{ "metadata": { "name": "", "signature": "sha256:29427f31780832bc8cc4408df79c16ff3ccb75ccef9505fa1e1ecfc67304244c" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "# - compatibility with Python 3\n", "from __future__ import print_function # print('me') instead of print 'me'\n", "from __future__ import division # 1/2 == 0.5, not 0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# - show figures inside the notebook\n", "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "# - import common modules\n", "import numpy as np # the Python array package\n", "import matplotlib.pyplot as plt # the Python plotting package" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# - import numpy.linalg with a shorter name\n", "import numpy.linalg as npl" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Load the image `ds114_sub009_t2r1.nii` with nibabel. Get the data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Load the image 'ds114_sub009_t2r1.nii' with nibabel\n", "# Get the data array from the image\n", "import nibabel as nib\n", "img = nib.load('ds114_sub009_t2r1.nii')\n", "data = img.get_data()\n", "data.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "(64, 64, 30, 173)" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can think of the shape of the data as two parts - the first 3 values are the 3D shape of the individual volumes, and the last value is the number of volumes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Put the 3D shape into a variable `vol_shape` and the number of volumes into a variable `n_vols`:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Make variables:\n", "# 'vol_shape' for shape of volumes\n", "# 'n_vols' for number of volumes\n", "vol_shape = data.shape[:-1]\n", "n_vols = data.shape[-1]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are going to start by looking at only the first two \"variables\" (time points)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Slice the data array to make a new array that contains only the first two volumes:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Slice the image data array to give array with only first two volumes\n", "first_two = data[..., :2]\n", "first_two.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "(64, 64, 30, 2)" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "How many voxels are there in one volume? Call this number variable `N`:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Set N to be the number of voxels in a volume\n", "N = np.prod(vol_shape)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Reshape the new two-volume data array to have a first dimension length `N` and second dimension length 2. So, each column corresponds to the voxels for one volume." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Reshape to 2D array with first dimension length N\n", "first_two = first_two.reshape((N, 2))\n", "first_two.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "(122880, 2)" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Take the transpose of this array to get a 2 by `N` array, ready for the PCA:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Transpose to 2 by N array\n", "first_two = first_two.T\n", "first_two.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "(2, 122880)" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate the mean across columns (row means):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculate the mean across columns\n", "row_means = np.mean(first_two, axis=1)\n", "row_means" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "memmap([ 414.40107422, 336.69940592])" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expand the row_means vector out to a 2 by N array by using `np.outer` and a vector of ones:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Row means copied N times to become a 2 by N array\n", "row_means = np.outer(row_means, np.ones(N))\n", "row_means.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "(2, 122880)" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Subtract this expanded 2 by N means array from the 2 by N data matrix and put the result into a variable `X`. Print the means across columns (row means) to check they are now very close to 0:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Subtract the means for each row, put the result into X\n", "# Show the means over the columns, after the subtraction\n", "X = first_two - row_means\n", "np.mean(X, axis=1)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "memmap([ -1.51582450e-14, 1.36424205e-13])" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the two rows against each other to get a feel for the variation. Remember that each row in `X` is a volume, so you are plotting the signal from the first volume against the signal for the second volume." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot the signal in the first row against the signal in the second\n", "plt.plot(X[0], X[1], '+')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 14, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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pan2EWV/pLIeZhL4pheLBFINR9IQCKVQGYZZL6JYJ6wIACsijR6kM+vooEKurmX309NPe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\nDMNYKBZDMeTkI2oPpsPxeBzxAkjGaL5/VxcwNET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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Time for the PCA.\n", "\n", "We are going to use the *unscaled* covariance. This is given by the matrix multiplication of `X` with its transpose. Calculate this:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculate unscaled covariance matrix for X\n", "unscaled_covariance = X.dot(first_two.T)\n", "unscaled_covariance" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 15, "text": [ "memmap([[ 8.04237807e+10, 6.12641298e+10],\n", " [ 6.12641298e+10, 4.92491046e+10]])" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use SVD to get the U, S and V matrices from the unscaled covariance:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Use SVD to return U, S, V matrices from unscaled covariance\n", "U, S, V = npl.svd(unscaled_covariance)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Confirm that the row vectors in `V` are both unit vectors. A unit vector has vector length (vector *norm* of 1):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Show that the rows in V each have vector length 1\n", "np.sum(V ** 2, axis=1)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ "memmap([ 1., 1.])" