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lschwetlick/sk1.ipynb

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Scikit-learn problem with PCA
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sk1.ipynb
{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Problems with PCA"
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
}
}
}
},
{
"cell_type": "code",
"source": [
"import numpy as np\n",
"from sklearn.decomposition import PCA\n",
"import scipy as sp\n",
"from sklearn.decomposition.pca import _assess_dimension\n",
"from sklearn.decomposition.pca import _infer_dimension"
],
"outputs": [],
"execution_count": 104,
"metadata": {
"collapsed": false,
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"shell.execute_reply": "2020-02-28T16:58:58.089Z"
}
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},
{
"cell_type": "markdown",
"source": [
"First, lets check out what `_assess_dim` does. It uses the output of the singular value decomposition as input."
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
}
}
}
},
{
"cell_type": "code",
"source": [
"a = np.random.randn(9, 6)\n",
"b = np.ones((9, 6))\n",
"c = np.zeros((9, 6))"
],
"outputs": [],
"execution_count": 105,
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": false,
"outputs_hidden": false
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"shell.execute_reply": "2020-02-28T16:58:58.844Z"
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},
{
"cell_type": "markdown",
"source": [
"The first matrix is of full rank and gives us a list of 6 eigenvalues."
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
}
}
}
},
{
"cell_type": "code",
"source": [
"print(\"rank=\", np.linalg.matrix_rank(a))\n",
"u1, s1, vh1 = np.linalg.svd(a, full_matrices=True)\n",
"s1"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"rank= 6\n"
]
},
{
"output_type": "execute_result",
"execution_count": 106,
"data": {
"text/plain": [
"array([4.58644552, 4.27596537, 2.93635641, 2.26594033, 1.66861791,\n",
" 1.0130635 ])"
]
},
"metadata": {}
}
],
"execution_count": 106,
"metadata": {
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"shell.execute_reply": "2020-02-28T16:58:59.998Z"
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},
{
"cell_type": "markdown",
"source": [
" The second matrix has no variance but is of rank 1. It still gives a list of 6, but 5 of 6 elements are 0."
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
}
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}
},
{
"cell_type": "code",
"source": [
"print(\"rank=\", np.linalg.matrix_rank(b))\n",
"u2, s2, vh2 = np.linalg.svd(b, full_matrices=True)\n",
"s2"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"rank= 1\n"
]
},
{
"output_type": "execute_result",
"execution_count": 107,
"data": {
"text/plain": [
"array([7.34846923, 0. , 0. , 0. , 0. ,\n",
" 0. ])"
]
},
"metadata": {}
}
],
"execution_count": 107,
"metadata": {
"collapsed": false,
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"execution": {
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"shell.execute_reply": "2020-02-28T16:59:04.776Z"
}
}
},
{
"cell_type": "markdown",
"source": [
"The third matrix has no variance and is of rank 0. It still gives a list of 6, all 6 elements are 0."
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
}
}
}
},
{
"cell_type": "code",
"source": [
"print(\"rank=\", np.linalg.matrix_rank(c))\n",
"u3, s3, vh3 = np.linalg.svd(c, full_matrices=True)\n",
"s3"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"rank= 0\n"
]
},
{
"output_type": "execute_result",
"execution_count": 108,
"data": {
"text/plain": [
"array([0., 0., 0., 0., 0., 0.])"
]
},
"metadata": {}
}
],
"execution_count": 108,
"metadata": {
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"jupyter": {
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"outputs_hidden": false
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"execution": {
"iopub.status.busy": "2020-02-28T16:59:10.343Z",
"iopub.execute_input": "2020-02-28T16:59:10.349Z",
"iopub.status.idle": "2020-02-28T16:59:10.365Z",
"shell.execute_reply": "2020-02-28T16:59:10.371Z"
}
}
},
{
"cell_type": "markdown",
"source": [
"What does pca's `_assess_dimension` do with this? It is capable of assessing the likelihood of each rank. Rank 0,1,2,3,4,5, and 6."
