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@ -693,13 +693,13 @@ class LplsOptions(Options):
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opt['mode'] = 'normal' # how much info to calculate
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opt['amax'] = 10
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opt['aopt'] = 3
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opt['xz_alpha'] = 0.4
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opt['xz_alpha'] = 0.6
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opt['auto_aopt'] = False
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opt['center'] = True
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opt['center_mth'] = [2, 2, 1]
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opt['center_mth'] = [2, 0, 2]
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opt['scale'] = 'scores'
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opt['calc_conf'] = True
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opt['n_sets'] = 75
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opt['calc_conf'] = False
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opt['n_sets'] = 7
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opt['strict'] = False
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opt['p_center'] = 'med'
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opt['alpha'] = .3
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@ -1,6 +1,6 @@
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from scipy import zeros,zeros_like,sqrt,dot,trace,sign,round_,argmax,\
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sort,ravel,newaxis,asarray,diag,sum,outer,argsort,arange,ones_like,\
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all,apply_along_axis,eye
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all,apply_along_axis,eye,atleast_2d
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from scipy.linalg import svd,inv,norm,det,sqrtm
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from scipy.stats import mean,median
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from cx_utils import mat_center
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@ -26,8 +26,8 @@ def hotelling(Pcv, P, p_center='med', cov_center='med',
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m, n = P.shape
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n_sets, n, amax = Pcv.shape
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# allocate
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T_sq = empty((n, ),dtype='f')
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Cov_i = zeros((n, amax, amax),dtype='f')
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T_sq = empty((n, ),dtype='d')
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Cov_i = zeros((n, amax, amax),dtype='d')
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# rotate sub_models to full model
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if crot:
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@ -56,10 +56,12 @@ def hotelling(Pcv, P, p_center='med', cov_center='med',
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reg_cov = (1. - alpha)*Cov_i + alpha*Cov
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for i in xrange(n):
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Pc = P_ctr[i,:][:,newaxis]
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#Pc = P_ctr[i,:][:,newaxis]
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Pc = P_ctr[i,:]
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sigma = reg_cov[i]
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#T_sq[i] = sqrt(dot(dot(Pc.T, inv(sigma)), Pc).ravel())
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T_sq[i] = dot(dot(Pc.T, inv(sigma)), Pc).ravel()
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# T_sq[i] = (dot(Pc, inv(sigma) )*Pc).sum() #slow
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T_sq[i] = dot(dot(Pc, inv(sigma)), Pc) # dont need to care about transposes
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#T_sq[i] = dot(dot(Pc.T, inv(sigma)), Pc).ravel()
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return T_sq
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def procrustes(A, B, strict=True, center=False, verbose=False):
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@ -147,10 +149,10 @@ def pls_qvals(a, b, aopt=None, alpha=.3,
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tsq_full = hotelling(Wcv, dat['W'], p_center=p_center,
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alpha=alpha, crot=crot, strict=strict,
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cov_center=cov_center)
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t0 = time.time()
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#t0 = time.time()
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Vs = shuffle_1d(bc, n_iter, axis=0)
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for i, b_shuff in enumerate(Vs):
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t1 = time.time()
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#t1 = time.time()
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if algo=='bridge':
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dat = bridge(ac, b_shuff, aopt, 'loads','fast')
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else:
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@ -159,23 +161,10 @@ def pls_qvals(a, b, aopt=None, alpha=.3,
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TSQ[:,i] = hotelling(Wcv, dat['W'], p_center=p_center,
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alpha=alpha, crot=crot, strict=strict,
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cov_center=cov_center)
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print time.time() - t1
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sort_index = argsort(tsq_full)[::-1]
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back_sort_index = sort_index.argsort()
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print time.time() - t0
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# count false positives
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tsq_full_sorted = tsq_full.take(sort_index)
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for i in xrange(n_iter):
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for j in xrange(n):
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n_false[j,i] = sum(TSQ[:,i]>=tsq_full[j]) # number of false pos. genes (0-n)
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false_pos = median(n_false, 1)
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ll = arange(1, len(false_pos)+1, 1)
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sort_qval = false_pos.take(sort_index)/ll
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qval = false_pos/ll.take(back_sort_index)
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print time.time() - t0
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#return qval, false_pos, TSQ, tsq_full
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return qval
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#print time.time() - t1
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return fdr(tsq_full, TSQ, median)
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def ensure_strict(C, only_flips=True):
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"""Ensure that a rotation matrix does only 90 degree rotations.
