Datasets:

MarcelPower

/

github-jupyter-text-code-pairs

like 0

Alias Names A dictionary of {zone: "alias"} pairs can be passed to replace the typical "ZONE_X" fieldnames of the ZoneBudget structured array with more descriptive names.

aliases = {1: 'SURF', 2:'CONF', 3: 'UFA'} zb = flopy.utils.ZoneBudget(cbc_f, zon, totim=[1097.], aliases=aliases) zb.get_budget()

examples/Notebooks/flopy3_ZoneBudget_example.ipynb

bdestombe/flopy-1

bsd-3-clause

49748467090e8ecdad07a764d5effde8

Return the Budgets as a Pandas DataFrame Set kstpkper and totim keyword args to None (or omit) to return all times. The get_dataframes() method will return a DataFrame multi-indexed on totim and name.

zon = np.ones((nlay, nrow, ncol), np.int) zon[1, :, :] = 2 zon[2, :, :] = 3 aliases = {1: 'SURF', 2:'CONF', 3: 'UFA'} zb = flopy.utils.ZoneBudget(cbc_f, zon, kstpkper=None, totim=None, aliases=aliases) df = zb.get_dataframes() print(df.head()) print(df.tail())

examples/Notebooks/flopy3_ZoneBudget_example.ipynb

bdestombe/flopy-1

bsd-3-clause

2df8475e0561680ec19170fee6b6e9b1

Slice the multi-index dataframe to retrieve a subset of the budget

dateidx1 = 1092. dateidx2 = 1097. names = ['RECHARGE_IN', 'WELLS_OUT'] zones = ['SURF', 'CONF'] df.loc[(slice(dateidx1, dateidx2), names), :][zones]

examples/Notebooks/flopy3_ZoneBudget_example.ipynb

bdestombe/flopy-1

bsd-3-clause

934ab8fef2068c42905b6b45e9d53cc5

Look at pumpage (WELLS_OUT) as a percentage of recharge (RECHARGE_IN)

dateidx1 = 1092. dateidx2 = 1097. zones = ['SURF'] # Pull out the individual records of interest rech = df.loc[(slice(dateidx1, dateidx2), ['RECHARGE_IN']), :][zones] pump = df.loc[(slice(dateidx1, dateidx2), ['WELLS_OUT']), :][zones] # Remove the "record" field from the index so we can # take the difference of the two DataFrames rech = rech.reset_index() rech = rech.set_index(['totim']) rech = rech[zones] pump = pump.reset_index() pump = pump.set_index(['totim']) pump = pump[zones] * -1 # Compute pumping as a percentage of recharge pump_as_pct = (pump / rech) * 100. pump_as_pct # Use "slice(None)" to return all records df.loc[(slice(dateidx1, dateidx2), slice(None)), :][zones] # Or all times df.loc[(slice(None), names), :][zones]

examples/Notebooks/flopy3_ZoneBudget_example.ipynb

bdestombe/flopy-1

bsd-3-clause

08b5c0bc5da18c8f87fd94cde095316f

Pass start_datetime and timeunit keyword arguments to return a dataframe with a datetime multi-index

df = zb.get_dataframes(start_datetime='1970-01-01', timeunit='D') dateidx1 = pd.Timestamp('1972-12-01') dateidx2 = pd.Timestamp('1972-12-06') names = ['RECHARGE_IN', 'WELLS_OUT'] zones = ['SURF', 'CONF'] df.loc[(slice(dateidx1, dateidx2), names), :][zones]

examples/Notebooks/flopy3_ZoneBudget_example.ipynb

bdestombe/flopy-1

bsd-3-clause

094a2bebbf5e4b1e65acba7ca7a20c4a

Pass index_key to indicate which fields to use in the multi-index (defualt is "totim"; valid keys are "totim" and "kstpkper")

df = zb.get_dataframes(index_key='kstpkper') df.head()

examples/Notebooks/flopy3_ZoneBudget_example.ipynb

bdestombe/flopy-1

bsd-3-clause

620b5c5cc8cbdd381336abb63415fae0

Write Budget Output to CSV We can write the resulting recarray to a csv file with the .to_csv() method of the ZoneBudget object.

zb = flopy.utils.ZoneBudget(cbc_f, zon, kstpkper=[(0, 0), (0, 1096)]) zb.to_csv(os.path.join(loadpth, 'zonbud.csv')) # Read the file in to see the contents fname = os.path.join(loadpth, 'zonbud.csv') try: import pandas as pd print(pd.read_csv(fname).to_string(index=False)) except: with open(fname, 'r') as f: for line in f.readlines(): print('\t'.join(line.split(',')))

