analysis_pca.ipynb

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    "Define various useful functions and classes.\n",
    "\n",
    "ImageSliceViewer3D is for the interactive visualization of a 3D image. The slices can be selected through a slider.\n",
    "\n",
    "InteractiveStem adds a movable line in a stem plot. It also constructs an instance of ImageSliceViewer3D from a 3D image. A point in the stem plot correspond to a 2D-image. The position of the movable line in the stem plot determines the images which are displayed in the viewer. "
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    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import nibabel as nib\n",
    "import SimpleITK as sitk\n",
    "import math\n",
    "import os\n",
    "import matplotlib.lines as lines\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.colors as colors\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from matplotlib.offsetbox import OffsetImage, AnnotationBbox\n",
    "import cv2\n",
    "import csv\n",
    "import pandas\n",
    "import ipywidgets as ipyw\n",
    "import scipy.misc\n",
    "from IPython.display import clear_output\n",
    "\n",
    "import esmraldi.segmentation as seg\n",
    "import esmraldi.imzmlio as imzmlio\n",
    "import esmraldi.fusion as fusion\n",
    "import esmraldi.speciesrule as sr\n",
    "import esmraldi.spectrainterpretation as si\n",
    "\n",
    "from esmraldi.theoreticalspectrum import TheoreticalSpectrum\n",
    "\n",
    "%matplotlib notebook\n",
    "\n",
    "def transpose_eigenvectors(M, eigenvectors, eigenvalues):\n",
    "    p, n = M.shape\n",
    "    evT = [np.divide( (np.dot(M, eigenvectors[i])), (np.sqrt(2 * eigenvalues[i] * (n-1)/(p-1)))) for i in range(n)]\n",
    "    return np.asarray(evT)\n",
    "\n",
    "class ImageSliceViewer3D:\n",
    "    \"\"\" \n",
    "    ImageSliceViewer3D is for viewing volumetric image slices in jupyter or\n",
    "    ipython notebooks. \n",
    "    \n",
    "    User can interactively change the slice plane selection for the image and \n",
    "    the slice plane being viewed. \n",
    "\n",
    "    Argumentss:\n",
    "    Volume = 3D input image\n",
    "    figsize = default(8,8), to set the size of the figure\n",
    "    cmap = default('plasma'), string for the matplotlib colormap. You can find \n",
    "    more matplotlib colormaps on the following link:\n",
    "    https://matplotlib.org/users/colormaps.html\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, volume, mzs, ax=None, figsize=(8,8), cmap='gray'):\n",
    "        self.volume = volume\n",
    "        self.mzs = mzs\n",
    "        self.figsize = figsize\n",
    "        self.cmap = cmap\n",
    "        self.ax = ax\n",
    "        self.v = [np.min(volume), np.max(volume)]\n",
    "        self.slider = ipyw.IntSlider(min=0, max=self.volume.shape[-1] - 1, step=1, continuous_update=False, \n",
    "            description='Image Slice:')\n",
    "        \n",
    "    def show(self):\n",
    "        # Call to select slice plane\n",
    "        ipyw.interact(self.view_selection, view=ipyw.RadioButtons(\n",
    "            options=['x-y','y-z', 'z-x'], value='x-y', \n",
    "            description='Slice plane selection:', disabled=False,\n",
    "            style={'description_width': 'initial'}))\n",
    "    \n",
    "    def view_selection(self, view):\n",
    "        # Transpose the volume to orient according to the slice plane selection\n",
    "        orient = {\"y-z\":[1,2,0], \"z-x\":[2,0,1], \"x-y\": [0,1,2]}\n",
    "        self.vol = np.transpose(self.volume, orient[view])\n",
    "        maxZ = self.vol.shape[2] - 1\n",
    "        self.slider = ipyw.IntSlider(min=0, max=self.vol.shape[-1] - 1, step=1, continuous_update=False, \n",
    "            description='Image Slice:')\n",
    "        # Call to view a slice within the selected slice plane\n",
    "        ipyw.interact(self.plot_slice, z=self.slider)\n",
    "        \n",
