Clustering for dataset exploration
A Summary of lecture "Unsupervised Learning with scikit-learn", via datacamp
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
Unsupervised Learning
- Unsupervised Learning
- Finds patterns in data (E.g., clustering customers by their purchase)
- Compressing the data using purchase patterns (dimension reduction)
-
Supervised vs unsupervised learning
-
Supervised learning finds patterns for a prediction task
e.g., classify tumors as benign or cancerous (labels)
- Unsupervised learning finds patterns in data, but without a specific prediction task in mind
-
- K-means clustering
- Finds clusters of samples
- Number of clusters must be specified
- Cluster labels for new samples
- New samples can be assigned to existing clusters
- k-means remembers the mean of each cluster (the "centroids")
- Finds the nearest centroid to each new sample
points = np.array([[ 0.06544649, -0.76866376],
[-1.52901547, -0.42953079],
[ 1.70993371, 0.69885253],
[ 1.16779145, 1.01262638],
[-1.80110088, -0.31861296],
[-1.63567888, -0.02859535],
[ 1.21990375, 0.74643463],
[-0.26175155, -0.62492939],
[-1.61925804, -0.47983949],
[-1.84329582, -0.16694431],
[ 1.35999602, 0.94995827],
[ 0.42291856, -0.7349534 ],
[-1.68576139, 0.10686728],
[ 0.90629995, 1.09105162],
[-1.56478322, -0.84675394],
[-0.0257849 , -1.18672539],
[ 0.83027324, 1.14504612],
[ 1.22450432, 1.35066759],
[-0.15394596, -0.71704301],
[ 0.86358809, 1.06824613],
[-1.43386366, -0.2381297 ],
[ 0.03844769, -0.74635022],
[-1.58567922, 0.08499354],
[ 0.6359888 , -0.58477698],
[ 0.24417242, -0.53172465],
[-2.19680359, 0.49473677],
[ 1.0323503 , -0.55688 ],
[-0.28858067, -0.39972528],
[ 0.20597008, -0.80171536],
[-1.2107308 , -0.34924109],
[ 1.33423684, 0.7721489 ],
[ 1.19480152, 1.04788556],
[ 0.9917477 , 0.89202008],
[-1.8356219 , -0.04839732],
[ 0.08415721, -0.71564326],
[-1.48970175, -0.19299604],
[ 0.38782418, -0.82060119],
[-0.01448044, -0.9779841 ],
[-2.0521341 , -0.02129125],
[ 0.10331194, -0.82162781],
[-0.44189315, -0.65710974],
[ 1.10390926, 1.02481182],
[-1.59227759, -0.17374038],
[-1.47344152, -0.02202853],
[-1.35514704, 0.22971067],
[ 0.0412337 , -1.23776622],
[ 0.4761517 , -1.13672124],
[ 1.04335676, 0.82345905],
[-0.07961882, -0.85677394],
[ 0.87065059, 1.08052841],
[ 1.40267313, 1.07525119],
[ 0.80111157, 1.28342825],
[-0.16527516, -1.23583804],
[-0.33779221, -0.59194323],
[ 0.80610749, -0.73752159],
[-1.43590032, -0.56384446],
[ 0.54868895, -0.95143829],
[ 0.46803131, -0.74973907],
[-1.5137129 , -0.83914323],
[ 0.9138436 , 1.51126532],
[-1.97233903, -0.41155375],
[ 0.5213406 , -0.88654894],
[ 0.62759494, -1.18590477],
[ 0.94163014, 1.35399335],
[ 0.56994768, 1.07036606],
[-1.87663382, 0.14745773],
[ 0.90612186, 0.91084011],
[-1.37481454, 0.28428395],
[-1.80564029, -0.96710574],
[ 0.34307757, -0.79999275],
[ 0.70380566, 1.00025804],
[-1.68489862, -0.30564595],
[ 1.31473221, 0.98614978],
[ 0.26151216, -0.26069251],
[ 0.9193121 , 0.82371485],
[-1.21795929, -0.20219674],
[-0.17722723, -1.02665245],
[ 0.64824862, -0.66822881],
[ 0.41206786, -0.28783784],
[ 1.01568202, 1.13481667],
[ 0.67900254, -0.91489502],
[-1.05182747, -0.01062376],
[ 0.61306599, 1.78210384],
