多維空間可視化

Recently, I was working on a project where I was trying to build a model that could predict housing prices in King County, Washington — the area that surrounds Seattle. After looking at the features, I wanted a way to determine the houses’ worth based on location.

最近，我在一個(gè)項(xiàng)目中嘗試建立一個(gè)可以預(yù)測(cè)華盛頓金縣(西雅圖周邊地區(qū))房?jī)r(jià)的模型。 在查看了這些功能之后，我想找到一種根據(jù)位置確定房屋價(jià)值的方法。

The dataset included latitude and longitude and it was easy to google them to take a look at the houses, their neighborhoods, their distance from the water, etc. But with over 17000 observations, that was a fool’s task. I had to find an easier way.

數(shù)據(jù)集包括緯度和經(jīng)度，可以很容易地用谷歌瀏覽一下房屋，附近，距水的距離等。但是，通過(guò)17000多個(gè)觀察，這是一個(gè)傻瓜的任務(wù)。 我必須找到一種更簡(jiǎn)單的方法。

I had used Geographic Information Systems (GIS) only once before but not in Python. So I did what I do best: I googled, and ran into this amazing package called GeoPandas. I am going to let the GeoPandas team sum up what they do because they can say much better than I can.

我以前只使用過(guò)一次地理信息系統(tǒng)(GIS)，而沒(méi)有在Python中使用過(guò)。 因此，我做了我最擅長(zhǎng)的事情：我搜索了Google，并遇到了一個(gè)名為GeoPandas的驚人軟件包。 我要讓GeoPandas團(tuán)隊(duì)總結(jié)他們所做的事情，因?yàn)樗麄兊陌l(fā)言能力比我更好。

GeoPandas is an open source project to make working with geospatial data in python easier. GeoPandas extends the datatypes used by pandas to allow spatial operations on geometric types. Geometric operations are performed by shapely. GeoPandas further depends on fiona for file access and descartes and matplotlib for plotting. — Description from GeoPandas Website (2020)

GeoPandas是一個(gè)開(kāi)源項(xiàng)目，可簡(jiǎn)化使用python中的地理空間數(shù)據(jù)的工作。 GeoPandas擴(kuò)展了熊貓使用的數(shù)據(jù)類型，以允許對(duì)幾何類型進(jìn)行空間操作。 幾何運(yùn)算是通過(guò)勻稱進(jìn)行的。 GeoPandas進(jìn)一步依賴于fiona進(jìn)行文件訪問(wèn)，并依賴笛卡爾和matplotlib進(jìn)行繪圖。 — GeoPandas網(wǎng)站(2020)的說(shuō)明

This blew my mind, and what I wanted was really just the most basic of the features. I am going to show you how to run this code and do what I did — plotting accurate points on a map.

這讓我大吃一驚，而我想要的實(shí)際上只是最基本的功能。 我將向您展示如何運(yùn)行此代碼并完成我的工作-在地圖上繪制準(zhǔn)確的點(diǎn)。

You are going to need several packages and some files in addition to the basic pandas and matplotlib. They include:

除了基本的pandas和matplotlib外，您還需要幾個(gè)軟件包和一些文件。 它們包括：

• geopandas — the package that makes all of this possible
  geopandas-使所有這些成為可能的軟件包

• shapely — package for manipulation and analysis of planar geometric objects

  勻稱 —用于處理和分析平面幾何對(duì)象的程序包

• descartes — provides a nicer integration of Shapely geometry objects with Matplotlib. It’s not needed every time but I import it just to be safe

  笛卡爾(笛卡爾) -將Shapely幾何對(duì)象與Matplotlib更好地集成。 并非每次都需要它，但為了安全起見(jiàn)我將其導(dǎo)入

• Any .shp file — this is going to be the backdrop of the plot. Mine is going to have King County, but you should be able to find one from any city’s data department. Don’t delete any files from the .zip file it comes in. Something always breaks.
  任何.shp文件-這將是情節(jié)的背景。 我的將有金縣，但您應(yīng)該可以從任何城市的數(shù)據(jù)部門中找到一個(gè)。 不要從它所包含的.zip文件中刪除任何文件。總有東西會(huì)中斷。

More information about shapefiles can be found here, but the long and short of it is that these aren’t normal images. They are a vector data storage format that has information linking to locations — coordinates and the rest.

