t-Distributed Stochastic Neighbor Embedding (t-SNE) is a (prize-winning) technique for dimensionality reduction that is particularly well suited for the visualization of high-dimensional datasets. The technique can be implemented via Barnes-Hut approximations, allowing it to be applied on large real-world datasets.
Below is some code which produce an embedding and output the results to d3js, something like the image below:
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from __future__ import division import numpy as np from collections import defaultdict import json import itertools from sklearn import cluster, preprocessing, manifold from datetime import datetime class KeplerMapper(object): def __init__(self, cluster_algorithm=cluster.DBSCAN(eps=0.5,min_samples=3), nr_cubes=10, overlap_perc=0.1, scaler=preprocessing.MinMaxScaler(), reducer=None, color_function="distance_origin", link_local=False, verbose=1): self.clf = cluster_algorithm self.nr_cubes = nr_cubes self.overlap_perc = overlap_perc self.scaler = scaler self.color_function = color_function self.verbose = verbose self.link_local = link_local self.reducer = reducer self.chunk_dist = [] self.overlap_dist = [] self.d = [] if self.verbose > 0: print("\nnr_cubes = %s \n\noverlap_perc = %s\n\nlink_local = %s\n\nClusterer = %s\n\nScaler = %s\n\n"%(self.nr_cubes, overlap_perc, self.link_local, str(self.clf),str(self.scaler))) def fit_transform(self, X): # Dimensionality Reduction if self.reducer != None: if self.verbose > 0: self.reducer.set_params(**{"verbose":self.verbose}) print("\n..Reducing Dimensionality using: \n\t%s\n"%str(self.reducer)) reducer = self.reducer X = reducer.fit_transform(X) # Scaling if self.scaler != None: if self.verbose > 0: print("\n..Scaling\n") scaler = self.scaler X = scaler.fit_transform(X) # We chop up the min-max column ranges into 'nr_cubes' parts self.chunk_dist = (np.max(X, axis=0) - np.min(X, axis=0))/self.nr_cubes # We calculate the overlapping windows distance self.overlap_dist = self.overlap_perc * self.chunk_dist # We find our starting point self.d = np.min(X, axis=0) return X def map(self, X, dimension_index=[0], dimension_name=""): # This maps the data to a simplicial complex. Returns a dictionary with nodes and links. start = datetime.now() def cube_coordinates_all(nr_cubes, nr_dimensions): # if there are 4 cubes per dimension and 3 dimensions # return the bottom left (origin) coordinates of 64 hypercubes, in a sorted list of Numpy arrays l = [] for x in range(nr_cubes): l += [x] * nr_dimensions return [np.array(list(f)) for f in sorted(set(itertools.permutations(l,nr_dimensions)))] nodes = defaultdict(list) links = defaultdict(list) complex = {} if self.verbose > 0: print("Mapping on data shaped %s using dimensions %s\n"%(str(X.shape),str(dimension_index))) # Scaling if self.scaler != None: scaler = self.scaler X = scaler.fit_transform(X) # Initialize Cluster Algorithm clf = self.clf # Prefix'ing the data with ID's ids = np.array([x for x in range(X.shape[0])]) X = np.c_[ids,X] # Subdivide the data X in intervals/hypercubes with overlap if self.verbose > 0: total_cubes = len(cube_coordinates_all(self.nr_cubes,len(dimension_index))) print("Creating %s hypercubes."%total_cubes) di = np.array(dimension_index) for i, coor in enumerate(cube_coordinates_all(self.nr_cubes,di.shape[0])): # Slice the hypercube hypercube = X[ np.invert(np.any((X[:,di+1] >= self.d[di] + (coor * self.chunk_dist[di])) & (X[:,di+1] < self.d[di] + (coor * self.chunk_dist[di]) + self.chunk_dist[di] + self.overlap_dist[di]) == False, axis=1 )) ] if self.verbose > 1: print("There are %s points in cube_%s / %s with starting range %s"% (hypercube.shape[0],i,total_cubes,self.d[di] + (coor * self.chunk_dist[di]))) # If at least one sample inside the hypercube if hypercube.shape[0] > 0: # Cluster the data point(s) inside the cube, skipping the id-column clf.fit(hypercube[:,1:]) if self.verbose > 1: print("Found %s clusters in cube_%s\n"%(np.unique(clf.labels_[clf.labels_ > -1]).shape[0],i)) #Now for every (sample id in cube, predicted cluster label) for a in np.c_[hypercube[:,0],clf.labels_]: if a[1] != -1: #if not predicted as noise cluster_id = str(coor[0])+"_"+str(i)+"_"+str(a[1])+"_"+str(coor)+"_"+str(self.d[di] + (coor * self.chunk_dist[di])) # Rudimentary cluster id nodes[cluster_id].append( int(a[0]) ) # Append the member id's as integers else: if self.verbose > 1: print("Cube_%s is empty.