[-1.50219748, -0.52308922],
[-1.72717293, -0.46173916],
[-1.60995631, -0.1821007 ],
[-1.09111021, -0.0781398 ],
[-0.01046978, -0.80913034],
[ 0.32782303, -0.80734754],
[ 1.22038503, 1.1959793 ],
[-1.33328681, -0.30001937],
[ 0.87959517, 1.11566491],
[-1.14829098, -0.30400762],
[-0.58019755, -1.19996018],
[-0.01161159, -0.78468854],
[ 0.17359724, -0.63398145],
[ 1.32738556, 0.67759969],
[-1.93467327, 0.30572472],
[-1.57761893, -0.27726365],
[ 0.47639 , 1.21422648],
[-1.65237509, -0.6803981 ],
[-0.12609976, -1.04327457],
[-1.89607082, -0.70085502],
[ 0.57466899, 0.74878369],
[-0.16660312, -0.83110295],
[ 0.8013355 , 1.22244435],
[ 1.18455426, 1.4346467 ],
[ 1.08864428, 0.64667112],
[-1.61158505, 0.22805725],
[-1.57512205, -0.09612576],
[ 0.0721357 , -0.69640328],
[-1.40054298, 0.16390598],
[ 1.09607713, 1.16804691],
[-2.54346204, -0.23089822],
[-1.34544875, 0.25151126],
[-1.35478629, -0.19103317],
[ 0.18368113, -1.15827725],
[-1.31368677, -0.376357 ],
[ 0.09990129, 1.22500491],
[ 1.17225574, 1.30835143],
[ 0.0865397 , -0.79714371],
[-0.21053923, -1.13421511],
[ 0.26496024, -0.94760742],
[-0.2557591 , -1.06266022],
[-0.26039757, -0.74774225],
[-1.91787359, 0.16434571],
[ 0.93021139, 0.49436331],
[ 0.44770467, -0.72877918],
[-1.63802869, -0.58925528],
[-1.95712763, -0.10125137],
[ 0.9270337 , 0.88251423],
[ 1.25660093, 0.60828073],
[-1.72818632, 0.08416887],
[ 0.3499788 , -0.30490298],
[-1.51696082, -0.50913109],
[ 0.18763605, -0.55424924],
[ 0.89609809, 0.83551508],
[-1.54968857, -0.17114782],
[ 1.2157457 , 1.23317728],
[ 0.20307745, -1.03784906],
[ 0.84589086, 1.03615273],
[ 0.53237919, 1.47362884],
[-0.05319044, -1.36150553],
[ 1.38819743, 1.11729915],
[ 1.00696304, 1.0367721 ],
[ 0.56681869, -1.09637176],
[ 0.86888296, 1.05248874],
[-1.16286609, -0.55875245],
[ 0.27717768, -0.83844015],
[ 0.16563267, -0.80306607],
[ 0.38263303, -0.42683241],
[ 1.14519807, 0.89659026],
[ 0.81455857, 0.67533667],
[-1.8603152 , -0.09537561],
[ 0.965641 , 0.90295579],
[-1.49897451, -0.33254044],
[-0.1335489 , -0.80727582],
[ 0.12541527, -1.13354906],
[ 1.06062436, 1.28816358],
[-1.49154578, -0.2024641 ],
[ 1.16189032, 1.28819877],
[ 0.54282033, 0.75203524],
[ 0.89221065, 0.99211624],
[-1.49932011, -0.32430667],
[ 0.3166647 , -1.34482915],
[ 0.13972469, -1.22097448],
[-1.5499724 , -0.10782584],
[ 1.23846858, 1.37668804],
[ 1.25558954, 0.72026098],
[ 0.25558689, -1.28529763],
[ 0.45168933, -0.55952093],
[ 1.06202057, 1.03404604],
[ 0.67451908, -0.54970299],
[ 0.22759676, -1.02729468],
[-1.45835281, -0.04951074],
[ 0.23273501, -0.70849262],
[ 1.59679589, 1.11395076],
[ 0.80476105, 0.544627 ],
[ 1.15492521, 1.04352191],
[ 0.59632776, -1.19142897],
[ 0.02839068, -0.43829366],
[ 1.13451584, 0.5632633 ],
[ 0.21576204, -1.04445753],
[ 1.41048987, 1.02830719],
[ 1.12289302, 0.58029441],
[ 0.25200688, -0.82588436],
[-1.28566081, -0.07390909],
[ 1.52849815, 1.11822469],
[-0.23907858, -0.70541972],
[-0.25792784, -0.81825035],
[ 0.59367818, -0.45239915],
[ 0.07931909, -0.29233213],
[-1.27256815, 0.11630577],
[ 0.66930129, 1.00731481],
[ 0.34791546, -1.20822877],
[-2.11283993, -0.66897935],
[-1.6293824 , -0.32718222],
[-1.53819139, -0.01501972],
[-0.11988545, -0.6036339 ],