examples/Notebooks/flopy3_ZoneBudget_example.ipynb

bdestombe/flopy-1

bsd-3-clause

59d0f210ede4b35022cdc11a21c2713b

베이지안 가우시안 혼합 모델 및 해밀턴 MCMC <table class="tfo-notebook-buttons" align="left"> <td><a target="_blank" href="https://www.tensorflow.org/probability/examples/Bayesian_Gaussian_Mixture_Model"><img src="https://www.tensorflow.org/images/tf_logo_32px.png">TensorFlow.org에서 보기</a></td> <td><a target="_blank" href="https://colab.research.google.com/github/tensorflow/docs-l10n/blob/master/site/ko/probability/examples/Bayesian_Gaussian_Mixture_Model.ipynb"><img src="https://www.tensorflow.org/images/colab_logo_32px.png">Google Colab에서 실행하기</a></td> <td><a target="_blank" href="https://github.com/tensorflow/docs-l10n/blob/master/site/ko/probability/examples/Bayesian_Gaussian_Mixture_Model.ipynb"><img src="https://www.tensorflow.org/images/GitHub-Mark-32px.png">GitHub에서 보기</a></td> <td><a href="https://storage.googleapis.com/tensorflow_docs/docs-l10n/site/ko/probability/examples/Bayesian_Gaussian_Mixture_Model.ipynb"><img src="https://www.tensorflow.org/images/download_logo_32px.png">노트북 다운로드하기</a></td> </table> 이 colab에서는 TensorFlow Probability 기본 형식만 사용하여 베이지안 가우시안 혼합 모델(BGMM)의 사후 확률에서 샘플링을 탐색합니다. 모델 각 차원 $D$의 $k\in{1,\ldots,K}$ 혼합 구성 요소에 대해 다음의 베이지안 가우시안 혼합 모델로 $i\in{1,\ldots,N}$ iid 샘플을 모델링하려고 합니다. $$\begin{align} \theta &\sim \text{Dirichlet}(\text{concentration}=\alpha_0)\ \mu_k &\sim \text{Normal}(\text{loc}=\mu_{0k}, \text{scale}=I_D)\ T_k &\sim \text{Wishart}(\text{df}=5, \text{scale}=I_D)\ Z_i &\sim \text{Categorical}(\text{probs}=\theta)\ Y_i &\sim \text{Normal}(\text{loc}=\mu_{z_i}, \text{scale}=T_{z_i}^{-1/2})\ \end{align}$$ scale 인수는 모두 cholesky 의미 체계를 가지고 있습니다. 이 규칙은 TF 분포의 규칙이기 때문에 사용됩니다(계산적으로 유리하므로 TF 분포에서 부분적으로 이 규칙을 사용합니다). 목표는 다음의 사후 확률에서 샘플을 생성하는 것입니다. $$p\left(\theta, {\mu_k, T_k}{k=1}^K \Big| {y_i}{i=1}^N, \alpha_0, {\mu_{ok}}_{k=1}^K\right)$$ ${Z_i}_{i=1}^N$는 존재하지 않는다는 점에 유의하세요. $N$로 조정되지 않는 확률 변수에만 관심을 둡니다(또한, 운 좋게도 $Z_i$를 무시하는 TF 분포가 있습니다). 계산적으로 다루기 힘든 정규화 항으로 인해 이 분포에서 직접 샘플링하는 것은 불가능합니다. 메트로폴리스-헤이스팅스 알고리즘은 다루기 힘든 정규화된 분포에서 샘플링하는 기술입니다. TensorFlow Probability는 메트로폴리스-헤이스팅스 기반의 여러 옵션을 포함하여 많은 MCMC 옵션을 제공합니다. 이 노트북에서는 해밀턴 몬테카를로(tfp.mcmc.HamiltonianMonteCarlo)를 사용합니다. 해밀턴 몬테카를로(HMC)는 신속하게 수렴하고 (좌표 방식이 아닌) 상태 공간을 공동으로 샘플링하며, TF의 장점 중 하나인 자동 미분을 활용하므로 종종 좋은 선택입니다. 즉, BGMM 사후 확률에서의 샘플링은 실제로 Gibb의 샘플링과 같은 다른 접근 방식을 사용하면 더 잘 수행될 수 있습니다.

%matplotlib inline import functools import matplotlib.pyplot as plt; plt.style.use('ggplot') import numpy as np import seaborn as sns; sns.set_context('notebook') import tensorflow.compat.v2 as tf tf.enable_v2_behavior() import tensorflow_probability as tfp tfd = tfp.distributions tfb = tfp.bijectors physical_devices = tf.config.experimental.list_physical_devices('GPU') if len(physical_devices) &gt; 0: tf.config.experimental.set_memory_growth(physical_devices[0], True)

