04_eofs/eof_covariance_vs_data_matrices.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Singular Value Decomposition on the Covariance vs. Data Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While we have thus far focused on applying singular value decomposition to square symmatric matrices, it turns out that any real matrix **A** (not just square matrices!) can be decomposed into a set of 3 special matrices such that:\n",
    "\n",
    "$\n",
    "\\mathbf{A} = \\mathbf{U} \\Sigma \\mathbf{V}^T\n",
    "$\n",
    "\n",
    "With **U** and **V** being the eigenvectors of $\\mathbf{AA}^{T}$ and $\\mathbf{A}^{T}\\mathbf{A}$, respectively.  We already know that when $\\mathbf{A}$ is square and symmetric like the covariance or correlation matrix, $\\mathbf{U}$ and $\\mathbf{V}$ are simply the transpose of one another and contain the eigenvectors, and then $\\Sigma$ in this case holds eigenvalues (in matrix form on the diagnonal, although Numpy and Scipy return them as a vector).  But for a non-square real matrix with dimensions $m \\times n$, you can still accomplish the singular value decomposition -- the different is that now $\\mathbf{U}$ is $m \\times m$ and $\\mathbf{V}$ is $n \\times n$.  Having the dimensions of the columns of our data matrix, $\\mathbf{V}^{T}$ therefore holds our eigenvectors, while $\\Sigma$ contains what are called 'singular values'.  If $\\mathbf{A}$ is positive semi-definite, the singular values $\\sigma$ in $\\Sigma$ and eigenvalues ($\\lambda$) are related via:\n",
    "\n",
    "$\n",
    "\\sigma = \\sqrt{\\lambda(n-1)}\n",
    "$\n",
    "\n",
    "So, squaring the singular values $\\sigma$ in $\\Sigma$ and dividing by the sample size less 1 recovers eigenvalues from singular values. \n",
    "\n",
    "Let's look at a simple example first to convince ourselves we can do SVD on the covariance or correlation matrix, but also in most cases directly on the centered data matrix.  \n",
    "\n",
    "First, let's import our packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import pandas as pd\n",
    "import xarray as xr\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# nicely render figures in the notebook \n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "%matplotlib inline\n",
    "\n",
    "# you can omit the line below if you'd like, but I really don't like the default fonts in Python, so I switch to Helvetica\n",
    "plt.rcParams['font.family'] = 'Helvetica'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example using the Iris dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's read in our Iris dataset - remember, we did a very simple initial EOF analysis of part of these data when we first learned about eigenvectors and eigenvalues.\n",
    "\n",
    "With this simple 2 column, 50 row matrix, I want to show you that performing the singular value decomposition on the data matrix can give us the same information we got using SVD on the covariance matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.66941065 -0.74289258]\n",
      " [-0.74289258  0.66941065]]\n",
      "[[-0.66941065 -0.74289258]\n",
      " [-0.74289258  0.66941065]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('iris.data') # use Pandas to read in the csv data\n",
    "\n",
    "# extract just one species and just the sepal measurements\n",
    "iris = df.loc[df[\" species(id)\"].str.contains('Iris-setosa'), [\"sepal length (cm)\",\" sepal width (cm)\"]].copy()\n",
    "\n",
    "# remove the mean of each of the 2 columns of data\n",
    "iris = iris - np.mean(iris,axis=0)\n",
    "\n",
    "# calculate the covariance matrix for the 50x2 data matrix\n",
    "C = np.cov(iris,rowvar=False,ddof=1)\n",
    "\n",
    "# do the SVD on the square covariance matrix (2x2)\n",
    "Uc,Sc,Vc = np.linalg.svd(C)\n",
    "print(Uc)\n",
    "\n",
    "# now, do the SVD directly on the centered data matrix (50x2)\n",
    "Ud, Sd, Vd = np.linalg.svd(iris)\n",
    "print(Vd.T)\n",
    "\n",
    "# by printing both eigenvector matrices above, we can see for ourselves that we can get the same eigenvectors!  \n",
    "# And we can check: are the two matrices the same (within machine tolerance)?  Yes they are!\n",
    "np.allclose(Uc,Vd.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So it is possible to get the eigenvectors directly from the centered data matrix!  \n",
    "\n",
    "Now, let's look at an example with a larger dataset - but in any case the principal is the same, whether a small array or a large one. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example using the SST dataset\n",
    "\n",
    "Now that we've done the simple example, let's do the same test on our SST dataset.  In theory, performing the SVD on the data matrix (which will have a smaller row dimension than the covariance matrix) will be faster and we can use `np.linalg.svd` directly on the data matrix.  First let's get the SST data ready for analysis - in previous notebooks we've done this step-by-step, but this part should be familiar by now:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 429,
       "width": 556
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# open our file into a DataSet \n",
    "ds = xr.open_dataset('HadISST_sst.nc') \n",
    "\n",
    "# pull the sst variable out of the DataSet. \n",
    "sst = ds.sst\n",
    "\n",
    "# turn negative SST values (sea ice) in NaNs\n",
    "sst = sst.where(sst >= 0, np.nan)\n",
    "\n",
    "# for working on the Pacific domain, we change the longitudes from -180,180 to 0,360 \n",
    "sst = sst.assign_coords(longitude=(sst.longitude % 360))\n",
    "sst = sst.sortby(sst.longitude)\n",
    "\n",
    "# defined our latitude bounds\n",
    "min_lat = -20.0\n",
    "max_lat = 60.00\n",
    "\n",
    "# define our longitude bounds\n",
    "min_lon = 120\n",
    "max_lon = 260\n",
    "\n",
    "# slice and overwrite sst with the output \n",