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
}
}
}
},
{
"cell_type": "code",
"source": [
"for r in range(7):\n",
" print(r)\n",
" print(_assess_dimension(np.asarray(s1), r, 9, 6))"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"0\n",
"-26.794487496983052\n",
"1\n",
"-27.59120266903175\n",
"2\n",
"-29.04631199386823\n",
"3\n",
"-30.397847556807104\n",
"4\n",
"-31.69273382607098\n",
"5\n",
"-32.95111461773282\n",
"6\n",
"-33.8239355537562\n"
]
}
],
"execution_count": 109,
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": false,
"outputs_hidden": false
},
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"transient": {
"deleting": false
}
},
"execution": {
"iopub.status.busy": "2020-02-28T16:59:20.017Z",
"iopub.execute_input": "2020-02-28T16:59:20.023Z",
"iopub.status.idle": "2020-02-28T16:59:20.034Z",
"shell.execute_reply": "2020-02-28T16:59:20.039Z"
}
}
},
{
"cell_type": "code",
"source": [
"for r in range(7):\n",
" print(r)\n",
" print(_assess_dimension(np.asarray(s2), r, 9, 6))"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"0\n",
"-4.554840426255549\n",
"1\n",
"-inf\n",
"2\n",
"-inf\n",
"3\n",
"-inf\n",
"4\n",
"-inf\n",
"5\n",
"-inf\n",
"6\n",
"nan\n"
]
},
{
"output_type": "stream",
"name": "stderr",
"text": [
"/Users/lisa/Documents/Projects/scikit-learn/sklearn/decomposition/_pca.py:68: RuntimeWarning: divide by zero encountered in log\n",
" pl = np.sum(np.log(spectrum[:rank]))\n",
"/Users/lisa/Documents/Projects/scikit-learn/sklearn/decomposition/_pca.py:98: RuntimeWarning: divide by zero encountered in double_scalars\n",
" (1. / spectrum_[j] - 1. / spectrum_[i])) + log(n_samples)\n",
"/Users/lisa/Documents/Projects/scikit-learn/sklearn/decomposition/_pca.py:100: RuntimeWarning: invalid value encountered in double_scalars\n",
" ll = pu + pl + pv + pp - pa / 2. - rank * log(n_samples) / 2.\n"
]
}
],
"execution_count": 110,
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": false,
"outputs_hidden": false
},
"nteract": {
"transient": {
"deleting": false
}
},
"execution": {
"iopub.status.busy": "2020-02-28T16:59:20.781Z",
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"iopub.status.idle": "2020-02-28T16:59:20.799Z",
"shell.execute_reply": "2020-02-28T16:59:20.804Z"
}
}
},
{
"cell_type": "code",
"source": [
"for r in range(7):\n",
" print(r)\n",
" print(_assess_dimension(np.asarray(s3), r, 9, 6))"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"0\n",
"-inf\n",
"1\n",
"-inf\n",
"2\n",
"-inf\n",
"3\n",
"-inf\n",
"4\n",
"-inf\n",
"5\n",
"-inf\n",
"6\n",
"inf\n"
]
}
],
"execution_count": 111,
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": false,
"outputs_hidden": false
},
"nteract": {
"transient": {
"deleting": false
}
},
"execution": {
"iopub.status.busy": "2020-02-28T16:59:27.300Z",
"iopub.execute_input": "2020-02-28T16:59:27.306Z",
"iopub.status.idle": "2020-02-28T16:59:27.317Z",
"shell.execute_reply": "2020-02-28T16:59:27.323Z"
}
}
},
{
"cell_type": "markdown",
"source": [
"But it does show strange behavior on the full rank on both of the edge case matrices (all zeros and all ones) with the 7th value being nan or +inf..."
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
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}
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},
{
"cell_type": "markdown",
"source": [
"Here are some more interesting cases that dont work"
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
}
}
}
},
{
"cell_type": "code",
"source": [
"d = np.zeros((9,6))\n",
"d[:,2]=1\n",
"d[:,5]=5\n",
"print(\"rank=\", np.linalg.matrix_rank(d))\n",
"u4, s4, vh4 = np.linalg.svd(d, full_matrices=True)\n",
"s4\n",
"d"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"rank= 1\n"
]
},
{
"output_type": "execute_result",
"execution_count": 118,
"data": {
"text/plain": [
"array([[0., 0., 1., 0., 0., 5.],\n",
" [0., 0., 1., 0., 0., 5.],\n",
" [0., 0., 1., 0., 0., 5.],\n",
" [0., 0., 1., 0., 0., 5.],\n",
" [0., 0., 1., 0., 0., 5.],\n",
" [0., 0., 1., 0., 0., 5.],\n",
" [0., 0., 1., 0., 0., 5.],\n",
" [0., 0., 1., 0., 0., 5.],\n",
" [0., 0., 1., 0., 0., 5.]])"