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@ -267,6 +256,7 @@ def pls_qvals_II(a, b, aopt=None, center=True, alpha=.3,
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qval = false_pos/ll.take(back_sort_index)
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print time.time() - t0
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#return qval, false_pos, TSQ, tsq_full
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return qval
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def leverage(aopt=1,*args):
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@ -333,3 +323,107 @@ def vnorm(x):
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This is considerably faster than linalg.norm
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"""
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return sqrt(dot(x,x.conj()))
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def mahalanobis(a, loc=None, acov=None, invcov=None):
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"""Returns the distance of each observation in a
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from the location estimate (loc) of the data,
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relative to the shape of the data.
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a : data matrix (n observations in rows, p variables in columns)
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loc : location estimate of the data (p-dimensional vector)
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covmat or invcov : scatter estimate of the data or the inverse of the scatter estimate (pxp matrix)
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:Returns:
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A vector containing the distances of all the observations to locvct.
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"""
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n, p = a.shape
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if loc==None:
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loc = a.mean(0)
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loc = atleast_2d(loc)
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if loc.shape[1]==1:
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loc = loc.T; #ensure rowvector
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assert(loc.shape[1]==p)
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xc = a - loc
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if acov==None and invcov==None:
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acov = dot(xc.T, xc)
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if invcov != None:
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covmat = atleast_2d(invcov)
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if min(covmat.shape)==1:
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covmat = diag(invcov.ravel())
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else:
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covmat = atleast_2d(acov)
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if min(covmat.shape)==1:
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covmat = diag(covmat.ravel())
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covmat = inv(covmat)
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# mdist = diag(dot(dot(xc, covmat),xc.T))
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mdist = (dot(xc, covmat)*xc).sum(1)
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return mdist
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def lpls_qvals(a, b, c, aopt=None, alpha=.3, zx_alpha=.5, n_iter=20,center=True,
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sim_method='shuffle',p_center='med', cov_center='med',crot=True, strict=False):
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"""Returns qvals for l-pls model.
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input:
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a -- data matrix
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b -- data matrix
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c -- data matrix
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aopt -- scalar, opt. number of components
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alpha -- [0,1] regularisation parameter for T2-test
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xz_alpha -- [0,1] how much z info to include
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n_iter -- number of permutations
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sim_method -- permutation method ['shuffle']
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p_center -- location estimator for sub models ['med']
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cov_center -- location estimator for covariance of submodels ['med']
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crot -- bool, use rotations of sub models?
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strict -- bool, use stict (rot/flips only) rotations?
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"""
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m, n = a.shape
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TSQ = zeros((n, n_iter), dtype='d') # (nvars x n_subsets)
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n_false = zeros((n, n_iter), dtype='d')
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# Full model
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dat = lpls(a, b, c, aopt, scale='loads')