[-1.54418956, -0.30389844],
[ 0.30026614, -0.77723173],
[ 0.00935449, -0.53888192],
[-1.33424393, -0.11560431],
[ 0.47504489, 0.78421384],
[ 0.59313264, 1.232239 ],
[ 0.41370369, -1.35205857],
[ 0.55840948, 0.78831053],
[ 0.49855018, -0.789949 ],
[ 0.35675809, -0.81038693],
[-1.86197825, -0.59071305],
[-1.61977671, -0.16076687],
[ 0.80779295, -0.73311294],
[ 1.62745775, 0.62787163],
[-1.56993593, -0.08467567],
[ 1.02558561, 0.89383302],
[ 0.24293461, -0.6088253 ],
[ 1.23130242, 1.00262186],
[-1.9651013 , -0.15886289],
[ 0.42795032, -0.70384432],
[-1.58306818, -0.19431923],
[-1.57195922, 0.01413469],
[-0.98145373, 0.06132285],
[-1.48637844, -0.5746531 ],
[ 0.98745828, 0.69188053],
[ 1.28619721, 1.28128821],
[ 0.85850596, 0.95541481],
[ 0.19028286, -0.82112942],
[ 0.26561046, -0.04255239],
[-1.61897897, 0.00862372],
[ 0.24070183, -0.52664209],
[ 1.15220993, 0.43916694],
[-1.21967812, -0.2580313 ],
[ 0.33412533, -0.86117761],
[ 0.17131003, -0.75638965],
[-1.19828397, -0.73744665],
[-0.12245932, -0.45648879],
[ 1.51200698, 0.88825741],
[ 1.10338866, 0.92347479],
[ 1.30972095, 0.59066989],
[ 0.19964876, 1.14855889],
[ 0.81460515, 0.84538972],
[-1.6422739 , -0.42296206],
[ 0.01224351, -0.21247816],
[ 0.33709102, -0.74618065],
[ 0.47301054, 0.72712075],
[ 0.34706626, 1.23033757],
[-0.00393279, -0.97209694],
[-1.64303119, 0.05276337],
[ 1.44649625, 1.14217033],
[-1.93030087, -0.40026146],
[-2.37296135, -0.72633645],
[ 0.45860122, -1.06048953],
[ 0.4896361 , -1.18928313],
[-1.02335902, -0.17520578],
[-1.32761107, -0.93963549],
[-1.50987909, -0.09473658],
[ 0.02723057, -0.79870549],
[ 1.0169412 , 1.26461701],
[ 0.47733527, -0.9898471 ],
[-1.27784224, -0.547416 ],
[ 0.49898802, -0.6237259 ],
[ 1.06004731, 0.86870008],
[ 1.00207501, 1.38293512],
[ 1.31161394, 0.62833956],
[ 1.13428443, 1.18346542],
[ 1.27671346, 0.96632878],
[-0.63342885, -0.97768251],
[ 0.12698779, -0.93142317],
[-1.34510812, -0.23754226],
[-0.53162278, -1.25153594],
[ 0.21959934, -0.90269938],
[-1.78997479, -0.12115748],
[ 1.23197473, -0.07453764],
[ 1.4163536 , 1.21551752],
[-1.90280976, -0.1638976 ],
[-0.22440081, -0.75454248],
[ 0.59559412, 0.92414553],
[ 1.21930773, 1.08175284],
[-1.99427535, -0.37587799],
[-1.27818474, -0.52454551],
[ 0.62352689, -1.01430108],
[ 0.14024251, -0.428266 ],
[-0.16145713, -1.16359731],
[-1.74795865, -0.06033101],
[-1.16659791, 0.0902393 ],
[ 0.41110408, -0.8084249 ],
[ 1.14757168, 0.77804528],
[-1.65590748, -0.40105446],
[-1.15306865, 0.00858699],
[ 0.60892121, 0.68974833],
[-0.08434138, -0.97615256],
[ 0.19170053, -0.42331438],
[ 0.29663162, -1.13357399],
[-1.36893628, -0.25052124],
[-0.08037807, -0.56784155],
[ 0.35695011, -1.15064408],
[ 0.02482179, -0.63594828],
[-1.49075558, -0.2482507 ],
[-1.408588 , 0.25635431],
[-1.98274626, -0.54584475]])
xs = points[:, 0]
ys = points[:, 1]
plt.scatter(xs, ys)
Clustering 2D points
From the scatter plot of the previous exercise, you saw that the points seem to separate into 3 clusters. You'll now create a KMeans model to find 3 clusters, and fit it to the data points from the previous exercise. After the model has been fit, you'll obtain the cluster labels for some new points using the .predict() method.