]
},
"metadata": {}
}
],
"execution_count": 118,
"metadata": {
"collapsed": false,
"jupyter": {
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"outputs_hidden": false
},
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"execution": {
"iopub.status.busy": "2020-02-28T17:00:47.965Z",
"iopub.execute_input": "2020-02-28T17:00:47.970Z",
"iopub.status.idle": "2020-02-28T17:00:47.982Z",
"shell.execute_reply": "2020-02-28T17:00:47.987Z"
}
}
},
{
"cell_type": "code",
"source": [
"for r in range(7):\n",
" print(r)\n",
" print(_assess_dimension(np.asarray(s4), r, 9, 6))"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"0\n",
"-24.35039085496681\n",
"1\n",
"-inf\n",
"2\n",
"-inf\n",
"3\n",
"-inf\n",
"4\n",
"-inf\n",
"5\n",
"-inf\n",
"6\n"
]
},
{
"output_type": "error",
"ename": "ValueError",
"evalue": "math domain error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-113-e282dbdd7bb2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mr\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m7\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_assess_dimension\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m9\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m~/Documents/Projects/scikit-learn/sklearn/decomposition/_pca.py\u001b[0m in \u001b[0;36m_assess_dimension\u001b[0;34m(spectrum, rank, n_samples, n_features)\u001b[0m\n\u001b[1;32m 96\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mspectrum\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 97\u001b[0m pa += log((spectrum[i] - spectrum[j]) *\n\u001b[0;32m---> 98\u001b[0;31m (1. / spectrum_[j] - 1. / spectrum_[i])) + log(n_samples)\n\u001b[0m\u001b[1;32m 99\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 100\u001b[0m \u001b[0mll\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpu\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mpl\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mpv\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mpp\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mpa\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;36m2.\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mrank\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn_samples\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;36m2.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: math domain error"
]
}
],
"execution_count": 113,
"metadata": {
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"jupyter": {
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"outputs_hidden": false
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"execution": {
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"shell.execute_reply": "2020-02-28T16:59:33.965Z"
}
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},
{
"cell_type": "markdown",
"source": [
"One Step higher, `_infer_dimension` is the function that does this iteration. It never tests full rank. It also kind of can't because it is meant to return an index into the spectrum vector which is of length 6. If we test full rank, the ll vector will be of length 7, so we can't take the argmax. "
],
"metadata": {
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}
}
}
},
{
"cell_type": "code",
"source": [
"_infer_dimension(s1, 9, 6)"
],
"outputs": [
{
"output_type": "execute_result",
"execution_count": 114,
"data": {
"text/plain": [
"0"
]
},
"metadata": {}
}
],
"execution_count": 114,
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"iopub.status.busy": "2020-02-28T16:59:41.188Z",
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}
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},
{
"cell_type": "code",
"source": [
"_infer_dimension(s2, 9, 6)"
],
"outputs": [
{
"output_type": "execute_result",
"execution_count": 115,
"data": {
"text/plain": [
"0"
]
},
"metadata": {}
}
],
"execution_count": 115,
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{
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"_infer_dimension(s3, 9, 6)"
],
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{
"output_type": "execute_result",
"execution_count": 116,
"data": {
"text/plain": [
"0"
]
},
"metadata": {}
}
],
"execution_count": 116,
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},
{
"cell_type": "code",
"source": [
"_infer_dimension(s4, 9, 6)"
],
"outputs": [
{
"output_type": "execute_result",
"execution_count": 117,
"data": {
"text/plain": [
"0"
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},
"metadata": {}
}
],
"execution_count": 117,
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"source_hidden": false,
"outputs_hidden": false
},
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}
},
"execution": {
"iopub.status.busy": "2020-02-28T16:59:48.033Z",
"iopub.execute_input": "2020-02-28T16:59:48.040Z",
"iopub.status.idle": "2020-02-28T16:59:48.051Z",
"shell.execute_reply": "2020-02-28T16:59:48.056Z"
}
}
},
{
"cell_type": "markdown",
"source": [
"I assume it's always returning zero here because the spectrum comes sorted and all of these matrices have rank 1 or full and spectrum is sorted by linalg"
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
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}
},
{
"cell_type": "markdown",
"source": [
"So next Ill construct a matrix that has the largest variation in the last column. In my understanding that would mean that should be the main component then."