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Wcv = lpls_jk(a, b, c ,aopt, n_blocks=None, algo=algo,center=center)
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tsq_x = hotelling(Wcv, dat['W'], p_center=p_center,alpha=alpha, crot=crot, strict=strict,
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cov_center=cov_center)
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Lcv = lpls_jk(a, b, c ,aopt, n_blocks=None, algo=algo,center=center)
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tsq_z = hotelling(Lcv, dat['L'], p_center=p_center,alpha=alpha, crot=crot, strict=strict,
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cov_center=cov_center)
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# Perturbations
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t0 = time.time()
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Vs = shuffle_1d(b, n_iter, axis=0)
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for i, b_shuff in enumerate(Vs):
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t1 = time.time()
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dat = pls(ac, b_shuff, aopt, 'loads', 'fast')
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Wcv = pls_jkW(a, b_shuff, aopt, n_blocks=None, algo=algo)
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TSQ[:,i] = hotelling(Wcv, dat['W'], p_center=p_center,
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alpha=alpha, crot=crot, strict=strict,
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cov_center=cov_center)
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print time.time() - t1
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return fdr(tsq_full, TSQ, median)
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def fdr(tsq, tsqp, loc_method=median):
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n, = tsq.shape
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k, m = tsqp.shape
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assert(n==k)
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n_false = empty((n, m), 'd')
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sort_index = argsort(tsq)[::-1]
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r_index = argsort(sort_index)
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for i in xrange(m):
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for j in xrange(n):
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n_false[j,i] = (tsqp[:,i]>tsq[j]).sum()
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fp = loc_method(n_false,1)
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n_signif = (arange(n) + 1.0)[r_index]
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fd_rate = fp/n_signif
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return fd_rate
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@ -4,15 +4,21 @@ There is almost no typechecking of any kind here, just focus on speed
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"""
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import math
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import warnings
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from scipy.linalg import svd,inv
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from scipy import dot,empty,eye,newaxis,zeros,sqrt,diag,\
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apply_along_axis,mean,ones,randn,empty_like,outer,r_,c_,\
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rand,sum,cumsum,matrix, expand_dims,minimum,where,arange
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has_sym=True
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rand,sum,cumsum,matrix, expand_dims,minimum,where,arange,inner,tile
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has_sym = True
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has_arpack = True
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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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try:
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from scipy.sandbox import arpack
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except:
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has_arpack = False
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def pca(a, aopt,scale='scores',mode='normal',center_axis=0):
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@ -45,7 +51,6 @@ def pca(a, aopt,scale='scores',mode='normal',center_axis=0):
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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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@ -101,6 +106,7 @@ def pca(a, aopt,scale='scores',mode='normal',center_axis=0):
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else:
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# residuals
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E = a - dot(T, P.T)
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#E = a
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SEP = E**2
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ssq = [SEP.sum(0), SEP.sum(1)]
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# leverages
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@ -256,7 +262,8 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', center_axis=-1, ab=None):
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Q = empty((l, aopt))
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T = empty((m, aopt))
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B = empty((aopt, n, l))