new_points = np.array([[ 4.00233332e-01, -1.26544471e+00],
[ 8.03230370e-01, 1.28260167e+00],
[-1.39507552e+00, 5.57292921e-02],
[-3.41192677e-01, -1.07661994e+00],
[ 1.54781747e+00, 1.40250049e+00],
[ 2.45032018e-01, -4.83442328e-01],
[ 1.20706886e+00, 8.88752605e-01],
[ 1.25132628e+00, 1.15555395e+00],
[ 1.81004415e+00, 9.65530731e-01],
[-1.66963401e+00, -3.08103509e-01],
[-7.17482105e-02, -9.37939700e-01],
[ 6.82631927e-01, 1.10258160e+00],
[ 1.09039598e+00, 1.43899529e+00],
[-1.67645414e+00, -5.04557049e-01],
[-1.84447804e+00, 4.52539544e-02],
[ 1.24234851e+00, 1.02088661e+00],
[-1.86147041e+00, 6.38645811e-03],
[-1.46044943e+00, 1.53252383e-01],
[ 4.98981817e-01, 8.98006058e-01],
[ 9.83962244e-01, 1.04369375e+00],
[-1.83136742e+00, -1.63632835e-01],
[ 1.30622617e+00, 1.07658717e+00],
[ 3.53420328e-01, -7.51320218e-01],
[ 1.13957970e+00, 1.54503860e+00],
[ 2.93995694e-01, -1.26135005e+00],
[-1.14558225e+00, -3.78709636e-02],
[ 1.18716105e+00, 6.00240663e-01],
[-2.23211946e+00, 2.30475094e-01],
[-1.28320430e+00, -3.93314568e-01],
[ 4.94296696e-01, -8.83972009e-01],
[ 6.31834930e-02, -9.11952228e-01],
[ 9.35759539e-01, 8.66820685e-01],
[ 1.58014721e+00, 1.03788392e+00],
[ 1.06304960e+00, 1.02706082e+00],
[-1.39732536e+00, -5.05162249e-01],
[-1.09935240e-01, -9.08113619e-01],
[ 1.17346758e+00, 9.47501092e-01],
[ 9.20084511e-01, 1.45767672e+00],
[ 5.82658956e-01, -9.00086832e-01],
[ 9.52772328e-01, 8.99042386e-01],
[-1.37266956e+00, -3.17878215e-02],
[ 2.12706760e-02, -7.07614194e-01],
[ 3.27049052e-01, -5.55998107e-01],
[-1.71590267e+00, 2.15222266e-01],
[ 5.12516209e-01, -7.60128245e-01],
[ 1.13023469e+00, 7.22451122e-01],
[-1.43074310e+00, -3.42787511e-01],
[-1.82724625e+00, 1.17657775e-01],
[ 1.41801350e+00, 1.11455080e+00],
[ 1.26897304e+00, 1.41925971e+00],
[ 8.04076494e-01, 1.63988557e+00],
[ 8.34567752e-01, 1.09956689e+00],
[-1.24714732e+00, -2.23522320e-01],
[-1.29422537e+00, 8.18770024e-02],
[-2.27378316e-01, -4.13331387e-01],
[ 2.18830387e-01, -4.68183120e-01],
[-1.22593414e+00, 2.55599147e-01],
[-1.31294033e+00, -4.28892070e-01],
[-1.33532382e+00, 6.52053776e-01],
[-3.01100233e-01, -1.25156451e+00],
[ 2.02778356e-01, -9.05277445e-01],
[ 1.01357784e+00, 1.12378981e+00],
[ 8.18324394e-01, 8.60841257e-01],
[ 1.26181556e+00, 1.46613744e+00],
[ 4.64867724e-01, -7.97212459e-01],
[ 3.60908898e-01, 8.44106720e-01],
[-2.15098310e+00, -3.69583937e-01],
[ 1.05005281e+00, 8.74181364e-01],
[ 1.06580074e-01, -7.49268153e-01],
[-1.73945723e+00, 2.52183577e-01],
[-1.12017687e-01, -6.52469788e-01],
[ 5.16618951e-01, -6.41267582e-01],
[ 3.26621787e-01, -8.80608015e-01],
[ 1.09017759e+00, 1.10952558e+00],
[ 3.64459576e-01, -6.94215622e-01],
[-1.90779318e+00, 1.87383674e-01],
[-1.95601829e+00, 1.39959126e-01],
[ 3.18541701e-01, -4.05271704e-01],
[ 7.36512699e-01, 1.76416255e+00],
[-1.44175162e+00, -5.72320429e-02],
[ 3.21757168e-01, -5.34283821e-01],
[-1.37317305e+00, 4.64484644e-02],
[ 6.87225910e-02, -1.10522944e+00],
[ 9.59314218e-01, 6.52316210e-01],
[-1.62641919e+00, -5.62423280e-01],
[ 1.06788305e+00, 7.29260482e-01],