site/ko/probability/examples/Bayesian_Gaussian_Mixture_Model.ipynb

tensorflow/docs-l10n

apache-2.0

43d5b274066cfed554d2a9875468e212

실제로 모델을 빌드하기 전에 새로운 유형의 분포를 정의해야 합니다. 위의 모델 사양에서 역공분산 행렬, 즉 정밀 행렬로 MVN을 매개변수화하고 있음이 분명합니다. 이를 TF에서 달성하려면, Bijector를 롤 아웃해야 합니다. 이 Bijector는 순방향 변환을 사용합니다. Y = tf.linalg.triangular_solve((tf.linalg.matrix_transpose(chol_precision_tril), X, adjoint=True) + loc. 그리고 log_prob 계산은 그 반대입니다. 즉, 이 계산은 다음과 같습니다. X = tf.linalg.matmul(chol_precision_tril, X - loc, adjoint_a=True). HMC에 필요한 것은 log_prob 뿐이므로, (tfd.MultivariateNormalTriL의 경우처럼) tf.linalg.triangular_solve를 호출하지 않습니다. 이는 tf.linalg.matmul이 일반적으로 더 나은 캐시 위치로 인해 더 빠르기 때문에 유리합니다.

class MVNCholPrecisionTriL(tfd.TransformedDistribution): """MVN from loc and (Cholesky) precision matrix.""" def __init__(self, loc, chol_precision_tril, name=None): super(MVNCholPrecisionTriL, self).__init__( distribution=tfd.Independent(tfd.Normal(tf.zeros_like(loc), scale=tf.ones_like(loc)), reinterpreted_batch_ndims=1), bijector=tfb.Chain([ tfb.Affine(shift=loc), tfb.Invert(tfb.Affine(scale_tril=chol_precision_tril, adjoint=True)), ]), name=name)

site/ko/probability/examples/Bayesian_Gaussian_Mixture_Model.ipynb

tensorflow/docs-l10n

apache-2.0

d910692e952bc8c6f109059905d1c261

tfd.Independent 분포는 한 분포의 독립적인 그리기를 통계적으로 독립된 좌표가 있는 다변량 분포로 바꿉니다. log_prob 계산 측면에서, 이 '메타 분포'는 이벤트 차원에 대한 단순 합계로 나타납니다. 또한 scale 행렬의 adjoint ('transpose')를 사용했습니다. 그 이유는 정밀도가 역공분산이면, 즉 $P=C^{-1}$이고 $C=AA^\top$이면, $P=BB^{\top}$이고 여기서 $B=A^{-\top}$입니다. 이 분포는 다소 까다로우므로 MVNCholPrecisionTriL이 예상되는 대로 동작하는지 빠르게 확인하겠습니다.

def compute_sample_stats(d, seed=42, n=int(1e6)): x = d.sample(n, seed=seed) sample_mean = tf.reduce_mean(x, axis=0, keepdims=True) s = x - sample_mean sample_cov = tf.linalg.matmul(s, s, adjoint_a=True) / tf.cast(n, s.dtype) sample_scale = tf.linalg.cholesky(sample_cov) sample_mean = sample_mean[0] return [ sample_mean, sample_cov, sample_scale, ] dtype = np.float32 true_loc = np.array([1., -1.], dtype=dtype) true_chol_precision = np.array([[1., 0.], [2., 8.]], dtype=dtype) true_precision = np.matmul(true_chol_precision, true_chol_precision.T) true_cov = np.linalg.inv(true_precision) d = MVNCholPrecisionTriL( loc=true_loc, chol_precision_tril=true_chol_precision) [sample_mean, sample_cov, sample_scale] = [ t.numpy() for t in compute_sample_stats(d)] print('true mean:', true_loc) print('sample mean:', sample_mean) print('true cov:\n', true_cov) print('sample cov:\n', sample_cov)

site/ko/probability/examples/Bayesian_Gaussian_Mixture_Model.ipynb

tensorflow/docs-l10n

apache-2.0

f7dbe7096bcaf1816035c89babf584b9

샘플 평균과 공분산이 실제 평균과 공분산에 가까우므로 분포가 올바르게 구현된 것처럼 보입니다. 이제 MVNCholPrecisionTriL tfp.distributions.JointDistributionNamed로 BGMM 모델을 지정합니다. 관찰 모델의 경우, tfd.MixtureSameFamily를 사용하여 ${Z_i}_{i=1}^N$ 그리기를 자동으로 통합합니다.