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tt = empty((aopt,))
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if ab==None:
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ab = dot(a.T, b)
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for i in range(aopt):
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@ -265,10 +272,10 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', center_axis=-1, ab=None):
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w = w/vnorm(w)
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elif n<l: # more yvars than xvars
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if has_sym:
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s, u = symeig(dot(ab, ab.T),range=[l,l],overwrite=True)
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s, w = symeig(dot(ab, ab.T),range=[n,n],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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w, s, vh = svd(dot(ab, ab.T))
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w = w[:,:1]
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else: # standard wide xdata
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if has_sym:
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s, q = symeig(dot(ab.T, ab),range=[l,l],overwrite=True)
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@ -283,16 +290,16 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', center_axis=-1, ab=None):
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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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tt = vnorm(t)**2
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p = dot(a.T, t)/tt
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q = dot(r.T, ab).T/tt
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ab = ab - dot(p, q.T)*tt
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tt[i] = tti = dot(t.T, t).ravel()
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p = dot(a.T, t)/tti
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q = dot(r.T, ab).T/tti
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ab = ab - dot(p, q.T)*tti
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T[:,i] = t.ravel()
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W[:,i] = w.ravel()
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if mode=='fast' and i==aopt-1:
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if scale=='loads':
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tnorm = apply_along_axis(vnorm, 0, T)
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tnorm = sqrt(tt)
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T = T/tnorm
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W = W*tnorm
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return {'T':T, 'W':W}
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@ -300,26 +307,54 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', center_axis=-1, ab=None):
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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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#B[i] = dot(R[:,:i+1], Q[:,:i+1].T)
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qnorm = apply_along_axis(vnorm, 0, Q)
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tnorm = sqrt(tt)
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pp = (P**2).sum(0)
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if mode=='detailed':
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E = empty((aopt, m, n))
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F = empty((aopt, k, l))
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for i in range(1, aopt+1, 1):
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E[i-1] = a - dot(T[:,:i], P[:,:i].T)
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ssqx, ssqy = [], []
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leverage = empty((aopt, m))
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h2x = [] #hotellings T^2
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h2y = []
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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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F[i-1] = b - dot(T[:,:i], Q[:,:i].T)
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ssqx.append([(E[ai,:,:]**2).mean(0), (E[ai,:,:]**2).mean(1)])
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ssqy.append([(F[ai,:,:]**2).mean(0), (F[ai,:,:]**2).mean(1)])
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leverage[ai,:] = 1./m + ((T[:,:ai+1]/tnorm[:ai+1])**2).sum(1)
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h2y.append(1./k + ((Q[:,:ai+1]/qnorm[:ai+1])**2).sum(1))
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else:
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E = a - dot(T[:,:aopt], P[:,:aopt].T)
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F = b - dot(T[:,:aopt], Q[:,:aopt].T)
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# residuals
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E = a - dot(T, P.T)
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F = b - dot(T, Q.T)
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sepx = E**2
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ssqx = [sepx.sum(0), sepx.sum(1)]
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sepy = F**2
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ssqy = [sepy.sum(0), sepy.sum(1)]
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# leverage