關(guān)于shapefile的更多信息可以在這里找到，但總的來(lái)說(shuō)，它們不是正常圖像。 它們是矢量數(shù)據(jù)存儲(chǔ)格式，具有鏈接到位置(坐標(biāo)和其余位置)的信息。

First I imported the basic packages that I needed and then the new packages:

首先，我導(dǎo)入了所需的基本軟件包，然后導(dǎo)入了新軟件包：

import matplotlib.pyplot as plt import numpy as np from shapely.geometry import Point,Polygon import geopandas as gpd import descartes

The Point and Polygon features are what help me match my data to the map I make.

點(diǎn)和多邊形功能可以幫助我將數(shù)據(jù)與我制作的地圖進(jìn)行匹配。

Next, I load in my data. This is basic pandas but for those that are new, everything in quotations is the name of the file I had to access the housing records.

接下來(lái)，我加載我的數(shù)據(jù)。 這是基本的大熊貓，但對(duì)于新熊貓，引號(hào)中的所有內(nèi)容都是我必須訪問(wèn)房屋記錄的文件的名稱。

df = pd.read_csv('kc_house_data_train.csv')

With all of the packages imported and the data ready to go, I wanted to take a look at the map I was going to be plotting. I did this by finding a shape file made by the King County government website. They have done all the hard work of surveying and cataloging the land — it would be rude to not use their freely offered services. Loading in the shape file is easy and comparable to loading in a csv file with pandas.

導(dǎo)入了所有軟件包并準(zhǔn)備好數(shù)據(jù)后，我想看一下我要繪制的地圖。 我通過(guò)查找金縣政府網(wǎng)站制作的形狀文件來(lái)完成此操作。 他們已經(jīng)完成了土地測(cè)量和分類的所有艱苦工作-不使用免費(fèi)提供的服務(wù)是不禮貌的。 加載到shape文件中很容易，并且與使用pandas加載到csv文件中相當(dāng)。

kings_county = gpd.read_file('*file_path_here*/School_Districts_in_King_County___schdst_area.shp')

You can open this up if you want to take a look at the data. The King County shape file was just a dataframe of locations matched with their school districts, geometry coordinates, and area. But the best part is when we plot it and yes, we have to plot it. This isn’t an image you can just call — it will have the coordinates built in so our data can be placed down like a point on a 5th grade (x,y) graph.

如果要查看數(shù)據(jù)，可以打開(kāi)此窗口。 金縣形狀文件只是與他們的學(xué)區(qū)，幾何坐標(biāo)和面積相匹配的位置的數(shù)據(jù)框。 但是最好的部分是當(dāng)我們繪制它時(shí)，是的，我們必須繪制它。 這不是您只能調(diào)用的圖像-它具有內(nèi)置的坐標(biāo)，因此我們的數(shù)據(jù)可以像5級(jí)(x，y)圖上的點(diǎn)一樣放置。

Using the below code (notice how I edited it the same way I would edit a graph):

使用下面的代碼(注意，我以與編輯圖形相同的方式對(duì)其進(jìn)行編輯)：

fig, ax = plt.subplots(figsize = (15,15)) kings_county.plot(ax=ax) ax.set_title('King County',fontdict = {'fontsize': 30}) ax.set_ylabel('Latitude',fontdict = {'fontsize': 20}) ax.set_xlabel('Longitude',fontdict = {'fontsize': 20})

My output looked like this:

我的輸出看起來(lái)像這樣：

Graphic by Author圖形作者

Before we start adding our housing data we should look at utilizing the shape file to the fullest. Let’s take a look at the file.