dtype = np.float64 dims = 2 components = 3 num_samples = 1000 bgmm = tfd.JointDistributionNamed(dict( mix_probs=tfd.Dirichlet( concentration=np.ones(components, dtype) / 10.), loc=tfd.Independent( tfd.Normal( loc=np.stack([ -np.ones(dims, dtype), np.zeros(dims, dtype), np.ones(dims, dtype), ]), scale=tf.ones([components, dims], dtype)), reinterpreted_batch_ndims=2), precision=tfd.Independent( tfd.WishartTriL( df=5, scale_tril=np.stack([np.eye(dims, dtype=dtype)]*components), input_output_cholesky=True), reinterpreted_batch_ndims=1), s=lambda mix_probs, loc, precision: tfd.Sample(tfd.MixtureSameFamily( mixture_distribution=tfd.Categorical(probs=mix_probs), components_distribution=MVNCholPrecisionTriL( loc=loc, chol_precision_tril=precision)), sample_shape=num_samples) )) def joint_log_prob(observations, mix_probs, loc, chol_precision): """BGMM with priors: loc=Normal, precision=Inverse-Wishart, mix=Dirichlet. Args: observations: `[n, d]`-shaped `Tensor` representing Bayesian Gaussian Mixture model draws. Each sample is a length-`d` vector. mix_probs: `[K]`-shaped `Tensor` representing random draw from `Dirichlet` prior. loc: `[K, d]`-shaped `Tensor` representing the location parameter of the `K` components. chol_precision: `[K, d, d]`-shaped `Tensor` representing `K` lower triangular `cholesky(Precision)` matrices, each being sampled from a Wishart distribution. Returns: log_prob: `Tensor` representing joint log-density over all inputs. """ return bgmm.log_prob( mix_probs=mix_probs, loc=loc, precision=chol_precision, s=observations)

site/ko/probability/examples/Bayesian_Gaussian_Mixture_Model.ipynb

tensorflow/docs-l10n

apache-2.0

23b099650f97a202951667343989a397

'훈련' 데이터를 생성합니다. 다음 데모에서는 무작위의 데이터를 샘플링합니다.

true_loc = np.array([[-2., -2], [0, 0], [2, 2]], dtype) random = np.random.RandomState(seed=43) true_hidden_component = random.randint(0, components, num_samples) observations = (true_loc[true_hidden_component] + random.randn(num_samples, dims).astype(dtype))

site/ko/probability/examples/Bayesian_Gaussian_Mixture_Model.ipynb

tensorflow/docs-l10n

apache-2.0

945fa2f21909f9bfdb5a8ba3f2e01900

HMC를 사용한 베이지안 추론 이제 TFD를 사용하여 모델을 지정하고 일부 관찰 데이터를 얻었으므로 HMC를 실행하는 데 필요한 모든 부분을 확보했습니다. HMC를 실행하려면 부분 적용을 사용하여 샘플링하고 싶지 않은 항목을 '고정'합니다. 이 경우에는 observations만 고정하면 됩니다(하이퍼 매개변수는 이미 사전 확률 분포에 적용되었으며 joint_log_prob 함수 서명의 일부가 아닙니다).

unnormalized_posterior_log_prob = functools.partial(joint_log_prob, observations) initial_state = [ tf.fill([components], value=np.array(1. / components, dtype), name='mix_probs'), tf.constant(np.array([[-2., -2], [0, 0], [2, 2]], dtype), name='loc'), tf.linalg.eye(dims, batch_shape=[components], dtype=dtype, name='chol_precision'), ]

site/ko/probability/examples/Bayesian_Gaussian_Mixture_Model.ipynb

tensorflow/docs-l10n

apache-2.0

c061e268db85d1f3f974a7add73d275d

제약 조건이 없는 표현 해밀턴 몬테카를로(HMC)는 인수와 관련하여 대상 로그 확률 함수를 미분할 수 있어야 합니다. 또한 HMC는 상태 공간에 제약 조건이 없는 경우 훨씬 더 높은 통계 효율성을 나타낼 수 있습니다. 즉, BGMM 사후 확률에서 샘플링할 때 두 가지 주요 문제를 해결해야 합니다. $\theta$는 이산 확률 벡터를 나타냅니다. 즉, $\sum_{k=1}^K \theta_k = 1$ 및 $\theta_k>0$와 같아야 합니다. $T_k$는 역공분산 행렬을 나타냅니다. 즉, $T_k \succ 0$가 되어야 합니다. 이는 양정치가 됩니다. 위의 요구 사항을 해결하려면 다음을 수행해야 합니다. 제약 조건이 있는 변수를 제약 조건이 없는 공간으로 변환합니다. 제약 조건이 없는 공간에서 MCMC를 실행합니다. 제약 조건이 없는 변수를 제약 조건이 있는 공간으로 다시 변환합니다. MVNCholPrecisionTriL과 마찬가지로, 제약 조건이 없는 공간으로 확률 변수를 변환하려면 Bijector를 사용합니다. Dirichlet은 softmax 함수를 통해 제약 조건이 없는 공간으로 변환됩니다. 정밀도 확률 변수는 준 양정치 행렬에 대한 분포입니다. 이들에 대한 제약 조건을 없애기 위해서는 FillTriangular 및 TransformDiagonal bijector를 사용합니다. 이들 bijector는 벡터를 하부 삼각 행렬로 변환하고 대각선이 양수인지 확인합니다. 전자는 $d^2$ 대신 $d(d+1)/2$ float만 샘플링할 수 있으므로 유용합니다.