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leverage = 1./m + ((T/tnorm)**2).sum(1)
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h2x = []
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h2y = []
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# variances
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tp= tt*pp
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tq = tt*qnorm*qnorm
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expvarx = r_[0, 100*tp/(a*a).sum()]
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expvary = r_[0, 100*tq/(b*b).sum()]
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if scale=='loads':
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tnorm = apply_along_axis(vnorm, 0, T)
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T = T/tnorm
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W = W*tnorm
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Q = Q*tnorm
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P = P*tnorm
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return {'B':B, 'Q':Q, 'P':P, 'T':T, 'W':W, 'R':R, 'E':E, 'F':F}
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return {'Q':Q, 'P':P, 'T':T, 'W':W, 'R':R, 'E':E, 'F':F,
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'expvarx':expvarx, 'expvary':expvary, 'ssqx':ssqx, 'ssqy':ssqy,
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'leverage':leverage, 'h2':h2x}
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def w_simpls(aat, b, aopt):
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""" Simpls for wide matrices.
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@ -423,16 +458,6 @@ def bridge(a, b, aopt, scale='scores', mode='normal', r=0):
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else: #normal
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F = b - dot(a, B[-1])
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E = a - dot(T, W.T)
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# leverages
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# fixme: probably need an orthogonal basis for row-space leverage
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# T (scores) are not orthogonal
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# Using a qr decomp to get an orthonormal basis for row-space
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#Tq = qr(T)[0]
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#s_lev,v_lev = leverage(aopt,Tq,W)
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# explained variance
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#var_x, exp_var_x = variances(a,T,W)
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#qnorm = apply_along_axis(norm, 0, Q)
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#var_y, exp_var_y = variances(b,U,Q/qnorm)
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if scale=='loads':
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T = T/tnorm
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@ -442,7 +467,7 @@ def bridge(a, b, aopt, scale='scores', mode='normal', r=0):
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return {'B':B, 'W':W, 'T':T, 'Q':Q, 'E':E, 'F':F, 'U':U, 'P':W}
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def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', scale='scores', verbose=False):
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def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], scale='scores', verbose=False):
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""" L-shaped Partial Least Sqaures Regression by the nipals algorithm.
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(X!Z)->Y
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@ -464,6 +489,9 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', sca
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evx : X-explained variance
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evy : Y-explained variance
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evz : Z-explained variance
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mnx : X location
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mny : Y location
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mnz : Z location
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:Notes:
|
||||
|
||||
@ -471,12 +499,12 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', sca
|
||||
if mean_ctr!=None:
|
||||
xctr, yctr, zctr = mean_ctr
|
||||
X, mnX = center(X, xctr)
|
||||
Y, mnY = center(Y, xctr)
|
||||
Y, mnY = center(Y, yctr)
|
||||
Z, mnZ = center(Z, zctr)
|
||||
|
||||
varX = pow(X, 2).sum()
|
||||
varY = pow(Y, 2).sum()
|
||||
varZ = pow(Z, 2).sum()
|
||||
varX = (X**2).sum()
|
||||
varY = (Y**2).sum()
|
||||
varZ = (Z**2).sum()
|
||||
|
||||
m, n = X.shape
|
||||
k, l = Y.shape
|
||||
@ -491,36 +519,40 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', sca
|
||||
K = empty((o, a_max))
|
||||
L = empty((u, a_max))
|
||||
B = empty((a_max, n, l))
|
||||
b0 = empty((a_max, m, l))
|
||||
#b0 = empty((a_max, 1, l))
|
||||
var_x = empty((a_max,))
|
||||
var_y = empty((a_max,))
|
||||
var_z = empty((a_max,))
|
||||
|
||||
|
||||
MAX_ITER = 250
|
||||
LIM = 1e-1
|
||||
for a in range(a_max):
|
||||
if verbose:
|
||||
print "\n Working on comp. %s" %a
|
||||
print "\nWorking on comp. %s" %a
|
||||
u = Y[:,:1]
|
||||
diff = 1
|
||||
MAX_ITER = 200
|
||||
lim = 1e-16
|
||||
niter = 0
|
||||
while (diff>lim and niter<MAX_ITER):
|
||||
while (diff>LIM and niter<MAX_ITER):
|
||||
niter += 1
|
||||
u1 = u.copy()
|
||||
w = dot(X.T, u)