    "    def update(self, image, mzs):\n",
    "        self.volume = image\n",
    "        self.vol = image\n",
    "        self.mzs = mzs\n",
    "        self.slider.max=self.volume.shape[-1] - 1\n",
    "    \n",
    "    def plot_slice(self, z):\n",
    "        # Plot slice for the given plane and slice\n",
    "        label = \"value: \"+ str(self.mzs[z])\n",
    "        #print(label)\n",
    "        if self.ax is None:\n",
    "            self.fig = plt.figure(figsize=self.figsize)\n",
    "            plt.title(label)\n",
    "            plt.axis('off')\n",
    "            plt.imshow(self.vol[:,:,z], cmap=plt.get_cmap(self.cmap))\n",
    "        else:\n",
    "            self.ax.set_title(label)\n",
    "            self.ax.axis('off')\n",
    "            self.ax.imshow(self.vol[:,:, z], cmap=plt.get_cmap(self.cmap))\n",
    "            \n",
    "            \n",
    "class InteractiveStem():\n",
    "    def __init__(self, ax, image, labels=None):\n",
    "        self.ax = ax\n",
    "        self.ax_stem = ax[1]\n",
    "        self.ax_viewer = ax[2]\n",
    "        self.c = self.ax_stem.get_figure().canvas\n",
    "        self.image = image\n",
    "\n",
    "        line = self.ax_stem.lines[0]\n",
    "        if labels is None:\n",
    "            self.mzs = line.get_xdata()\n",
    "        else:\n",
    "            self.mzs = labels\n",
    "        self.eigenvector = line.get_ydata()\n",
    "                \n",
    "        self.position = 0.1\n",
    "        left, right = self.ax_stem.get_xlim()\n",
    "        self.line = lines.Line2D([left, right], [self.position, self.position], picker=5, color=\"g\")\n",
    "        self.ax_stem.add_line(self.line)\n",
    "        \n",
    "        self.text = self.ax_stem.text(0,0, \"\", va=\"bottom\", ha=\"left\")\n",
    "        \n",
    "        self.viewer_restricted = ImageSliceViewer3D(image, [i for i in range(image.shape[-1])], ax=self.ax_viewer)\n",
    "        self.viewer_restricted.show()\n",
    "        \n",
    "        self.c.draw_idle()\n",
    "        self.sid = self.c.mpl_connect('pick_event', self.clickonline)\n",
    "\n",
    "    def clickonline(self, event):\n",
    "        self.text.set_text(event.artist)\n",
    "        if event.artist == self.line:\n",
    "            self.follower = self.c.mpl_connect(\"motion_notify_event\", self.followmouse)\n",
    "            self.releaser = self.c.mpl_connect('button_press_event', self.releaseonclick)\n",
    "\n",
    "    def followmouse(self, event):\n",
    "        self.line.set_ydata([event.ydata, event.ydata])\n",
    "        self.c.draw_idle()\n",
    "    \n",
    "    def releaseonclick(self, event):\n",
    "        self.position = event.ydata\n",
    "        self.text.set_text(\"\")\n",
    "        indices = np.arange(0, len(self.mzs))\n",
    "        cond = self.eigenvector > self.position if self.position > 0 else self.eigenvector < self.position\n",
    "        indices_above_line = indices[cond]\n",
    "        images_selected = self.image[..., indices_above_line]\n",
    "        mzs_selected = self.mzs[indices_above_line]\n",
    "        #self.text.set_text(str(self.image.shape) + \" \" + str(images_selected.shape) + \" \" + str(mzs_selected.shape))\n",
    "        self.viewer_restricted.update(images_selected, mzs_selected)\n",
    "        self.c.mpl_disconnect(self.releaser)\n",
    "        self.c.mpl_disconnect(self.follower)"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "Read the MALDI image (.nii) and the m/z information (.csv)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 10,
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   "source": [
    "inputname = \"data/peaksel_prominence75.nii\"\n",
    "mzsname = \"data/peaksel_prominence75.csv\"\n",
    "theoreticalname=\"data/species_rule.json\"\n",
    "is_ratio = False\n",
    "threshold = 0\n",
    "normname = None\n",
    "\n",
    "## Theoretical spectrum\n",
    "species = sr.json_to_species(theoreticalname)\n",