unconstraining_bijectors = [ tfb.SoftmaxCentered(), tfb.Identity(), tfb.Chain([ tfb.TransformDiagonal(tfb.Softplus()), tfb.FillTriangular(), ])] @tf.function(autograph=False) def sample(): return tfp.mcmc.sample_chain( num_results=2000, num_burnin_steps=500, current_state=initial_state, kernel=tfp.mcmc.SimpleStepSizeAdaptation( tfp.mcmc.TransformedTransitionKernel( inner_kernel=tfp.mcmc.HamiltonianMonteCarlo( target_log_prob_fn=unnormalized_posterior_log_prob, step_size=0.065, num_leapfrog_steps=5), bijector=unconstraining_bijectors), num_adaptation_steps=400), trace_fn=lambda _, pkr: pkr.inner_results.inner_results.is_accepted) [mix_probs, loc, chol_precision], is_accepted = sample()

site/ko/probability/examples/Bayesian_Gaussian_Mixture_Model.ipynb

tensorflow/docs-l10n

apache-2.0

c65f4e01f84b09f50f1da949e1fa0f4d

이제 chain을 실행하고 사후 확률 분포의 평균을 출력합니다.

acceptance_rate = tf.reduce_mean(tf.cast(is_accepted, dtype=tf.float32)).numpy() mean_mix_probs = tf.reduce_mean(mix_probs, axis=0).numpy() mean_loc = tf.reduce_mean(loc, axis=0).numpy() mean_chol_precision = tf.reduce_mean(chol_precision, axis=0).numpy() precision = tf.linalg.matmul(chol_precision, chol_precision, transpose_b=True) print('acceptance_rate:', acceptance_rate) print('avg mix probs:', mean_mix_probs) print('avg loc:\n', mean_loc) print('avg chol(precision):\n', mean_chol_precision) loc_ = loc.numpy() ax = sns.kdeplot(loc_[:,0,0], loc_[:,0,1], shade=True, shade_lowest=False) ax = sns.kdeplot(loc_[:,1,0], loc_[:,1,1], shade=True, shade_lowest=False) ax = sns.kdeplot(loc_[:,2,0], loc_[:,2,1], shade=True, shade_lowest=False) plt.title('KDE of loc draws');

site/ko/probability/examples/Bayesian_Gaussian_Mixture_Model.ipynb

tensorflow/docs-l10n

apache-2.0

e9d2f515aaeb742095f4ea9a83bc6ae1

<h2>Linear Regression</h2>

c = ['mpg', 'cylinders', 'displacement', 'horsepower', 'weight', 'acceleration', 'model year', 'origin'] limit = int(3*cars.shape[0]/4) X_train = cars.iloc[:limit,1:] y_train = cars.iloc[:limit,0] X_test = cars.iloc[limit:,1:] y_test = cars.iloc[limit:,0] lr = LinearRegression() #Remember the [[]], is the data in 1 column lr.fit(X_train, y_train) predictions = lr.predict(X_test) #mean_squared_error mse = mean_squared_error(y_test, predictions) # The coefficients print('Coefficients: ', lr.coef_) # The mean square error print("Residual sum of squares: %.2f" % mse) # Explained variance score: 1 is perfect prediction print('Variance score: %.2f' % lr.score(X_test, y_test)) plt.scatter(X_test["weight"], y_test, c='b') plt.scatter(X_test["weight"], prediction, c='r') plt.show()

AutoMPG/AutoMPG.ipynb

JavierVLAB/DataAnalysisScience

gpl-3.0

53b0c19d8bb23406b251c28ae45c5e59

<p>The variance score is very low due to we use all the features.</p> <p>For a better solution we aplied a feature selection. </p> <p>From the pair graph, we can see that the features 'cylinders', 'model year' and 'origin' dont'show a clear correlation with the 'mpg' variable, so those are rejected.</p>

c = ['mpg','horsepower', "weight",'acceleration'] limit = int(3*cars.shape[0]/4) X_train = cars[c].iloc[:limit,1:] y_train = cars.iloc[:limit,0] X_test = cars[c].iloc[limit:,1:] y_test = cars.iloc[limit:,0] lr2 = LinearRegression() #Remember the [[]], is the data in 1 column lr2.fit(X_train, y_train) predictions = lr2.predict(X_test) #mean_squared_error mse = mean_squared_error(y_test, predictions) # The coefficients print('Coefficients: ', lr2.coef_) # The mean square error print("Residual sum of squares: %.2f" % mse) # Explained variance score: 1 is perfect prediction print('Variance score: %.2f' % lr2.score(X_test, y_test)) feature = "weight" plt.scatter(X_test[feature], y_test, c='b') plt.scatter(X_test[feature], prediction, c='r') plt.ylim([10,45]) plt.xlim([1500,4000]) plt.ylabel('MPG') plt.xlabel(feature) plt.show()

AutoMPG/AutoMPG.ipynb

JavierVLAB/DataAnalysisScience

gpl-3.0

7682d916f902e5a65f415f84ba21ec7d

Date/Time data handling Date and time data are inherently problematic. There are an unequal number of days in every month, an unequal number of days in a year (due to leap years), and time zones that vary over space. Yet information about time is essential in many analyses, particularly in the case of time series analysis. The datetime built-in library handles temporal information down to the nanosecond.