在開(kāi)始添加房屋數(shù)據(jù)之前，我們應(yīng)該充分利用形狀文件。 讓我們看一下文件。

OID D# NAME geometry 0 1 1 Seattle MULTIPOLYGON (((-122.40324 47.66637... 1 2 210 Federal Way POLYGON ((-122.29057 47.39374... 2 3 216 Enumclaw POLYGON ((-121.84898 47.34708... 3 4 400 Mercer Island POLYGON ((-122.24475 47.59601... 4 5 401 Highline POLYGON ((-122.35853 47.51553...- Truncated for clarity

As you can see, the county is divided on school districts — each with a shape used as boundaries. We will now try to plot the shape file and annotate the districts using the data provided like so:

如您所見(jiàn)，該縣分為多個(gè)學(xué)區(qū)-每個(gè)學(xué)區(qū)的形狀都用作邊界。 現(xiàn)在，我們將嘗試?yán)L制形狀文件并使用提供的數(shù)據(jù)對(duì)區(qū)域進(jìn)行注釋，如下所示：

left = ['Riverview','Snoqualmie Valley'] center = ['Skykomish','Kent','Auburn','Tahoma','VashonIsland','Northshore','Shoreline','Renton','Highline','Issaquah','Enumclaw','Seattle','FederalWay','Bellevue','Mercer Island','LakeWashington','Tukwila'] right = ['Fife'] kings_county.plot(figsize = (15,15),cmap = 'gist_earth') for idx, row in kings_county.iterrows():if row['NAME'] in left:plt.annotate(s=row['NAME'], xy=row['coords'],ha='left', color = 'red')elif row['NAME'] in center:plt.annotate(s=row['NAME'], xy=row['coords'],ha='center', color = 'red')elif row['NAME'] in right:plt.annotate(s=row['NAME'], xy=row['coords'],ha='right', color = 'red') plt.title('School Districts in Kings County, WA', fontdict = {'fontsize': 20}) plt.ylabel('Latitude',fontdict = {'fontsize': 20}) plt.xlabel('Longitude',fontdict = {'fontsize': 20})

The lists — left, right, center — are from trial and error with the placement of the district names. Some overlapped or needed to be manipulated so that they did not stray too far from their actual district.

列表(左，右，中心)來(lái)自地區(qū)名稱的放置，反復(fù)嘗試。 有些重疊或需要進(jìn)行操縱，以使它們不會(huì)偏離實(shí)際區(qū)域。

I’ve changed the color map to gist_earth for clarity. Next, I iterated through each row using the entry in the NAME series, and placing the title at a point that was definitely in the polygon. I aligned the names based on the lists I had made earlier. And this was out output:

為了清楚起見(jiàn)，我將顏色映射更改為gist_earth 。 接下來(lái)，我使用NAME系列中的條目遍歷每一行，并將標(biāo)題放置在肯定位于多邊形中的點(diǎn)上。 我根據(jù)之前的清單排列了名稱。 這是輸出：

School Districts of King County. Graphic by Author金縣學(xué)區(qū)。 圖形作者

Each of the regions signifies a school district in King County. This matches the data I found about the twenty school districts in the county. I never really thought about the size and shape of a county, so I googled it just to be sure.

每個(gè)地區(qū)都代表金縣的學(xué)區(qū)。 這與我發(fā)現(xiàn)的有關(guān)該縣二十個(gè)學(xué)區(qū)的數(shù)據(jù)相匹配。 我從來(lái)沒(méi)有真正考慮過(guò)一個(gè)縣的大小和形狀，所以我用谷歌搜索只是為了確定。

Source: Google Maps資料來(lái)源：Google地圖

It seemed like the Google Maps image was the perfect hole for my puzzle piece. From here, it was just a matter of formatting my data to fit the shape file. I did that by initiating my coordinate system and creating applicable points using the latitude and longitude of my houses.

似乎Google Maps圖像是我的拼圖的完美選擇。 從這里開(kāi)始，只需要格式化我的數(shù)據(jù)以適合形狀文件即可。 我通過(guò)啟動(dòng)坐標(biāo)系并使用房屋的緯度和經(jīng)度來(lái)創(chuàng)建適用的點(diǎn)來(lái)完成此操作。

crs = {'init': 'epsg:4326'} # initiating my coordinate system geometry = [Point(x,y) for x,y in zip(df.long,df.lat)] # creating points

If you were to look at an entry in geometry, you only get back that they are shapely objects. They need to be applied to our original dataframe. Below, you can see as I make a brand new dataframe that has the coordinate system built in, the old dataframe, and the addition of the points created by the intersection of the Latitude and Longitude of the houses.

