pls_val(X, Y, amax=2, n_blocks=10, algo='pls', metric=None):
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EE[a,out,:] = E
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PRESS[:,a+1] = PRESS[:,a+1] + sum(E**2,0)
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rmsep = sqrt(PRESS/(k-1.))
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aopt = find_aopt_from_sep(rmsep)
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return rmsep, Yhat, aopt
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#rmsep = sqrt(PRESS/(k-1.))
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msep = PRESS
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aopt = find_aopt_from_sep(msep)
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return msep, Yhat, aopt
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def lpls_val(X, Y, Z, a_max=2, nsets=None,alpha=.5):
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"""Performs crossvalidation to get generalisation error in lpls"""
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@ -270,7 +269,7 @@ def lpls_jk(X, Y, Z, a_max, nsets=None, alpha=.5):
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def find_aopt_from_sep(sep, method='75perc'):
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"""Returns an estimate of optimal number of components from rmsecv.
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"""
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sep = sep.copy()
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if method=='vanilla':
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# min rmsep
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rmsecv = sqrt(sep.mean(0))
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@ -282,7 +281,7 @@ def find_aopt_from_sep(sep, method='75perc'):
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med = median(sep)
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prc_75 = []
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for col in sep.T:
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col.sort()
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col.sort() #this is inplace -> ruins sep, so we are doing a copy
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prc_75.append(col[int(ind)])
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prc_75 = array(prc_75)
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for i in range(1, sep.shape[1], 1):
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