\n"%(i)) # Create links when clusters from different hypercubes have members with the same sample id. for k in nodes: for kn in nodes: if k != kn: if len(nodes[k] + nodes[kn]) != len(set(nodes[kn] + nodes[k])): # there are non-unique id's in the union links[k].append( kn ) # Create links between local hypercube clusters if setting link_local = True if self.link_local: if k.split("_")[0] == kn.split("_")[0]: links[k].append( kn ) # Reporting if self.verbose > 0: nr_links = 0 for k in links: nr_links += len(links[k]) print("\ncreated %s edges and %s nodes in %s."%(nr_links,len(nodes),str(datetime.now()-start))) complex["nodes"] = nodes complex["links"] = links complex["meta"] = dimension_name return complex def visualize(self, complex, path_html="mapper_visualization_output.html", title="My Data", graph_link_distance=30, graph_gravity=0.1, graph_charge=-120, custom_tooltips=None): # Turns the dictionary 'complex' in a html file with d3.js # Format JSON json_s = {} json_s["nodes"] = [] json_s["links"] = [] k2e = {} # a key to incremental int dict, used for id's when linking for e, k in enumerate(complex["nodes"]): # Tooltip formatting if custom_tooltips is not None: tooltip_s = "<h2>Cluster %s</h2>"%k + " ".join([str(f) for f in custom_tooltips[complex["nodes"][k]]]) if self.color_function == "average_signal_cluster": tooltip_i = int(((sum([f for f in custom_tooltips[complex["nodes"][k]]]) / len(custom_tooltips[complex["nodes"][k]])) * 30) ) json_s["nodes"].append({"name": str(k), "tooltip": tooltip_s, "group": 2 * int(np.log(len(complex["nodes"][k]))), "color": str(tooltip_i)}) else: json_s["nodes"].append({"name": str(k), "tooltip": tooltip_s, "group": 2 * int(np.log(len(complex["nodes"][k]))), "color": str(k.split("_")[0])}) else: tooltip_s = "<h2>Cluster %s</h2>Contains %s members."%(k,len(complex["nodes"][k])) json_s["nodes"].append({"name": str(k), "tooltip": tooltip_s, "group": 2 * int(np.log(len(complex["nodes"][k]))), "color": str(k.split("_")[0])}) #json_s["nodes"].append({"name": str(k), "tooltip": tooltip_s, "group": 2 * int(np.log(len(complex["nodes"][k]))), "color": str(tooltip_i)}) k2e[k] = e for k in complex["links"]: for link in complex["links"][k]: json_s["links"].append({"source": k2e[k], "target":k2e[link],"value":1}) with open(path_html,"wb") as outfile: html = """<!DOCTYPE html> <meta charset="utf-8"> <meta name="generator" content="KeplerMapper"> <title>%s | KeplerMapper</title> <link href='https://fonts.googleapis.com/css?family=Roboto:700,300' rel='stylesheet' type='text/css'> <style> * {margin: 0; padding: 0;} html { height: 100%%;} body {background: #111; height: 100%%; font: 100 16px Roboto, Sans-serif;} .link { stroke: #999; stroke-opacity: .333; } .divs div { border-radius: 50%%; background: red; position: absolute; } .divs { position: absolute; top: 0; left: 0; } #holder { position: relative; width: 1300px; height: 900px; background: #111; display: block;} h1 { padding: 20px; color: #fafafa; text-shadow: 0px 1px #000,0px -1px #000; position: absolute; font: 300 30px Roboto, Sans-serif;} h2 { text-shadow: 0px 1px #000,0px -1px #000; font: 700 16px Roboto, Sans-serif;} p { position: absolute; opacity: 0.9; width: 220px; top: 80px; left: 20px; display: block; background: #000; line-height: 25px; color: #fafafa; border: 20px solid #000; font: 100 16px Roboto, Sans-serif;} div.tooltip { position: absolute; width: 380px; display: block; padding: 20px; background: #000; border: 0px; border-radius: 3px; pointer-events: none; z-index: 999; color: #FAFAFA;} } </style> <body> <div id="holder"> <h1>%s</h1> <p> <b>Lens</b><br>%s<br><br> <b>Cubes per dimension</b><br>%s<br><br> <b>Overlap percentage</b><br>%s%%<br><br> <b>Linking locally</b><br>%s<br><br> <b>Color Function</b><br>%s( %s )<br><br> <b>Clusterer</b><br>%s<br><br> <b>Scaler</b><br>%s </p> </div> <script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.5/d3.min.js"></script> <script> var