    "ions = [mol for mol in species if mol.category==\"Ion\"]\n",
    "adducts = [mol for mol in species if mol.category==\"Adduct\"]\n",
    "theoretical_spectrum = TheoreticalSpectrum(ions, adducts)\n",
    "\n",
    "## Observed spectrum\n",
    "if inputname.lower().endswith(\".imzml\"):\n",
    "    imzml = imzmlio.open_imzml(inputname)\n",
    "    image = imzmlio.to_image_array(imzml)\n",
    "    mzs, intensities = imzml.getspectrum(0)\n",
    "else:\n",
    "    image = sitk.GetArrayFromImage(sitk.ReadImage(inputname)).T\n",
    "    if mzsname:\n",
    "        with open(mzsname) as csv_file:\n",
    "            csv_reader = csv.reader(csv_file, delimiter=\";\")\n",
    "            mzs = [float(row[0]) for row in csv_reader]\n",
    "    else:\n",
    "        mzs = [i for i in range(image.shape[2])]\n",
    "    mzs = np.asarray(mzs)\n",
    "\n",
    "image = image[..., mzs >= threshold]\n",
    "mzs = mzs[mzs >= threshold]\n",
    "mzs = np.around(mzs, decimals=2)\n",
    "\n",
    "\n",
    "\n",
    "if normname is not None:\n",
    "    print(\"Norm image detected\")\n",
    "    norm_img = sitk.ReadImage(normname)\n",
    "    norm_img = sitk.GetArrayFromImage(norm_img).T\n",
    "    norm_img_3D = norm_img[..., None]\n",
    "    before = image.max()\n",
    "    image = np.divide(image, norm_img_3D, out=np.zeros_like(image, dtype=np.float), where=norm_img_3D!=0)\n",
    "    after = image.max()\n",
    "    print(\"Before max=\", before, \", after=\", after)\n",
    "\n",
    "\n",
    "if is_ratio:\n",
    "    ratio_images, ratio_mzs = fusion.extract_ratio_images(image, mzs)\n",
    "    image = np.concatenate((image, ratio_images), axis=2)\n",
    "    mzs = np.concatenate((mzs, ratio_mzs))\n",
    "    \n",
    "annotation = si.annotation(mzs, theoretical_spectrum.spectrum, 1)\n",
    "labels = np.array([str(val) + \"(\" + str(key) +\")\" for key, val in annotation.items()])"
   ]
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   "source": [
    "Normalize the images such that their intensity is scaled between 0 and 255, according to the minimum and maximum value of each image.\n",
    "Visualize the results with an image slider."
   ]
  },
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       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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   ],
   "source": [
    "image = imzmlio.normalize(image)\n",
    "image_shape = (image.shape[0], image.shape[1])\n",
    "image_norm = fusion.flatten(image)\n",
    "M = image_norm.T\n",
    "spectra_image = pandas.DataFrame(data=M, columns=mzs)\n",
    "\n",
    "\n",
    "viewerSlice = ImageSliceViewer3D(image, mzs, figsize=(4,4))\n",
    "viewerSlice.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Compute the PCA on both the original and transposed matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
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    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing PCA\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(249, 249) (249,)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Done\n"
     ]
    }
   ],
   "source": [
    "print(\"Computing PCA\")\n",
    "p, n = M.shape\n",
    "fit_pca = fusion.pca(M, n)\n",
    "eigenvectors = fit_pca.components_\n",
    "eigenvalues = fit_pca.singular_values_\n",
    "print(eigenvectors.shape, eigenvalues.shape)\n",
    "eigenvectors_transposed = transpose_eigenvectors(M, eigenvectors, eigenvalues)\n",
    "print(\"Done\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Else use other dimension reduction techniques, such as NMF :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing NMF\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Done\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import NMF\n",
    "print(\"Computing NMF\")\n",
    "p, n = M.shape\n",
    "nb_comp = 6\n",
    "nmf = NMF(n_components=nb_comp, init='nndsvda', solver='cd', random_state=0)\n",