from datetime import datetime now = datetime.now() now now.day now.weekday()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

cb8bffd3b50768ed6108819e111a5dc9

In addition to datetime there are simpler objects for date and time information only, respectively.

from datetime import date, time time(3, 24) date(1970, 9, 3)

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

899da0483ae6749c071437d07ddc9322

Having a custom data type for dates and times is convenient because we can perform operations on them easily. For example, we may want to calculate the difference between two times:

my_age = now - datetime(1970, 1, 1) my_age print(type(my_age)) my_age.days/365

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

8694a1a1052863ab32e1b927234eeb39

In this section, we will manipulate data collected from ocean-going vessels on the eastern seaboard. Vessel operations are monitored using the Automatic Identification System (AIS), a safety at sea navigation technology which vessels are required to maintain and that uses transponders to transmit very high frequency (VHF) radio signals containing static information including ship name, call sign, and country of origin, as well as dynamic information unique to a particular voyage such as vessel location, heading, and speed. The International Maritime Organization’s (IMO) International Convention for the Safety of Life at Sea requires functioning AIS capabilities on all vessels 300 gross tons or greater and the US Coast Guard requires AIS on nearly all vessels sailing in U.S. waters. The Coast Guard has established a national network of AIS receivers that provides coverage of nearly all U.S. waters. AIS signals are transmitted several times each minute and the network is capable of handling thousands of reports per minute and updates as often as every two seconds. Therefore, a typical voyage in our study might include the transmission of hundreds or thousands of AIS encoded signals. This provides a rich source of spatial data that includes both spatial and temporal information. For our purposes, we will use summarized data that describes the transit of a given vessel through a particular administrative area. The data includes the start and end time of the transit segment, as well as information about the speed of the vessel, how far it travelled, etc.

segments = pd.read_csv("Data/AIS/transit_segments.csv") segments.head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

49667933f0a07b91a1dbfae091bb96c6

For example, we might be interested in the distribution of transit lengths, so we can plot them as a histogram:

segments.seg_length.hist(bins=500)

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

fa8c938fbc933d3bd09301ea4faf2d0f

Though most of the transits appear to be short, there are a few longer distances that make the plot difficult to read. This is where a transformation is useful:

segments.seg_length.apply(np.log).hist(bins=500)

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

010a165ce25a88b7a73518d99e832f22

We can see that although there are date/time fields in the dataset, they are not in any specialized format, such as datetime.

segments.st_time.dtype

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

c0df7a73db0861702ba41c8cb0b55814

Our first order of business will be to convert these data to datetime. The strptime method parses a string representation of a date and/or time field, according to the expected format of this information.

datetime.strptime(segments.st_time.ix[0], '%m/%d/%y %H:%M')

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

93d5057b70ac5df596d0aa9d42a64762

The dateutil package includes a parser that attempts to detect the format of the date strings, and convert them automatically.

from dateutil.parser import parse parse(segments.st_time.ix[0])

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

f46dfba79fa956521f6d45d5cf722dbf

We can convert all the dates in a particular column by using the apply method.

segments.st_time.apply(lambda d: datetime.strptime(d, '%m/%d/%y %H:%M'))

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

db7b6d164eb186593344189936f15036

As a convenience, Pandas has a to_datetime method that will parse and convert an entire Series of formatted strings into datetime objects.

pd.to_datetime(segments.st_time[:10])

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

d4d1b2d32491514ef7b41e49fdb993cc

Pandas also has a custom NA value for missing datetime objects, NaT.

pd.to_datetime([None])

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

3ff6c4a3627e6b234ece23dc677e7a6b

Also, if to_datetime() has problems parsing any particular date/time format, you can pass the spec in using the format= argument. The read_* functions now have an optional parse_dates argument that try to convert any columns passed to it into datetime format upon import:

segments = pd.read_csv("Data/AIS/transit_segments.csv", parse_dates=['st_time', 'end_time']) segments.dtypes

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

7a917cdf7262c0d5ea7a27fc2de8f5a5

Columns of the datetime type have an accessor to easily extract properties of the data type. This will return a Series, with the same row index as the DataFrame. For example:

segments.st_time.dt.month.head() segments.st_time.dt.hour.head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

9ccf3198626476fabcbf79735b7d0eac

This can be used to easily filter rows by particular temporal attributes:

segments[segments.st_time.dt.month==2].head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

247c3350964523e65a60b926c7dad480

In addition, time zone information can be applied:

segments.st_time.dt.tz_localize('UTC').head() segments.st_time.dt.tz_localize('UTC').dt.tz_convert('US/Eastern').head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

1b6c2bf682ed42e0e5e7f8b5706212fb

Merging and joining DataFrame objects Now that we have the vessel transit information as we need it, we may want a little more information regarding the vessels themselves. In the data/AIS folder there is a second table that contains information about each of the ships that traveled the segments in the segments table.