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Confirm that the first row in `V` is orthogonal to the second:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Confirm orthogonality of rows in V\n", "V[0].dot(V[1])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ "0.0" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Show the total sum of squares in `X`. Confirm that the total sum of squares in `X` is the same as the sum of the *singular values* in the `S` vector from the SVD:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Show the total sum of squares in X\n", "# Is this (nearly) the same as the sum of the values in S?\n", "print(np.sum(X ** 2))\n", "print(np.sum(S))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1.29672885307e+11\n", "129672885307.0\n" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the first row in `X` against the second row in `X` again. This time add a line corresponding to the first principal component. You'll have to scale this line (a unit vector) to make it long enough to see on the axes of the plot. If the first principal component is flipped ($\\vec{r}$ defines same line as $-\\vec{r}$) you may need to scale by a negative number for it to look nice on the plot:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot the signal in the first row against the signal in the second\n", "# Plot line corresponding to a scaled version of the first principal component\n", "# (Scaling may need to be negative)\n", "plt.plot(X[0], X[1], '+')\n", "scaled_v = V[0] * -4000\n", "plt.plot([0, scaled_v[0]], [0, scaled_v[1]], 'r')\n", "scaled_v[0]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 20, "text": [ "3157.9395737007017" ] }, { "metadata": {}, "output_type": "display_data", "png": 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FTw/57IGB7B5F+/bJ0/9xxwX3kKJxiZNOkhjBxo2SJXT33SH9VlNSa2rk/JNO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\n3nvvnCvUoi3nvpbIUqRSKVKj/DGy0NNyvBB9Rwf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"text": [ "" ] } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remember the projection formula $c = \\hat{u} \\cdot \\vec{v}$. \n", "\n", "We now need to calculate the projection coefficients $c$ for each component $\\hat{u}$ and each voxel (each $\\vec{v}$).\n", "\n", "This will give us a new output matrix of coefficients $C$ which is shape `(2, N)`, where the rows give the coefficients for one component, and the columns give the coefficients for one voxel.\n", "\n", "For example, `C[0, 0]` will be the result of `V[0].dot(X[:, 0])`, `C[0, 1]` will be the result of `V[0].dot(X[:, 1])`, and `C[1, 0]` will be the result of `V[1].dot(X[:, 0])`.\n", "\n", "With that background, see if you can use matrix multiplication to calculate the projection coefficients `C` for projecting the data `X` onto the vectors in `V`:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculate the projection coefficients for projecting X onto the vectors in V\n", "# Put the result into a new array C.\n", "C = V.dot(first_two)\n", "C.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 21, "text": [ "(2, 122880)" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remember that `C` - the projection coefficients - has one column per voxel. We can think of each row as corresponding to a volume where the volumes are contained in: `C[0]` (first row of `C`) - projection coefficients for first principal component; `C[1]` (second row of C) - projection coefficients for second principal component." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Take the transpose of `C` and reshape the resulting first dimension (length `N`) back to `vol_shape` - the original shape of the 3D volumes in the data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Transpose C\n", "# Reshape the first dimension of C to have the 3D shape of the original data volumes.\n", "C_vols = C.T.reshape(vol_shape + (2,))\n", "C_vols.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 22, "text": [ "(64, 64, 30, 2)" ] } ], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Break this 4D array up into two volumes (volume for first component, volume for second component) using slicing:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Break 4D array into two 3D volumes\n", "vol0 = C_vols[..., 0]\n", "vol1 = C_vols[..., 1]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Show the middle slice (slice over the third dimension) from the volume of coefficients for the first component:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Show middle slice (over third dimension) from volume of coefficients for first component\n", "plt.imshow(vol0[:, :, 14], cmap='gray')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 24, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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p67z8NA27cQeZHvOfmbmYzmvfIcg0Qrjw99l2tv29Z6L1rZIqZZGTRxPpJb3P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\nj729Pezt7ZVoMdNWSk0fXgGsU3oJDAJSFcVgMCj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YyxhCWAPwtwD8VIxxbxLliTGexwt6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\nrkJggg==\n", "text": [ "" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Show the middle slice (slice over the third dimension) from the volume of coefficients for the second component:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Show middle slice (over third dimension) from volume of coefficients for second component\n", "plt.imshow(vol1[:, :, 14], cmap='gray')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 25, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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XgTsWLq3AOA9rP71uR52Hbk+rDqn6cRkaBVj3BImwpdcQ3lJIGgVwvh5fOR8/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\noac4xSIzP1IfWfvOb5uRXXH7+/s4Ojq6NNXI/Sx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"text": [ "" ] } ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we are ready to do the same thing for all the time points, instead of just the first two." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Take the original array data matrix with `n_vols` volumes. Reshape to be shape `(N, nvols)`. Take the transpose to get an array shape `(n_vols, N)`:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Reshape first dimension of whole image data array to N, and take transpose\n", "arr = data.reshape(N, n_vols).T\n", "arr.