如果要查看幾何圖形中的條目，您只會(huì)發(fā)現(xiàn)它們是勻稱的對(duì)象。 它們需要應(yīng)用于我們的原始數(shù)據(jù)框。 在下面，您可以看到當(dāng)我制作一個(gè)全新的數(shù)據(jù)框時(shí)，該數(shù)據(jù)框內(nèi)置了坐標(biāo)系，舊的數(shù)據(jù)框，并添加了房屋的經(jīng)度和緯度相交點(diǎn)。

geo_df = gpd.GeoDataFrame(df, # the dataframecrs = crs, # coordinate systemgeometry = geometry) # geometric points

That was the last step before we can plot the houses. Now, we put it all together.

那是我們繪制房屋之前的最后一步。 現(xiàn)在，我們將所有內(nèi)容放在一起。

fig, ax = plt.subplots(figsize = (15,16)) kings_county.plot(ax=ax, alpha = 0.8, color = 'black') geo_df.plot(ax = ax , markersize = 2, color = 'blue',marker ='o',label = 'House', aspect = 1) plt.legend(prop = {'size':10} ) ax.set_title('Houses in Kings County, WA', fontdict = {'fontsize':20}) ax.set_ylabel('Latitude',fontdict = {'fontsize': 20}) ax.set_xlabel('Longitude',fontdict = {'fontsize': 20})

在上面的代碼中，步驟包括： (In the code above, the steps include:)

Calling an object to plot.

調(diào)用對(duì)象進(jìn)行繪圖。

Plotting the King County shape file.

繪制金縣形狀文件。

Plotting the data I made that includes the geometry point.

繪制我制作的包括幾何點(diǎn)的數(shù)據(jù)。

This includes making markers, choosing the aspect, and adding the label for the legend.

這包括制作標(biāo)記，選擇外觀以及為圖例添加標(biāo)簽。

Adding a legend, title, and axis labels.

添加圖例，標(biāo)題和軸標(biāo)簽。

These steps were done for each of the graphs.

對(duì)每個(gè)圖形都完成了這些步驟。

Our output:

我們的輸出：

This is a great product but our goal is to learn something from this visualization. While this gives some information, like the outliers far to the eastern part of the county, it doesn’t give much else. We have to play with parameters. Let’s try splitting the data by price. These are the houses that are listed for less than $750,000.

這是一個(gè)很棒的產(chǎn)品，但是我們的目標(biāo)是從可視化中學(xué)習(xí)一些東西。 盡管這提供了一些信息，例如該縣東部的離群值，但它并沒(méi)有提供其他信息。 我們必須使用參數(shù)。 讓我們嘗試按價(jià)格劃分?jǐn)?shù)據(jù)。 這些房屋的標(biāo)價(jià)低于750,000美元。

fig, ax = plt.subplots(figsize = (15,25)) kings_county.plot(ax=ax, alpha = 0.8, color = 'black') geo_df[geo_df['price'] < 750000].plot(ax = ax , markersize = 2,color = 'red',marker = 's',label = 'Price < 750k',aspect = 1.5) plt.legend(prop = {'size':15} ) ax.set_title('Houses by Price in Kings County, WA', fontdict ={'fontsize': 20}) ax.set_ylabel('Latitude',fontdict = {'fontsize': 20}) ax.set_xlabel('Longitude',fontdict = {'fontsize': 20})Houses priced below $750,000. Graphic by Author價(jià)格低于750,000美元的房屋。 圖形作者

Now we graph the houses greater than or equal to $750,000.