vessels = pd.read_csv("Data/AIS/vessel_information.csv", index_col='mmsi') vessels.head() [v for v in vessels.type.unique() if v.find('/')==-1] vessels.type.value_counts()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

0da1b4ae07b6f00b84dc289e88056b4d

The challenge, however, is that several ships have travelled multiple segments, so there is not a one-to-one relationship between the rows of the two tables. The table of vessel information has a one-to-many relationship with the segments. In Pandas, we can combine tables according to the value of one or more keys that are used to identify rows, much like an index. Using a trivial example:

df1 = pd.DataFrame(dict(id=range(4), age=np.random.randint(18, 31, size=4))) df2 = pd.DataFrame(dict(id=list(range(3))+list(range(3)), score=np.random.random(size=6))) df1 df2 pd.merge(df1, df2)

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

1e420c2e6a187caa5d832c266b2db40e

Notice that without any information about which column to use as a key, Pandas did the right thing and used the id column in both tables. Unless specified otherwise, merge will used any common column names as keys for merging the tables. Notice also that id=3 from df1 was omitted from the merged table. This is because, by default, merge performs an inner join on the tables, meaning that the merged table represents an intersection of the two tables.

pd.merge(df1, df2, how='outer')

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

e583108f3ff50e34eafb3df101db73b3

The outer join above yields the union of the two tables, so all rows are represented, with missing values inserted as appropriate. One can also perform right and left joins to include all rows of the right or left table (i.e. first or second argument to merge), but not necessarily the other. Looking at the two datasets that we wish to merge:

segments.head(1) vessels.head(1)

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

1191a1e0520f3aada6e6c76ab140d403

we see that there is a mmsi value (a vessel identifier) in each table, but it is used as an index for the vessels table. In this case, we have to specify to join on the index for this table, and on the mmsi column for the other.

segments_merged = pd.merge(vessels, segments, left_index=True, right_on='mmsi') segments_merged.head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

db4a5decf299d899467ea7b20f1a8f8e

In this case, the default inner join is suitable; we are not interested in observations from either table that do not have corresponding entries in the other. Notice that mmsi field that was an index on the vessels table is no longer an index on the merged table. Here, we used the merge function to perform the merge; we could also have used the merge method for either of the tables:

vessels.merge(segments, left_index=True, right_on='mmsi').head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

094437cd64ba43f74caad74dced7a450

Occasionally, there will be fields with the same in both tables that we do not wish to use to join the tables; they may contain different information, despite having the same name. In this case, Pandas will by default append suffixes _x and _y to the columns to uniquely identify them.

segments['type'] = 'foo' pd.merge(vessels, segments, left_index=True, right_on='mmsi').head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

2e6df2fbfdea8a86fae410848ff7e646

This behavior can be overridden by specifying a suffixes argument, containing a list of the suffixes to be used for the columns of the left and right columns, respectively. Concatenation A common data manipulation is appending rows or columns to a dataset that already conform to the dimensions of the exsiting rows or colums, respectively. In NumPy, this is done either with concatenate or the convenience "functions" c_ and r_:

np.concatenate([np.random.random(5), np.random.random(5)]) np.r_[np.random.random(5), np.random.random(5)] np.c_[np.random.random(5), np.random.random(5)]

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

2521df56aa9d2e7ee7760ab57197d59a

Notice that c_ and r_ are not really functions at all, since it is performing some sort of indexing operation, rather than being called. They are actually class instances, but they are here behaving mostly like functions. Don't think about this too hard; just know that they are there. This operation is also called binding or stacking. With Pandas' indexed data structures, there are additional considerations as the overlap in index values between two data structures affects how they are concatenate. Lets import two microbiome datasets, each consisting of counts of microorganiams from a particular patient. We will use the first column of each dataset as the index.

mb1 = pd.read_excel('Data/microbiome/MID1.xls', 'Sheet 1', index_col=0, header=None) mb2 = pd.read_excel('Data/microbiome/MID2.xls', 'Sheet 1', index_col=0, header=None) mb1.shape, mb2.shape mb1.head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

e706ca7f76bba84305d5def74c3bea31

Let's give the index and columns meaningful labels:

mb1.columns = mb2.columns = ['Count'] mb1.index.name = mb2.index.name = 'Taxon' mb1.head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

0a99318edf1b897e5744fae985d5d887

The index of these data is the unique biological classification of each organism, beginning with domain, phylum, class, and for some organisms, going all the way down to the genus level.

mb1.index[:3] mb1.index.is_unique

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

2c5a12745daabb708d8603719a80ea5e

If we concatenate along axis=0 (the default), we will obtain another data frame with the the rows concatenated:

pd.concat([mb1, mb2], axis=0).shape

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

815819a68e68760e48a29f3122326b26

However, the index is no longer unique, due to overlap between the two DataFrames.