width = 1300, height = 900; var color = d3.scale.ordinal() .domain(["0","1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13","14","15","16","17","18","19","20","21","22","23","24","25","26","27","28","29","30"]) .range(["#FF0000","#FF1400","#FF2800","#FF3c00","#FF5000","#FF6400","#FF7800","#FF8c00","#FFa000","#FFb400","#FFc800","#FFdc00","#FFf000","#fdff00","#b0ff00","#65ff00","#17ff00","#00ff36","#00ff83","#00ffd0","#00e4ff","#00c4ff","#00a4ff","#00a4ff","#0084ff","#0064ff","#0044ff","#0022ff","#0002ff","#0100ff","#0300ff","#0500ff"]); var force = d3.layout.force() .charge(%s) .linkDistance(%s) .gravity(%s) .size([width, height]); var svg = d3.select("#holder").append("svg") .attr("width", width) .attr("height", height); var div = d3.select("#holder").append("div") .attr("class", "tooltip") .style("opacity", 0.0); var divs = d3.select('#holder').append('div') .attr('class', 'divs') .attr('style', function(d) { return 'overflow: hidden; width: ' + width + 'px; height: ' + height + 'px;'; }); graph = %s; force .nodes(graph.nodes) .links(graph.links) .start(); var link = svg.selectAll(".link") .data(graph.links) .enter().append("line") .attr("class", "link") .style("stroke-width", function(d) { return Math.sqrt(d.value); }); var node = divs.selectAll('div') .data(graph.nodes) .enter().append('div') .on("mouseover", function(d) { div.transition() .duration(200) .style("opacity", .9); div .html(d.tooltip + "<br/>") .style("left", (d3.event.pageX + 100) + "px") .style("top", (d3.event.pageY - 28) + "px"); }) .on("mouseout", function(d) { div.transition() .duration(500) .style("opacity", 0); }) .call(force.drag); node.append("title") .text(function(d) { return d.name; }); force.on("tick", function() { link.attr("x1", function(d) { return d.source.x; }) .attr("y1", function(d) { return d.source.y; }) .attr("x2", function(d) { return d.target.x; }) .attr("y2", function(d) { return d.target.y; }); node.attr("cx", function(d) { return d.x; }) .attr("cy", function(d) { return d.y; }) .attr('style', function(d) { return 'width: ' + (d.group * 2) + 'px; height: ' + (d.group * 2) + 'px; ' + 'left: '+(d.x-(d.group))+'px; ' + 'top: '+(d.y-(d.group))+'px; background: '+color(d.color)+'; box-shadow: 0px 0px 3px #111; box-shadow: 0px 0px 33px '+color(d.color)+', inset 0px 0px 5px rgba(0, 0, 0, 0.2);'}) ; }); </script>"""%(title,title,complex["meta"],self.nr_cubes,self.overlap_perc*100,self.link_local,self.color_function,complex["meta"],str(self.clf),str(self.scaler),graph_charge,graph_link_distance,graph_gravity,json.dumps(json_s)) outfile.write(html.encode("utf-8")) if self.verbose > 0: print("\nWrote d3.js graph to '%s'"%path_html) if __name__ == "__main__": # Get data import pandas as pd train = pd.read_csv("./train.csv") features = [c for c in train.columns if c not in "label"] data = np.array(train[features])[:4000] y = np.array(train["label"])[:4000] # Create images for a custom tooltip array from io import BytesIO from scipy.misc import imsave, toimage import base64 tooltip_s = [] for image_data in data: output = BytesIO() img = toimage(image_data.reshape((28,28))) # Data was a flat row of 64 "pixels". img.save(output, format="PNG") contents = "<img src='data:image/png;base64,"+base64.encodebytes(output.getvalue()).decode()+"'>" tooltip_s.append( contents ) output.close() tooltip_s = np.array(tooltip_s) # need to make sure to feed it as a NumPy array, not a list # Initialize to use t-SNE with 2 components (reduces data to 2 dimensions). Also note high overlap_percentage. mapper = KeplerMapper(cluster_algorithm=cluster.DBSCAN(eps=0.3, min_samples=15), reducer = manifold.TSNE(), nr_cubes=35, overlap_perc=0.5, link_local=False, verbose=1) # Fit and transform data data = mapper.fit_transform(data) # Create the graph complex = mapper.map(data, dimension_index=[0,1], dimension_name="t-SNE(2) 2D") # Create the visualizations (increased the graph_gravity for a tighter graph-look.) # Tooltips with image data for every cluster member mapper.visualize(complex, "results.html", "t-SNE on first 4k images", graph_charge=-50, graph_gravity=0.15, custom_tooltips=tooltip_s) |