|
||||
w = w/sqrt(dot(w.T, w))
|
||||
#w = w/dot(w.T, w)
|
||||
l = dot(Z, w)
|
||||
k = dot(Z.T, l)
|
||||
k = k/sqrt(dot(k.T, k))
|
||||
#k = k/dot(k.T, k)
|
||||
w = alpha*k + (1-alpha)*w
|
||||
#print sqrt(dot(w.T, w))
|
||||
w = w/sqrt(dot(w.T, w))
|
||||
t = dot(X, w)
|
||||
c = dot(Y.T, t)
|
||||
c = c/sqrt(dot(c.T, c))
|
||||
u = dot(Y, c)
|
||||
diff = abs(u1 - u).max()
|
||||
diff = dot((u-u1).T, (u-u1))
|
||||
if verbose:
|
||||
print "Converged after %s iterations" %niter
|
||||
print "Error: %.2E" %diff
|
||||
tt = dot(t.T, t)
|
||||
p = dot(X.T, t)/tt
|
||||
q = dot(Y.T, t)/tt
|
||||
@ -543,7 +575,8 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', sca
|
||||
var_z[a] = pow(Z, 2).sum()
|
||||
|
||||
B[a] = dot(dot(W[:,:a+1], inv(dot(P[:,:a+1].T, W[:,:a+1]))), Q[:,:a+1].T)
|
||||
b0[a] = mnY - dot(mnX, B[a])
|
||||
#b0[a] = mnY - dot(mnX, B[a])
|
||||
|
||||
|
||||
# variance explained
|
||||
evx = 100.0*(1 - var_x/varX)
|
||||
@ -558,7 +591,7 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', sca
|
||||
L = L*knorm
|
||||
K = K/knorm
|
||||
|
||||
return {'T':T, 'W':W, 'P':P, 'Q':Q, 'U':U, 'L':L, 'K':K, 'B':B, 'b0':b0, 'evx':evx, 'evy':evy, 'evz':evz}
|
||||
return {'T':T, 'W':W, 'P':P, 'Q':Q, 'U':U, 'L':L, 'K':K, 'B':B, 'evx':evx, 'evy':evy, 'evz':evz,'mnx': mnX, 'mny': mnY, 'mnz': mnZ}
|
||||
|
||||
|
||||
|
||||
@ -670,7 +703,8 @@ def nipals_pls(X, Y, a_max, alpha=.7, ax_center=0, mode='normal', scale='scores'
|
||||
W = W*tnorm
|
||||
Q = Q*tnorm
|
||||
|
||||
return {'T':T, 'W':W, 'P':P, 'Q':Q, 'U':U, 'B':B, 'b0':b0, 'evx':evx, 'evy':evy}
|
||||
return {'T':T, 'W':W, 'P':P, 'Q':Q, 'U':U, 'B':B, 'b0':b0, 'evx':evx, 'evy':evy,
|
||||
'mnx': mnX, 'mny': mnY, 'xc': X, 'yc': Y}
|
||||
|
||||
|
||||
########### Helper routines #########
|
||||
@ -691,6 +725,11 @@ def esvd(data, amax=None):
|
||||
m, n = data.shape
|
||||
if m>=n:
|
||||
kernel = dot(data.T, data)
|
||||
if has_arpack:
|
||||
if amax==None:
|
||||
amax = n
|
||||
s, v = arpack.eigen_symmetric(kernel,k=amax, which='LM',
|
||||
maxiter=200,tol=1e-5)
|
||||
if has_sym:
|
||||
if amax==None:
|
||||
amax = n
|
||||
@ -728,16 +767,34 @@ def vnorm(x):
|
||||
return math.sqrt(dot(x.T, x))
|
||||
|
||||
def center(a, axis):
|
||||
# 0 = col center, 1 = row center, 2 = double center
|
||||
# -1 = nothing
|
||||
# 0 = col center, 1 = row center, 2 = double center
|
||||
# -1 = nothing
|
||||
|
||||
# check if we have a vector
|
||||
is_vec = len(a.shape)==1
|
||||
if not is_vec:
|
||||
is_vec = a.shape[0]==1 or a.shape[1]==1
|
||||
if is_vec:
|
||||
if axis==2:
|
||||
warnings.warn("Double centering of vecor ignored, using ordinary centering")
|
||||
if axis==-1:
|
||||
mn = 0
|
||||
else:
|
||||
mn = a.mean()
|
||||
return a - mn, mn
|
||||
# !!!fixme: use broadcasting
|
||||
if axis==-1:
|
||||
mn = zeros((a.shape[1],))
|
||||
mn = zeros((1,a.shape[1],))
|
||||
#mn = tile(mn, (a.shape[0], 1))
|
||||
elif axis==0:
|
||||
mn = a.mean(0)
|
||||
mn = a.mean(0)[newaxis]
|
||||
#mn = tile(mn, (a.shape[0], 1))
|
||||
elif axis==1:
|
||||
mn = a.mean(1)[:,newaxis]
|
||||
#mn = tile(mn, (1, a.shape[1]))
|
||||
elif axis==2:
|
||||
mn = a.mean(0) + a.mean(1)[:,newaxis] - a.mean()
|
||||
mn = a.mean(0)[newaxis] + a.mean(1)[:,newaxis] - a.mean()
|
||||
return a - mn , a.mean(0)[newaxis]
|
||||
else:
|
||||
raise IOError("input error: axis must be in [-1,0,1,2]")
|
||||
|
||||
@ -755,3 +812,64 @@ def scale(a, axis):
|
||||
|
||||
return a - sc, sc
|
||||
|
||||
|
||||
|
||||
## #PCA CALCS
|
||||
|
||||
## % Calculate Q limit using unused eigenvalues
|
||||
## temp = diag(s);
|
||||
## if n < m
|
||||
## emod = temp(lv+1:n,:);
|
||||
## else
|
||||
## emod = temp(lv+1:m,:);
|
||||
## end
|
||||
## th1 = sum(emod);
|
||||
## th2 = sum(emod.^2);
|
||||
## th3 = sum(emod.^3);
|
||||
## h0 = 1 - ((2*th1*th3)/(3*th2^2));
|
||||
## if h0 <= 0.0
|
||||
## h0 = .0001;
|
||||
## disp(' ')
|
||||
## disp('Warning: Distribution of unused eigenvalues indicates that')
|
||||
## disp(' you should probably retain more PCs in the model.')
|
||||
## end
|
||||
## q = th1*(((1.65*sqrt(2*th2*h0^2)/th1) + 1 + th2*h0*(h0-1)/th1^2)^(1/h0));
|
||||
## disp(' ')
|
||||
## disp('The 95% Q limit is')
|
||||
## disp(q)
|
||||
## if plots >= 1
|
||||
## lim = [q q];
|
||||
## plot(scl,res,scllim,lim,'--b')
|
||||
## str = sprintf('Process Residual Q with 95 Percent Limit Based on %g PC Model',lv);
|
||||
## title(str)
|
||||
## xlabel('Sample Number')
|
||||
## ylabel('Residual')
|
||||
## pause
|
||||
## end
|
||||
## % Calculate T^2 limit using ftest routine
|
||||
## if lv > 1
|
||||
## if m > 300
|
||||
## tsq = (lv*(m-1)/(m-lv))*ftest(.95,300,lv,2);
|
||||
## else
|
||||
## tsq = (lv*(m-1)/(m-lv))*ftest(.95,m-lv,lv,2);
|
||||
## end
|
||||
## disp(' ')
|
||||
## disp('The 95% T^2 limit is')
|
||||
## disp(tsq)
|
||||
## % Calculate the value of T^2 by normalizing the scores to
|
||||
## % unit variance and summing them up
|
||||
## if plots >= 1.0
|
||||
## temp2 = scores*inv(diag(ssq(1:lv,2).^.5));
|
||||
## tsqvals = sum((temp2.^2)');
|
||||
## tlim = [tsq tsq];
|
||||
## plot(scl,tsqvals,scllim,tlim,'--b')
|
||||
## str = sprintf('Value of T^2 with 95 Percent Limit Based on %g PC Model',lv);
|
||||
## title(str)
|
||||
## xlabel('Sample Number')
|
||||
## ylabel('Value of T^2')
|
||||
## end
|
||||
## else
|
||||
## disp('T^2 not calculated when number of latent variables = 1')
|
||||
## tsq = 1.96^2;
|
||||
## end
|
||||
|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
"""This module implements some common validation schemes from pca and pls.