    "sst = sst.sel(longitude=slice(min_lon,max_lon),latitude=slice(max_lat,min_lat))\n",
    "\n",
    "# extract coordinates from the DataArray as well \n",
    "lat = sst.latitude\n",
    "lon = sst.longitude\n",
    "\n",
    "# Calculate the 5-month rolling mean\n",
    "sst_ = sst.rolling(time=5).mean(skipna=True)\n",
    "\n",
    "# Select out month 3 (March) to get the average over NDJFM\n",
    "winter = sst_[sst_.time.dt.month == 3]\n",
    "\n",
    "# use drop_isel to drop the first year\n",
    "winter = winter.drop_isel(time=0)\n",
    "\n",
    "# get the values from the winter DataArray - at this point they are still 3-dimensional\n",
    "sst2d = winter.values\n",
    "\n",
    "# record their original dimensions before we reshape\n",
    "ntime, nrow, ncol = sst2d.shape\n",
    "\n",
    "# now reshape, we want rows of the time variable and columns of location - we use 'order=F' because this gives us the correct reshaping\n",
    "sst2d = np.reshape(sst2d, (ntime, nrow * ncol), order='F')\n",
    "\n",
    "# index for where theere are no missing values at all (will eliminate land and some sea ice locations)\n",
    "noMissing = ~np.isnan(sst2d).any(axis=0)\n",
    "\n",
    "# create a new array with only the columns of sst2d that are not missing any data \n",
    "sst2dcomplete = sst2d[:, noMissing]\n",
    "\n",
    "# calculate the anomalies from the long-term seasonal mean for each column\n",
    "sst_anomalies = sst2dcomplete - np.mean(sst2dcomplete,axis=0)\n",
    "plt.hist(np.mean(sst_anomalies,axis=0)); # and then a quick sanity check on the mean of the columns before we move on\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we're ready.  Let's do SVD _both_ on the covariance matrix (using `sp.sparse.linalg.svds` to speed things up) and then on the on the centered data matrix using `np.linalg.svd`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(153, 153) (153,) (153, 9329)\n"
     ]
    }
   ],
   "source": [
    "# using the covariance matrix now:\n",
    "C = np.cov(sst_anomalies,rowvar=False,ddof=1)\n",
    "Ux, Sx, Vx = sp.sparse.linalg.svds(C,k=9) # economy sized, only get the first ten eigenvalues/eigenvectors\n",
    "sort_index = np.argsort(Sx)[::-1] # sort in descending order from high to low\n",
    "Sx = Sx[sort_index] # apply the index\n",
    "Ux = Ux[:,sort_index] # apply the index\n",
    "Vx = Vx[sort_index,:] # apply the index\n",
    "\n",
    "## we could use sp.sparse.linalg.svds for the data matrix, too, but let's us np.linalg. svd to prove we can do it quickly enough in the section below this one\n",
    "# U, S, V = sp.sparse.linalg.svds(sst_anomalies,k=9) # \n",
    "# sort_index2 = np.argsort(S)[::-1] # sort in descending order from high to low\n",
    "# S = S[sort_index2] # apply the index\n",
    "# U = U[:,sort_index2] # apply the index\n",
    "# V = V.conj().T # for the non-square data matrix, the eigenvectors are in the columns of the (conjugate) transpose of V\n",
    "# V = V[:,sort_index2] # apply the sort index\n",
    "\n",
    "# using the data matrix here - np.linalg.svd should be properly sorted from highest to lowest singular value\n",
    "U, S, V = np.linalg.svd(sst_anomalies,full_matrices=False) # 4.1 seconds on my computer\n",
    "\n",
    "print(U.shape, S.shape, V.shape)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the output from the SVD on the data matrix, we see the following:\n",
    "\n",
    "* U is 153 by 153 (so, square with the dimensions of the time dimesion of our data matrix)\n",
    "* S has 153 singular values (but not eigenvalues, yet!)\n",
    "* V is 9329 vy 9329 (so, square with the spatial dimensions - the columns - so this must be the eigenvectors)\n",
    "\n",
    "If we want the eigenvalues, we'll need to convert them, but also be aware that the singular values are proportional to the eigenvalues, so if all we are interested in is the variance accounted for by each mode, we could just use the singular values are they are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12c244c10>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 412,
       "width": 556
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the eigenvalues are the squared singular values divided by the unbiased sample size (n-1)\n",
    "eigenvalues_from_singular_values = (S**2)/(len(S)-1)\n",
    "\n",
    "# let's prove to ourselves this works - let's scatter plot the first 10 eigenvectors and the converted singular values:\n",
    "plt.scatter(eigenvalues_from_singular_values[0:9],Sx[0:9])\n",
    "plt.plot([0,1200],[0,1200],color=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's compare the leading eigenvectors from the SVD on the covariance matrix and on the data matrix.  Just remember that since the sign is arbitrary (and often linked to how the computer is doing the maths behind the scenes), they could be opposite signed (indeed, if you run this notebook multiple times, the sign may change between consecutive runs!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12c544ad0>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 412,
       "width": 560
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Take a look at the leading eigenvectors - here in the transpose of V (remember they could be differently signed, but that sign is arbitary)\n",
    "plt.scatter(Ux[:,0],V.T[:,0])\n",
    "plt.plot([-0.04,0.04],[-0.04,0.04],color=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is worth thinking for a moment why I had you use SVD on the covariance or correlation matrix when we first learned about EOF analysis - I wanted to make the connection explicit about where the space-time patterns we isolate in EOF analysis come from and the connection to the variance and covariance within our dataset.  In the future, applying SVD directly to the data matrix may in some cases be faster and more efficient that using the covariance matrix."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}