[-1.79643547e+00, -9.88307418e-01],
[-9.88628377e-02, -6.81198092e-02],
[-1.05135700e-01, 1.17022143e+00],
[ 8.79964699e-01, 1.25340317e+00],
[ 9.80753407e-01, 1.15486539e+00],
[-8.33224966e-02, -9.24844368e-01],
[ 8.48759673e-01, 1.09397425e+00],
[ 1.32941649e+00, 1.13734563e+00],
[ 3.23788068e-01, -7.49732451e-01],
[-1.52610970e+00, -2.49016929e-01],
[-1.48598116e+00, -2.68828608e-01],
[-1.80479553e+00, 1.87052700e-01],
[-2.01907347e+00, -4.49511651e-01],
[ 2.87202402e-01, -6.55487415e-01],
[ 8.22295102e-01, 1.38443234e+00],
[-3.56997036e-02, -8.01825807e-01],
[-1.66955440e+00, -1.38258505e-01],
[-1.78226821e+00, 2.93353033e-01],
[ 7.25837138e-01, -6.23374024e-01],
[ 3.88432593e-01, -7.61283497e-01],
[ 1.49002783e+00, 7.95678671e-01],
[ 6.55423228e-04, -7.40580702e-01],
[-1.34533116e+00, -4.75629937e-01],
[-8.03845106e-01, -3.09943013e-01],
[-2.49041295e-01, -1.00662418e+00],
[-1.41095118e+00, -7.06744127e-02],
[-1.75119594e+00, -3.00491336e-01],
[-1.27942724e+00, 1.73774600e-01],
[ 3.35028183e-01, 6.24761151e-01],
[ 1.16819649e+00, 1.18902251e+00],
[ 7.15210457e-01, 9.26077419e-01],
[ 1.30057278e+00, 9.16349565e-01],
[-1.21697008e+00, 1.10039477e-01],
[-1.70707935e+00, -5.99659536e-02],
[ 1.20730655e+00, 1.05480463e+00],
[ 1.86896009e-01, -9.58047234e-01],
[ 8.03463471e-01, 3.86133140e-01],
[-1.73486790e+00, -1.49831913e-01],
[ 1.31261499e+00, 1.11802982e+00],
[ 4.04993148e-01, -5.10900347e-01],
[-1.93267968e+00, 2.20764694e-01],
[ 6.56004799e-01, 9.61887161e-01],
[-1.40588215e+00, 1.17134403e-01],
[-1.74306264e+00, -7.47473959e-02],
[ 5.43745412e-01, 1.47209224e+00],
[-1.97331669e+00, -2.27124493e-01],
[ 1.53901171e+00, 1.36049081e+00],
[-1.48323452e+00, -4.90302063e-01],
[ 3.86748484e-01, -1.26173400e+00],
[ 1.17015716e+00, 1.18549415e+00],
[-8.05381721e-02, -3.21923627e-01],
[-6.82273156e-02, -8.52825887e-01],
[ 7.13500028e-01, 1.27868520e+00],
[-1.85014378e+00, -5.03490558e-01],
[ 6.36085266e-02, -1.41257040e+00],
[ 1.52966062e+00, 9.66056572e-01],
[ 1.62165714e-01, -1.37374843e+00],
[-3.23474497e-01, -7.06620269e-01],
[-1.51768993e+00, 1.87658302e-01],
[ 8.88895911e-01, 7.62237161e-01],
[ 4.83164032e-01, 8.81931869e-01],
[-5.52997766e-02, -7.11305016e-01],
[-1.57966441e+00, -6.29220313e-01],
[ 5.51308645e-02, -8.47206763e-01],
[-2.06001582e+00, 5.87697787e-02],
[ 1.11810855e+00, 1.30254175e+00],
[ 4.87016164e-01, -9.90143937e-01],
[-1.65518042e+00, -1.69386383e-01],
[-1.44349738e+00, 1.90299243e-01],
[-1.70074547e-01, -8.26736022e-01],
[-1.82433979e+00, -3.07814626e-01],
[ 1.03093485e+00, 1.26457691e+00],
[ 1.64431169e+00, 1.27773115e+00],
[-1.47617693e+00, 2.60783872e-02],
[ 1.00953067e+00, 1.14270181e+00],
[-1.45285636e+00, -2.55216207e-01],
[-1.74092917e+00, -8.34443177e-02],
[ 1.22038299e+00, 1.28699961e+00],
[ 9.16925397e-01, 7.32070275e-01],
[-1.60754185e-03, -7.26375571e-01],
[ 8.93841238e-01, 8.41146643e-01],
[ 6.33791961e-01, 1.00915134e+00],
[-1.47927075e+00, -6.99781936e-01],
[ 5.44799374e-02, -1.06441970e+00],
[-1.51935568e+00, -4.89276929e-01],
[ 2.89939026e-01, -7.73145523e-01],
[-9.68154061e-03, -1.13302207e+00],