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
}
}
}
},
{
"cell_type": "code",
"source": [
"e = np.zeros((9,6))\n",
"e[:,0]=1\n",
"e[:,1]=1\n",
"e[:,2]=1\n",
"e[:,3]=2\n",
"e[:,4]=[1,2,1,1,1,1,1,1,2]\n",
"e[:,5]=[1,2,3,4,5,6,7,8,9]\n",
"print(\"rank =\", np.linalg.matrix_rank(e))\n",
"u5, s5, vh5 = np.linalg.svd(e, full_matrices=True)\n",
"s5"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"rank = 3\n"
]
},
{
"output_type": "execute_result",
"execution_count": 95,
"data": {
"text/plain": [
"array([1.86723970e+01, 3.61449172e+00, 1.13006188e+00, 3.96930995e-16,\n",
" 4.51401869e-17, 2.22329483e-17])"
]
},
"metadata": {}
}
],
"execution_count": 95,
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": false,
"outputs_hidden": false
},
"nteract": {
"transient": {
"deleting": false
}
},
"execution": {
"iopub.status.busy": "2020-02-28T16:55:06.091Z",
"iopub.execute_input": "2020-02-28T16:55:06.097Z",
"iopub.status.idle": "2020-02-28T16:55:06.113Z",
"shell.execute_reply": "2020-02-28T16:55:06.118Z"
}
}
},
{
"cell_type": "code",
"source": [
"ll = []\n",
"for r in range(7):\n",
" print(r)\n",
" ll1 = _assess_dimension(np.asarray(s5), r, 9, 6)\n",
" print(ll1)\n",
" ll.append(ll1)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"0\n",
"-35.846979706242\n",
"1\n",
"-22.764631367309146\n",
"2\n",
"-17.637601080831697\n",
"3\n",
"-inf\n",
"4\n",
"-inf\n",
"5\n",
"-inf\n",
"6\n",
"287.3210868655406\n"
]
}
],
"execution_count": 120,
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": false,
"outputs_hidden": false
},
"nteract": {
"transient": {
"deleting": false
}
},
"execution": {
"iopub.status.busy": "2020-02-28T17:17:16.479Z",
"iopub.execute_input": "2020-02-28T17:17:16.485Z",
"iopub.status.idle": "2020-02-28T17:17:16.496Z",
"shell.execute_reply": "2020-02-28T17:17:16.501Z"
}
}
},
{
"cell_type": "markdown",
"source": [
"Here the last value (the rank we never test) clearly has the biggest number. `infer_dimension` returns 2 though."
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
}
}
}
},
{
"cell_type": "code",
"source": [
"_infer_dimension(s5, 9, 6)"
],
"outputs": [
{
"output_type": "execute_result",
"execution_count": 98,
"data": {
"text/plain": [
"2"
]
},
"metadata": {}
}
],
"execution_count": 98,
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": false,
"outputs_hidden": false
},
"nteract": {
"transient": {
"deleting": false
}
},
"execution": {
"iopub.status.busy": "2020-02-28T16:56:30.021Z",
"iopub.execute_input": "2020-02-28T16:56:30.027Z",
"iopub.status.idle": "2020-02-28T16:56:30.041Z",
"shell.execute_reply": "2020-02-28T16:56:30.046Z"
}
}
},
{
"cell_type": "markdown",
"source": [
"The trouble is that even if we do test for the last rank, we can't really use the argmax because we are always testing the number of values in the spectrum AND rank 0."
],
"metadata": {
"nteract": {
"transient": {
"deleting": false
}
}
}
},
{
"cell_type": "code",
"source": [
"print(np.argmax(ll))\n",
"print(len(s5))\n",
"s5[np.argmax(ll)]\n"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"6\n",
"6\n"
]
},
{
"output_type": "error",
"ename": "IndexError",
"evalue": "index 6 is out of bounds for axis 0 with size 6",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mIndexError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-122-368585a97f86>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mll\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0ms5\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mll\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;31mIndexError\u001b[0m: index 6 is out of bounds for axis 0 with size 6"
]
}
],
"execution_count": 122,
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": false,
"outputs_hidden": false
},
"nteract": {
"transient": {
"deleting": false
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},
"execution": {
"iopub.status.busy": "2020-02-28T17:17:52.521Z",
"iopub.execute_input": "2020-02-28T17:17:52.527Z",
"iopub.status.idle": "2020-02-28T17:17:52.542Z",
"shell.execute_reply": "2020-02-28T17:17:52.548Z"
}
}
},
{
"cell_type": "code",
"source": [
"pca = PCA(n_components=\"mle\")\n",
"my_fit = pca.fit(e)\n",
"#print(pca.explained_variance_ratio_)\n",
"#print(pca.singular_values_)\n",
"print(my_fit)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"PCA(copy=True, iterated_power='auto', n_components='mle', random_state=None,\n",
" svd_solver='auto', tol=0.0, whiten=False)\n"
]
}
],
"execution_count": 103,
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": false,
"outputs_hidden": false
},
"nteract": {
"transient": {
"deleting": false
}
},
"execution": {
"iopub.status.busy": "2020-02-28T16:57:30.462Z",
"iopub.execute_input": "2020-02-28T16:57:30.469Z",
"iopub.status.idle": "2020-02-28T16:57:30.480Z",
"shell.execute_reply": "2020-02-28T16:57:30.486Z"
}
}
}
],
"metadata": {
"kernel_info": {
"name": "scenewalk"
},
"language_info": {
"name": "python",
"version": "3.6.3",
"mimetype": "text/x-python",
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"kernelspec": {
"argv": [
"/Users/lisa/Documents/virtual_envs/scenewalk/bin/python3",
"-m",
"ipykernel_launcher",
"-f",
"{connection_file}"
],
"display_name": "SceneWalk",
"language": "python",
"name": "scenewalk"
},
"nteract": {
"version": "0.22.0"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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