|
||||
"""
|
||||
from scipy import ones,mean,sqrt,dot,newaxis,zeros,sum,empty,\
|
||||
apply_along_axis,eye,kron,array,sort,zeros_like,argmax
|
||||
apply_along_axis,eye,kron,array,sort,zeros_like,argmax,atleast_2d
|
||||
from scipy.stats import median
|
||||
from scipy.linalg import triu,inv,svd,norm
|
||||
|
||||
@ -9,7 +9,7 @@ from select_generators import w_pls_gen,w_pls_gen_jk,pls_gen,pca_gen,diag_pert
|
||||
from engines import w_simpls,pls,bridge,pca,nipals_lpls
|
||||
from cx_utils import m_shape
|
||||
|
||||
def w_pls_cv_val(X, Y, amax, n_blocks=None, algo='simpls'):
|
||||
def w_pls_cv_val(X, Y, amax, n_blocks=None):
|
||||
"""Returns rmsep and aopt for pls tailored for wide X.
|
||||
|
||||
The root mean square error of cross validation is calculated
|
||||
@ -62,12 +62,10 @@ def w_pls_cv_val(X, Y, amax, n_blocks=None, algo='simpls'):
|
||||
for Din, Doi, Yin, Yout in V:
|
||||
ym = -sum(Yout, 0)[newaxis]/(1.0*Yin.shape[0])
|
||||
PRESS[:,0] = PRESS[:,0] + ((Yout - ym)**2).sum(0)
|
||||
if algo=='simpls':
|
||||
dat = w_simpls(Din, Yin, amax)
|
||||
Q, U, H = dat['Q'], dat['U'], dat['H']
|
||||
That = dot(Doi, dot(U, inv(triu(dot(H.T, U))) ))
|
||||
else:
|
||||
raise NotImplementedError
|
||||
|
||||
dat = w_simpls(Din, Yin, amax)
|
||||
Q, U, H = dat['Q'], dat['U'], dat['H']
|
||||
That = dot(Doi, dot(U, inv(triu(dot(H.T, U))) ))
|
||||
|
||||
Yhat = []
|
||||
for j in range(l):
|
||||
@ -78,7 +76,7 @@ def w_pls_cv_val(X, Y, amax, n_blocks=None, algo='simpls'):
|
||||
#Yhat = Yin - dot(That,Q.T)
|
||||
msep = PRESS/(Y.shape[0])
|
||||
aopt = find_aopt_from_sep(msep)
|
||||
return sqrt(msep)
|
||||
return sqrt(msep), aopt
|
||||
|
||||
def pls_val(X, Y, amax=2, n_blocks=10, algo='pls'):
|
||||
k, l = m_shape(Y)
|
||||
@ -108,29 +106,54 @@ def pls_val(X, Y, amax=2, n_blocks=10, algo='pls'):
|
||||
aopt = find_aopt_from_sep(msep)
|
||||
return msep, Yhat, aopt
|
||||
|
||||
def lpls_val(X, Y, Z, a_max=2, nsets=None,alpha=.5):
|
||||
def lpls_val(X, Y, Z, a_max=2, nsets=None,alpha=.5, mean_ctr=[2,0,2]):
|
||||
"""Performs crossvalidation to get generalisation error in lpls"""
|
||||
assert(nsets<=X.shape[0])
|
||||
|
||||
cv_iter = pls_gen(X, Y, n_blocks=nsets,center=False,index_out=True)
|
||||
k, l = Y.shape
|
||||
Yhat = empty((a_max,k,l), 'd')
|
||||
Yc = empty((k, l), 'd')
|
||||
Yhat = empty((a_max, k, l), 'd')
|
||||
Yhatc = empty((a_max, k, l), 'd')
|
||||
sep2 = empty((a_max, k, l), 'd')
|
||||
for i, (xcal,xi,ycal,yi,ind) in enumerate(cv_iter):
|
||||
dat = nipals_lpls(xcal,ycal,Z,
|
||||
a_max=a_max,
|
||||
alpha=alpha,
|
||||
mean_ctr=[2,0,1],
|
||||
mean_ctr=mean_ctr,
|
||||
verbose=False)
|
||||
|
||||
B = dat['B']
|
||||
b0 = dat['b0']
|
||||
#b0 = dat['b0']
|
||||
for a in range(a_max):
|
||||
Yhat[a,ind,:] = b0[a][0][0] + dot(xi-xcal.mean(0), B[a])
|
||||
Yhat_class = zeros_like(Yhat)
|
||||
for a in range(a_max):
|
||||
for i in range(k):
|
||||
Yhat_class[a,i,argmax(Yhat[a,i,:])]=1.0
|
||||
class_err = 100*((Yhat_class+Y)==2).sum(1)/Y.sum(0).astype('d')
|
||||
if mean_ctr[0] in [0, 2]:
|
||||
xi = xi - dat['mnx']
|
||||
else:
|
||||
xi = xi - xi.mean(1)[:,newaxis] #???: cheating?