[ 1.13474639e+00, 9.71541744e-01],
[ 5.36421406e-01, -8.47906388e-01],
[ 1.14759864e+00, 6.89915205e-01],
[ 5.73291902e-01, 7.90802710e-01],
[ 2.12377397e-01, -6.07569808e-01],
[ 5.26579548e-01, -8.15930264e-01],
[-2.01831641e+00, 6.78650740e-02],
[-2.35512624e-01, -1.08205132e+00],
[ 1.59274780e-01, -6.00717261e-01],
[ 2.28120356e-01, -1.16003549e+00],
[-1.53658378e+00, 8.40798808e-02],
[ 1.13954609e+00, 6.31782001e-01],
[ 1.01119255e+00, 1.04360805e+00],
[-1.42039867e-01, -4.81230337e-01],
[-2.23120182e+00, 8.49162905e-02],
[ 1.25554811e-01, -1.01794793e+00],
[-1.72493509e+00, -6.94426177e-01],
[-1.60434630e+00, 4.45550868e-01],
[ 7.37153979e-01, 9.26560744e-01],
[ 6.72905271e-01, 1.13366030e+00],
[ 1.20066456e+00, 7.26273093e-01],
[ 7.58747209e-02, -9.83378326e-01],
[ 1.28783262e+00, 1.18088601e+00],
[ 1.06521930e+00, 1.00714746e+00],
[ 1.05871698e+00, 1.12956519e+00],
[-1.12643410e+00, 1.66787744e-01],
[-1.10157218e+00, -3.64137806e-01],
[ 2.35118217e-01, -1.39769949e-01],
[ 1.13853795e+00, 1.01018519e+00],
[ 5.31205654e-01, -8.81990792e-01],
[ 4.33085936e-01, -7.64059042e-01],
[-4.48926156e-03, -1.30548411e+00],
[-1.76348589e+00, -4.97430739e-01],
[ 1.36485681e+00, 5.83404699e-01],
[ 5.66923900e-01, 1.51391963e+00],
[ 1.35736826e+00, 6.70915318e-01],
[ 1.07173397e+00, 6.11990884e-01],
[ 1.00106915e+00, 8.93815326e-01],
[ 1.33091007e+00, 8.79773879e-01],
[-1.79603740e+00, -3.53883973e-02],
[-1.27222979e+00, 4.00156642e-01],
[ 8.47480603e-01, 1.17032364e+00],
[-1.50989129e+00, -7.12318330e-01],
[-1.24953576e+00, -5.57859730e-01],
[-1.27717973e+00, -5.99350550e-01],
[-1.81946743e+00, 7.37057673e-01],
[ 1.19949867e+00, 1.56969386e+00],
[-1.25543847e+00, -2.33892826e-01],
[-1.63052058e+00, 1.61455865e-01],
[ 1.10611305e+00, 7.39698224e-01],
[ 6.70193192e-01, 8.70567001e-01],
[ 3.69670156e-01, -6.94645306e-01],
[-1.26362293e+00, -6.99249285e-01],
[-3.66687507e-01, -1.35310260e+00],
[ 2.44032147e-01, -6.59470793e-01],
[-1.27679142e+00, -4.85453412e-01],
[ 3.77473612e-02, -6.99251605e-01],
[-2.19148539e+00, -4.91199500e-01],
[-2.93277777e-01, -5.89488212e-01],
[-1.65737397e+00, -2.98337786e-01],
[ 7.36638861e-01, 5.78037057e-01],
[ 1.13709081e+00, 1.30119754e+00],
[-1.44146601e+00, 3.13934680e-02],
[ 5.92360708e-01, 1.22545114e+00],
[ 6.51719414e-01, 4.92674894e-01],
[ 5.94559139e-01, 8.25637315e-01],
[-1.87900722e+00, -5.21899626e-01],
[ 2.15225041e-01, -1.28269851e+00],
[ 4.99145965e-01, -6.70268634e-01],
[-1.82954176e+00, -3.39269731e-01],
[ 7.92721403e-01, 1.33785606e+00],
[ 9.54363372e-01, 9.80396626e-01],
[-1.35359846e+00, 1.03976340e-01],
[ 1.05595062e+00, 8.07031927e-01],
[-1.94311010e+00, -1.18976964e-01],
[-1.39604137e+00, -3.10095976e-01],
[ 1.28977624e+00, 1.01753365e+00],
[-1.59503139e+00, -5.40574609e-01],
[-1.41994046e+00, -3.81032569e-01],
[-2.35569801e-02, -1.10133702e+00],
[-1.26038568e+00, -6.93273886e-01],
[ 9.60215981e-01, -8.11553694e-01],
[ 5.51803308e-01, -1.01793176e+00],
[ 3.70185085e-01, -1.06885468e+00],
[ 8.25529207e-01, 8.77007060e-01],
[-1.87032595e+00, 2.87507199e-01],
[-1.56260769e+00, -1.89196712e-01],