    "fit_nmf = nmf.fit(M)\n",
    "eigenvectors = fit_nmf.components_ #H\n",
    "eigenvalues = nmf.fit_transform(M); #W\n",
    "eigenvectors_transposed = eigenvalues.T\n",
    "print(\"Done\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 249)\n",
      "[[5.55312207e+01 1.78923791e+02 3.80409272e+02 ... 2.05152291e+02\n",
      "  1.80129795e+02 5.95556406e+01]\n",
      " [0.00000000e+00 1.63135789e+01 4.18146334e+00 ... 2.78530951e+01\n",
      "  2.89462199e+01 4.06861496e+01]\n",
      " [2.12674958e+01 6.51035883e+01 0.00000000e+00 ... 2.30647464e+01\n",
      "  1.48933872e+01 0.00000000e+00]\n",
      " [0.00000000e+00 2.09164754e-01 1.60666299e+00 ... 7.97426765e+01\n",
      "  3.04579722e+01 1.05413495e+00]\n",
      " [2.51818165e+00 1.43115577e+01 0.00000000e+00 ... 1.95488406e+01\n",
      "  5.85366978e+01 8.59743330e+01]\n",
      " [1.33249085e+01 2.80685609e+01 0.00000000e+00 ... 4.26928817e+01\n",
      "  3.45805743e+01 1.03343152e+01]]\n",
      "(20976, 6)\n"
     ]
    }
   ],
   "source": [
    "print(eigenvectors.shape)\n",
    "print(eigenvectors)\n",
    "print(eigenvalues.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "After the PCA is computed, explore the loadings of the transposed matrix (image for each axis, on the left) and the loadings of the original matrix on the same axis (stem plot, in the middle). Move the first slider to select an axis in the PCA. \n",
    "\n",
    "Move the green horizontal line ($y = a$) in the stem plot to visualize the images (on the right) :\n",
    "  1. whose score is above $a$ for the selected axis, if $a > 0$.\n",
    "  2. whose score is below $a$ for the selected axis, if $a \\leq 0$\n",
    "  \n",
    "Move the second slider to visualize all of these images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
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    "collapsed": false,
    "ein.hycell": false,
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    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'AX4_Na+': 569.1696000000001, 'AX5_Na+': 701.2119000000001, 'AX6_Na+': 833.2542000000001, 'AX7_Na+': 965.2965, 'AX8_Na+': 1097.3388, 'AX9_Na+': 1229.3811, 'AX10_Na+': 1361.4234000000001, 'AX11_Na+': 1493.4657, 'AX12_Na+': 1625.508, 'AX13_Na+': 1757.5503, 'AX14_Na+': 1889.5926, 'AX15_Na+': 2021.6349, 'AX16_Na+': 2153.6772, 'AX17_Na+': 2285.7195, 'AX18_Na+': 2417.7618, 'AX19_Na+': 2549.8041000000003, 'AX20_Na+': 2681.8464000000004, 'AX21_Na+': 2813.8887, 'AX22_Na+': 2945.931, 'AX4_K+': 585.1435, 'AX5_K+': 717.1858000000001, 'AX6_K+': 849.2281, 'AX7_K+': 981.2704, 'AX8_K+': 1113.3127000000002, 'AX9_K+': 1245.3550000000002, 'AX10_K+': 1377.3973000000003, 'AX11_K+': 1509.4396000000002, 'AX12_K+': 1641.4819000000002, 'AX13_K+': 1773.5242000000003, 'AX14_K+': 1905.5665000000001, 'AX15_K+': 2037.6088000000002, 'AX16_K+': 2169.6511, 'AX17_K+': 2301.6934, 'AX18_K+': 2433.7357, 'AX19_K+': 2565.7780000000002, 'AX20_K+': 2697.8203000000003, 'AX21_K+': 2829.8626, 'AX22_K+': 2961.9049}\n"
     ]
    }
   ],
   "source": [
    "def plot_slice(viewer, z, ax):\n",
    "    # Plot slice for the given plane and slice\n",
    "    ImageSliceViewer3D.plot_slice(viewer, z)\n",
    "    ax[1].clear()\n",
    "    ax[2].clear()\n",
    "    ax[1].stem(mzs, eigenvectors[z], use_line_collection=True)\n",
    "    viewer.hline = InteractiveStem(ax, image, labels)\n",
    "\n",
    "plt.close()\n",
    "\n",
    "\n",
    "image_eigenvectors = eigenvectors_transposed.T\n",
    "new_shape = image_shape + (image_eigenvectors.shape[-1],)\n",
    "print(new_shape)\n",
    "image_eigenvectors = image_eigenvectors.reshape(new_shape)\n",
    "fig, ax = plt.subplots(1, 3, figsize=(10,4))\n",
    "viewer = ImageSliceViewer3D(image_eigenvectors, mzs=[i for i in range(new_shape[-1])], ax=ax[0])\n",
    "viewer.plot_slice = lambda z: plot_slice(viewer,z, ax)\n",
    "viewer.show()\n",
    "print(theoretical_spectrum.spectrum)"
   ]
  }
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