# Statistical Learning¶

ants.sparse_decom2(inmatrix, inmask=(None, None), sparseness=(0.01, 0.01), nvecs=3, its=20, cthresh=(0, 0), statdir=None, perms=0, uselong=0, z=0, smooth=0, robust=0, mycoption=0, initialization_list=[], initialization_list2=[], ell1=10, prior_weight=0, verbose=False, rejector=0, max_based=False, version=1)[source]

Decomposes two matrices into paired sparse eigenevectors to maximize canonical correlation - aka Sparse CCA. Note: we do not scale the matrices internally. We leave scaling choices to the user.

ANTsR function: sparseDecom2

Parameters: inmatrix (2-tuple of ndarrays) – input as inmatrix=(mat1,mat2). n by p input matrix and n by q input matrix , spatial variable lies along columns. inmask (2-tuple of ANTsImage python:types (optional - one or both)) – optional pair of image masks sparseness (tuple) – a pair of float values e.g c(0.01,0.1) enforces an unsigned 99 percent and 90 percent sparse solution for each respective view nvecs (integer) – number of eigenvector pairs its (integer) – number of iterations, 10 or 20 usually sufficient cthresh (2-tuple) – cluster threshold pair statdir (string (optional)) – temporary directory if you want to look at full output perms (integer) – number of permutations. settings permutations greater than 0 will estimate significance per vector empirically. For small datasets, these may be conservative. p-values depend on how one scales the input matrices. uselong (boolean) – enforce solutions of both views to be the same - requires matrices to be the same size z (float) – subject space (low-dimensional space) sparseness value smooth (float) – smooth the data (only available when mask is used) robust (boolean) – rank transform input matrices mycoption (integer) – enforce 1 - spatial orthogonality, 2 - low-dimensional orthogonality or 0 - both initialization_list (list) – initialization for first view initialization_list2 (list) – initialization for 2nd view ell1 (float) – gradient descent parameter, if negative then l0 otherwise use l1 prior_weight (scalar) – Scalar value weight on prior between 0 (prior is weak) and 1 (prior is strong). Only engaged if initialization is used verbose (boolean) – activates verbose output to screen rejector (scalar) – rejects small correlation solutions max_based (boolean) – whether to choose max-based thresholding projections : ndarray X projections projections2 : ndarray Y projections eig1 : ndarray X components eig2 : ndarray Y components summary : pd.DataFrame first column is canonical correlations, second column is p-values (these are None if perms > 0) dict w/ following key/value pairs

Example

>>> import numpy as np
>>> import ants
>>> mat = np.random.randn(20, 100)
>>> mat2 = np.random.randn(20, 90)
>>> mydecom = ants.sparse_decom2(inmatrix = (mat,mat2),
sparseness=(0.1,0.3), nvecs=3,
its=3, perms=0)

ants.eig_seg(mask, img_list, apply_segmentation_to_images=False, cthresh=0, smooth=1)[source]

Segment a mask into regions based on the max value in an image list. At a given voxel the segmentation label will contain the index to the image that has the largest value. If the 3rd image has the greatest value, the segmentation label will be 3 at that voxel.

Parameters: mask (ANTsImage) – D-dimensional mask > 0 defining segmentation region. img_list (collection of ANTsImage or np.ndarray) – images to use apply_segmentation_to_images (boolean) – determines if original image list is modified by the segmentation. cthresh (integer) – throw away isolated clusters smaller than this value smooth (float) – smooth the input data first by this value ANTsImage

Example

>>> import ants

ants.initialize_eigenanatomy(initmat, mask=None, initlabels=None, nreps=1, smoothing=0)[source]

InitializeEigenanatomy is a helper function to initialize sparseDecom and sparseDecom2. Can be used to estimate sparseness parameters per eigenvector. The user then only chooses nvecs and optional regularization parameters.

Parameters: initmat (np.ndarray or ANTsImage) – input matrix where rows provide initial vector values. alternatively, this can be an antsImage which contains labeled regions. mask (ANTsImage) – mask if available initlabels (list/tuple of python:integers) – which labels in initmat to use as initial components nreps (integer) – nrepetitions to use smoothing (float) – if using an initial label image, optionally smooth each roi initlist : list of ANTsImage types initialization list(s) for sparseDecom(2) mask : ANTsImage mask(s) for sparseDecom(2) enames : list of strings string names of components for sparseDecom(2) dict w/ the following key/value pairs

Example

>>> import ants
>>> import numpy as np
>>> mat = np.random.randn(4,100).astype('float32')
>>> init = ants.initialize_eigenanatomy(mat)