|
||||
if mean_ctr[1] in [0, 2]:
|
||||
ym = dat['mny']
|
||||
else:
|
||||
ym = yi.mean(1)[:,newaxis] #???: check this
|
||||
|
||||
Yhat[a,ind,:] = atleast_2d(ym + dot(xi, B[a]))
|
||||
#Yhat[a,ind,:] = atleast_2d(b0[a] + dot(xi, B[a]))
|
||||
|
||||
# todo: need a better support for class validation
|
||||
y_is_class = Y.dtype.char.lower() in ['i','p', 'b', 'h','?']
|
||||
print Y.dtype.char
|
||||
if y_is_class:
|
||||
Yhat_class = zeros_like(Yhat)
|
||||
for a in range(a_max):
|
||||
for i in range(k):
|
||||
Yhat_class[a,i,argmax(Yhat[a,i,:])] = 1.0
|
||||
class_err = 100*((Yhat_class+Y)==2).sum(1)/Y.sum(0).astype('d')
|
||||
|
||||
sep = (Y - Yhat)**2
|
||||
rmsep = sqrt(sep.mean(1))
|
||||
rmsep = sqrt(sep.mean(1)).T
|
||||
#rmsep2 = sqrt(sep2.mean(1))
|
||||
|
||||
aopt = find_aopt_from_sep(rmsep)
|
||||
|
||||
return rmsep, Yhat, aopt
|
||||
|
||||
def pca_alter_val(a, amax, n_sets=10, method='diag'):
|
||||
@ -247,7 +270,7 @@ def pca_jkP(a, aopt, n_blocks=None):
|
||||
return PP
|
||||
|
||||
|
||||
def lpls_jk(X, Y, Z, a_max, nsets=None, alpha=.5):
|
||||
def lpls_jk(X, Y, Z, a_max, nsets=None, xz_alpha=.5, mean_ctr=[2,0,2]):
|
||||
cv_iter = pls_gen(X, Y, n_blocks=nsets,center=False,index_out=False)
|
||||
m, n = X.shape
|
||||
k, l = Y.shape
|
||||
@ -258,8 +281,8 @@ def lpls_jk(X, Y, Z, a_max, nsets=None, alpha=.5):
|
||||
WWz = empty((nsets, o, a_max), 'd')
|
||||
#WWy = empty((nsets, l, a_max), 'd')
|
||||
for i, (xcal,xi,ycal,yi) in enumerate(cv_iter):
|
||||
dat = nipals_lpls(xcal,ycal,Z,a_max=a_max,alpha=alpha,
|
||||
mean_ctr=[2,0,1],scale='loads',verbose=False)
|
||||
dat = nipals_lpls(xcal,ycal,Z,a_max=a_max,alpha=xz_alpha,
|
||||
mean_ctr=mean_ctr,scale='loads',verbose=False)
|
||||
WWx[i,:,:] = dat['W']
|
||||
WWz[i,:,:] = dat['L']
|
||||
#WWy[i,:,:] = dat['Q']
|
||||
|
||||
Reference in New Issue
Block a user