[-1.26346548e+00, -7.74725237e-01],
[-6.33800421e-02, -7.59400611e-01],
[ 8.85298280e-01, 8.85620519e-01],
[-1.43324686e-01, -1.16083678e+00],
[-1.83908725e+00, -3.26655515e-01],
[ 2.74709229e-01, -1.04546829e+00],
[-1.45703573e+00, -2.91842036e-01],
[-1.59048842e+00, 1.66063031e-01],
[ 9.25549284e-01, 7.41406406e-01],
[ 1.97245469e-01, -7.80703225e-01],
[ 2.88401697e-01, -8.32425551e-01],
[ 7.24141618e-01, -7.99149200e-01],
[-1.62658639e+00, -1.80005543e-01],
[ 5.84481588e-01, 1.13195640e+00],
[ 1.02146732e+00, 4.59657799e-01],
[ 8.65050554e-01, 9.57714887e-01],
[ 3.98717766e-01, -1.24273147e+00],
[ 8.62234892e-01, 1.10955561e+00],
[-1.35999430e+00, 2.49942654e-02],
[-1.19178505e+00, -3.82946323e-02],
[ 1.29392424e+00, 1.10320509e+00],
[ 1.25679630e+00, -7.79857582e-01],
[ 9.38040302e-02, -5.53247258e-01],
[-1.73512175e+00, -9.76271667e-02],
[ 2.23153587e-01, -9.43474351e-01],
[ 4.01989100e-01, -1.10963051e+00],
[-1.42244158e+00, 1.81914703e-01],
[ 3.92476267e-01, -8.78426277e-01],
[ 1.25181875e+00, 6.93614996e-01],
[ 1.77481317e-02, -7.20304235e-01],
[-1.87752521e+00, -2.63870424e-01],
[-1.58063602e+00, -5.50456344e-01],
[-1.59589493e+00, -1.53932892e-01],
[-1.01829770e+00, 3.88542370e-02],
[ 1.24819659e+00, 6.60041803e-01],
[-1.25551377e+00, -2.96172009e-02],
[-1.41864559e+00, -3.58230179e-01],
[ 5.25758326e-01, 8.70500543e-01],
[ 5.55599988e-01, 1.18765072e+00],
[ 2.81344439e-02, -6.99111314e-01]])
from sklearn.cluster import KMeans
# Create a KMeans instance with 3 clusters: model
model = KMeans(n_clusters=3)
# Fit model to points
model.fit(points)
# Determine the cluster labels of new_points: labels
labels = model.predict(new_points)
# Print cluster labels of new_points
print(labels)
xs = new_points[:, 0]
ys = new_points[:, 1]
# Make a scatter plot of xs and ys, using labels to define the colors
plt.scatter(xs, ys, c=labels, alpha=0.5)
# Assign the cluster centers: centroids
centroids = model.cluster_centers_
# Assign the columns of centroids: centroids_x, centroids_y
centroids_x = centroids[:, 0]
centroids_y = centroids[:, 1]
# Make a scatter plot of centroids_x and centroids_y
plt.scatter(centroids_x, centroids_y, marker='D', s=50, color='red')
plt.savefig('../images/kmeans-centroid.png')
Evaluating a clustering
- Evaluating a clustering
- Can check correspondence with e.g. iris species, but what if there are no species to check against?
- Measure quality of a clustering
- Informs choice of how many clusters to look for
- Cross-tabulation with pandas
- Clusters vs species is a "cross-tabulation"
- Measuring clustering quality
- Using only samples and their cluster labels
- A good clustering has tight clusters
- Samples in each cluster bunched together
- Inertia measures clustering quality
- Measures how spread out the clusters are (lower is better)
- Distance from each sample to centroid of its cluster
- k-means attempts to minimize the inertia when choosing clusters
- How many clusters to choose?
- Choose an "elbow" in the inertia plot
- Where inertia begins to decrease more slowly
How many clusters of grain?