現(xiàn)在我們繪制大于或等于750,000美元的房子的圖。

fig, ax = plt.subplots(figsize = (15,25)) kings_county.plot(ax=ax, alpha = 0.8, color = 'black') geo_df[geo_df['price'] >= 750000].plot(ax = ax , markersize = 2,color = 'yellow',marker = 'v',label = 'Price >=750k', aspect = 1.5) plt.legend(prop = {'size':15}) ax.set_title('Houses by Price in Kings County, WA', fontdict ={'fontsize': 20}) ax.set_ylabel('Latitude',fontdict = {'fontsize': 20}) ax.set_xlabel('Longitude',fontdict = {'fontsize': 20})Houses priced above $750,000. Graphic by Author價(jià)格在750,000美元以上的房屋。 圖形作者

There is a big difference in terms of both location and quantity. But that is not the end, we can also layer them one on top of the other. We will be doing the expensive on top of the cheap because it is scarcer.

在位置和數(shù)量上都存在很大差異。 但這還沒(méi)有結(jié)束，我們也可以將它們一個(gè)接一個(gè)地放置。 我們將在便宜的基礎(chǔ)上再做昂貴的，因?yàn)樗∪薄?

fig, ax = plt.subplots(figsize = (15,25)) kings_county.plot(ax=ax, alpha = 0.8, color = 'black') geo_df[geo_df['price'] < 750000].plot(ax = ax , markersize = 1,color = 'red',marker = 's',label = 'Price <750k = Red', aspect = 1.5) geo_df[geo_df['price'] >= 750000].plot(ax = ax , markersize = 1,color = 'yellow',marker = 'v',label = 'Price>= 750k = Yellow',aspect = 1.5) plt.legend(prop = {'size':12}) ax.set_title('Houses by Price in Kings County, WA', fontdict ={'fontsize': 20}) ax.set_ylabel('Latitude',fontdict = {'fontsize': 20}) ax.set_xlabel('Longitude',fontdict = {'fontsize': 20})Side by side comparison. Graphic by Author并排比較。 圖形作者

The picture painted by this map is interesting. There is a plethora of housing in King County that falls below the bar we’ve set. Most of the houses on the lower end of the price scale falls more inland than the more expensive classes.

該地圖繪制的圖片很有趣。 金縣的住房過(guò)多，低于我們?cè)O(shè)定的標(biāo)準(zhǔn)。 價(jià)格范圍較低端的大多數(shù)房屋比昂貴的房屋價(jià)格下跌的地區(qū)更多。

If you zoom in, the more expensive houses dot the waterside. They also are more centrally located around the Seattle city center. There are several physical outliers but the trend is clear.

如果放大，則較貴的房屋將點(diǎn)綴在水邊。 它們還位于西雅圖市中心附近的中心位置。 有幾個(gè)物理異常值，但趨勢(shì)很明顯。

Overall, the visualization has done its job. We have made several determinations from the houses on the map. Pricier houses are collected around the downtown area and spread around Puget Sound. They are also a minority in the data, which could be telling for predicting housing prices. The houses priced on the cheaper side are much more numerous and have a varied location. This will be useful for further EDA.

總體而言，可視化已完成工作。 我們已經(jīng)從地圖上的房屋中做出了一些決定。 價(jià)格較高的房屋在市區(qū)周圍收集，并分布在普吉特海灣附近。 他們也是數(shù)據(jù)中的少數(shù)，這可能有助于預(yù)測(cè)房?jī)r(jià)。 價(jià)格便宜的房屋數(shù)量更多，并且位置各異。 這對(duì)于進(jìn)一步的EDA很有用。

If you want to connect to talk more about this technique, you can find me on LinkedIn. If you would like to check out the code, take a look at my Github.

如果您想聯(lián)系以更多地談?wù)撨@種技術(shù)，可以在LinkedIn上找到我。 如果您想查看代碼，請(qǐng)查看我的Github 。

資料來(lái)源 (Sources)

• King County Dataset — here

  金縣數(shù)據(jù)集- 此處

  King County Shape File —

  金縣形狀文件—

  here

  這里

• Geopandas

  大熊貓

• Shapely

  勻稱

• Descartes

  笛卡爾

• Fiona

  菲奧娜

翻譯自: https://towardsdatascience.com/using-geopandas-for-spatial-visualization-21e78984dc37

多維空間可視化

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