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 26, "text": [ "(173, 122880)" ] } ], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate the mean across columns (mean per volume). Expand this 1D shape `(173,)` vector to an array shape `(173, N)`, using `np.outer` and a vector of ones. Subtract this array from the `(173, N)` data array to remove the mean across columns (mean per volume). Call this mean-corrected variable `X`:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculate mean across columns\n", "# Expand to (173, N) shape using np.outer\n", "# Subtract from data array to remove mean over columns (row means)\n", "# Put result into array X\n", "row_means = np.outer(np.mean(arr, axis=1), np.ones(N))\n", "X = arr - row_means" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Get the unscaled covariance matrix of X:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculate unscaled covariance matrix of X\n", "unscaled_covariance = X.dot(X.T)\n", "unscaled_covariance.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 28, "text": [ "(173, 173)" ] } ], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Get U, S, V outputs from the SVD of the unscaled covariance" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculate U, S, V with SVD on unscaled covariance matrix\n", "U, S, V = npl.svd(unscaled_covariance)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 29 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use `plt.subplots` to make a column of 10 axes. Iterate over these axes, plotting one principal component vector per axis. You should then have a plot of each of the first 10 principal component vectors:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Use subplots to make axes to plot first 10 principle component vectors\n", "# Plot one component vector per sub-plot.\n", "fig, axes = plt.subplots(10, 1)\n", "for i, ax in enumerate(axes):\n", " ax.plot(V[i])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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cndhDKXW1U2ZPPhl9bovmkq4YE0VZOUUFTVP+oGnKP0ojXZomZ0RGRp7jk0Wx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\nJ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"text": [ "" ] } ], "prompt_number": 30 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use `V` and matrix multiplication to calculate the projection coefficients for projecting the data `X` onto the principal components `V`. Put the result into `C`:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculate projection coefficients for projecting X onto V\n", "# Put results into array C.\n", "C = V.dot(X)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remember, each row of `C` is a full volume of projection coefficients, one row per principal component." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Reconstruct these rows as volumes by taking the transpose of `C` and reshaping the first dimension length `N` to the original three dimensions of the original data volumes." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Transpose C\n", "# Reshape the first dimension of C to have the 3D shape of the original data volumes.\n", "C_vols = C.T.reshape(img.shape)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Take the first volume (corresponding to the first principal component) and display the middle slice (slicing over the third dimension):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Show middle slice (over third dimension) of first principal component volume\n", "plt.imshow(C_vols[:, :, 14, 0], cmap='gray')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 33, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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bmg/NnVjnYVsH46ivCQAmu47HczkU/FBSGp07LpOb01AXo8zEVaLrJw/lWVpe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\n2bg8xzaY9Bansa2vbt26hbt37+LBgwe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"text": [ "" ] } ], "prompt_number": 33 }, { "cell_type": "markdown", "metadata": {}, "source": [ "What does this first component show us?\n", "\n", "Remember that the projections coefficients tell us how much of the component vector there is in the data, at each voxel. If the voxel has a high value it means there is a large amplitude of the component time-course at this voxel, and if the component is dark it means there is a large negative amplitude of the component time course.\n", "\n", "Have a look again at the first component time course. How would a large positive or negative amplitude of the time course come about?\n", "\n", "As a hint while you are thinking, get the mean over time from the image data (mean over the last axis), and show the middle slice (slicing over the third axis):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Make the mean volume (mean over the last axis)\n", "# Show the middle slice (slicing over the third axis)\n", "mean_vol = data.mean(axis=-1)\n", "plt.imshow(mean_vol[:, :, 14], cmap='gray')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 34, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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11SJgonpBpU4elEcGz8xl8rLW0jFf1aidkF5jG17wy6CxCGsPI5PnTnjplwkg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\nHzZ6zXMk77IbFJgQGgRKXedFui0YtLW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"text": [ "" ] } ], "prompt_number": 34 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display the middle slice (slicing over the third dimension) for the second principal component volume.\n", "\n", "Looking at the principal component plot - what kind of changes over time does this principal component represent?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Show middle slice (over third dimension) of second principal component volume\n", "plt.imshow(C_vols[:, :, 14, 1], cmap='gray')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 35, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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NePxeXV3dmvAKy1M786bqsVDeG48SOF5n3b1+sdH8XNt1/Z48aT8wq9C2wRP4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\nwjNoyAQeWrazs7Mqd4ACRqEaj8cVCrBvuWU7KFB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"text": [ "" ] } ], "prompt_number": 35 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Do the same for the third principal component volume:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Show middle slice (over third dimension) of third principal component volume\n", "plt.imshow(C_vols[:, :, 14, 2], cmap='gray')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 36, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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QX/7yl3FycoK3334b77zzDo6OjrC9vY1bt241+Y8oyRiFVtH48/Ha5YC65IWj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\nqk/J69VM6c1rOnGesmhdxhoLtddoWWQpboy5qDKj1WWz1DO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