In the video, you learned how to choose a good number of clusters for a dataset using the k-means inertia graph. You are given an array samples containing the measurements (such as area, perimeter, length, and several others) of samples of grain. What's a good number of clusters in this case?
df = pd.read_csv('./dataset/seeds.csv', header=None)
df[7] = df[7].map({1:'Kama wheat', 2:'Rosa wheat', 3:'Canadian wheat'})
df.head()
samples = df.iloc[:, :-1].values
varieties = df.iloc[:, -1].values
ks = range(1,6)
inertias = []
for k in ks:
# Create a KMeans instance with k clusters: model
model = KMeans(n_clusters=k)
# Fit model to samples
model.fit(samples)
# Append the inertia to the list of inertias
inertias.append(model.inertia_)
# Plot ks vs inertias
plt.plot(ks, inertias, '-o')
plt.xlabel('number of clusters, k')
plt.ylabel('inertia')
plt.xticks(ks)
Evaluating the grain clustering
In the previous exercise, you observed from the inertia plot that 3 is a good number of clusters for the grain data. In fact, the grain samples come from a mix of 3 different grain varieties: "Kama", "Rosa" and "Canadian". In this exercise, cluster the grain samples into three clusters, and compare the clusters to the grain varieties using a cross-tabulation.
model = KMeans(n_clusters=3)
# Use fit_predict to fit model and obtain cluster labels: labels
labels = model.fit_predict(samples)
# Create a DataFrame with labels and varieties as columns: df
df = pd.DataFrame({'labels': labels, 'varieties': varieties})
# Create crosstab: ct
ct = pd.crosstab(df['labels'], df['varieties'])
# Display ct
print(ct)
Transforming features for better clusterings
- StandardScaler
- In kmeans, feature variance = feature influence
-
StandardScalertransforms each feature to have mean 0 and variance 1 - Features are said to be "standardized"
- StandardScaler, then KMeans
- Need to perform two steps:
StandardScaler, thenKMeans - Use
sklearnpipeline to combine multiple steps - Data flows from one step into the next
- Need to perform two steps:
Scaling fish data for clustering
You are given an array samples giving measurements of fish. Each row represents an individual fish. The measurements, such as weight in grams, length in centimeters, and the percentage ratio of height to length, have very different scales. In order to cluster this data effectively, you'll need to standardize these features first. In this exercise, you'll build a pipeline to standardize and cluster the data.
These fish measurement data were sourced from the Journal of Statistics Education.
df = pd.read_csv('./dataset/fish.csv', header=None)
df.head()
samples = df.iloc[:, 1:].values
species = df.iloc[:, 0].values
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.cluster import KMeans
# Create scaler: scaler
scaler = StandardScaler()
# Create KMeans instance: kmeans
kmeans = KMeans(n_clusters=4)
# Create pipeline: pipeline
pipeline = make_pipeline(scaler, kmeans)
pipeline.fit(samples)
# Calculate the cluster labels: labels
labels = pipeline.predict(samples)
# Create a DataFrame with labels and species as columns: df
df = pd.DataFrame({'labels': labels, 'species': species})
# Create crosstab: ct
ct = pd.crosstab(df['labels'], df['species'])
# Display ct
print(ct)
Clustering stocks using KMeans
In this exercise, you'll cluster companies using their daily stock price movements (i.e. the dollar difference between the closing and opening prices for each trading day). You are given a NumPy array movements of daily price movements from 2010 to 2015 (obtained from Yahoo! Finance), where each row corresponds to a company, and each column corresponds to a trading day.
Some stocks are more expensive than others. To account for this, include a Normalizer at the beginning of your pipeline. The Normalizer will separately transform each company's stock price to a relative scale before the clustering begins.
Note that Normalizer() is different to StandardScaler(), which you used in the previous exercise. While StandardScaler() standardizes features (such as the features of the fish data from the previous exercise) by removing the mean and scaling to unit variance, Normalizer() rescales each sample - here, each company's stock price - independently of the other.
df = pd.read_csv('./dataset/company-stock-movements-2010-2015-incl.csv', index_col=0)
df.head()
movements = df.values
companies = df.index.values
from sklearn.preprocessing import Normalizer
# Create a normalizer: normalizer
normalizer = Normalizer()
# Create a KMeans model with 10 clusters: kmeans
kmeans = KMeans(n_clusters=10)
# Make a pipeline chaining normalizer and kmeans: pipeline
pipeline = make_pipeline(normalizer, kmeans)
# Fit pipeline to the daily price movements
pipeline.fit(movements)
labels = pipeline.predict(movements)
# Create a DataFrame aligning labels and companies: df
df = pd.DataFrame({'labels': labels, 'companies': companies})
# Display df sorted by cluster label
print(df.sort_values('labels'))