pd.concat([mb1, mb2], axis=0).index.is_unique

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

1dc9e7c3b39d7a05128a60e4ef30fda4

Concatenating along axis=1 will concatenate column-wise, but respecting the indices of the two DataFrames.

pd.concat([mb1, mb2], axis=1).shape pd.concat([mb1, mb2], axis=1).head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

5c37d5acb75710dda508a12c95abd7fb

If we are only interested in taxa that are included in both DataFrames, we can specify a join=inner argument.

pd.concat([mb1, mb2], axis=1, join='inner').head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

3de78675e0ccbc086ebb3b887e8c8a29

If we wanted to use the second table to fill values absent from the first table, we could use combine_first.

mb1.combine_first(mb2).head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

688bdf138eb765935780e8af0da188d6

We can also create a hierarchical index based on keys identifying the original tables.

pd.concat([mb1, mb2], keys=['patient1', 'patient2']).head() pd.concat([mb1, mb2], keys=['patient1', 'patient2']).index.is_unique

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

20d937c158808275fbf73faddb05c0af

Alternatively, you can pass keys to the concatenation by supplying the DataFrames (or Series) as a dict, resulting in a "wide" format table.

pd.concat(dict(patient1=mb1, patient2=mb2), axis=1).head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

1d6504aca0cfb739fe3f1ee1864e4817

If you want concat to work like numpy.concatanate, you may provide the ignore_index=True argument. Exercise 1 In the data/microbiome subdirectory, there are 9 spreadsheets of microbiome data that was acquired from high-throughput RNA sequencing procedures, along with a 10th file that describes the content of each. Write code that imports each of the data spreadsheets and combines them into a single DataFrame, adding the identifying information from the metadata spreadsheet as columns in the combined DataFrame.

# Write solution here

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

64727bc2a00baf42b460b4803fe4ad8b

Reshaping DataFrame objects In the context of a single DataFrame, we are often interested in re-arranging the layout of our data. This dataset is from Table 6.9 of Statistical Methods for the Analysis of Repeated Measurements by Charles S. Davis, pp. 161-163 (Springer, 2002). These data are from a multicenter, randomized controlled trial of botulinum toxin type B (BotB) in patients with cervical dystonia from nine U.S. sites. Randomized to placebo (N=36), 5000 units of BotB (N=36), 10,000 units of BotB (N=37) Response variable: total score on Toronto Western Spasmodic Torticollis Rating Scale (TWSTRS), measuring severity, pain, and disability of cervical dystonia (high scores mean more impairment) TWSTRS measured at baseline (week 0) and weeks 2, 4, 8, 12, 16 after treatment began

cdystonia = pd.read_csv("Data/cdystonia.csv", index_col=None) cdystonia.head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

726de42414175ea86d96ef5a06660066

This dataset includes repeated measurements of the same individuals (longitudinal data). Its possible to present such information in (at least) two ways: showing each repeated measurement in their own row, or in multiple columns representing multiple measurements. The stack method rotates the data frame so that columns are represented in rows:

stacked = cdystonia.stack() stacked

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

835ef8b917a120a560f6b4bc650d93a6

To complement this, unstack pivots from rows back to columns.

stacked.unstack().head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

4c7b0945da28dd2cea3f46ec27273ef0

For this dataset, it makes sense to create a hierarchical index based on the patient and observation:

cdystonia2 = cdystonia.set_index(['patient','obs']) cdystonia2.head() cdystonia2.index.is_unique

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

f5522049abb61e6ac0e4073d8ab6ff54

If we want to transform this data so that repeated measurements are in columns, we can unstack the twstrs measurements according to obs.

twstrs_wide = cdystonia2['twstrs'].unstack('obs') twstrs_wide.head() cdystonia_wide = (cdystonia[['patient','site','id','treat','age','sex']] .drop_duplicates() .merge(twstrs_wide, right_index=True, left_on='patient', how='inner') .head()) cdystonia_wide

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

777535e81f68e2949cd1a91085445d5e

A slightly cleaner way of doing this is to set the patient-level information as an index before unstacking:

(cdystonia.set_index(['patient','site','id','treat','age','sex','week'])['twstrs'] .unstack('week').head())

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

237aa64c0acc34d4c7c9b230e8e68b9e

To convert our "wide" format back to long, we can use the melt function, appropriately parameterized. This function is useful for DataFrames where one or more columns are identifier variables (id_vars), with the remaining columns being measured variables (value_vars). The measured variables are "unpivoted" to the row axis, leaving just two non-identifier columns, a variable and its corresponding value, which can both be renamed using optional arguments.

pd.melt(cdystonia_wide, id_vars=['patient','site','id','treat','age','sex'], var_name='obs', value_name='twsters').head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

dd7c2d385c53af10f72d4c56fd59f475

This illustrates the two formats for longitudinal data: long and wide formats. Its typically better to store data in long format because additional data can be included as additional rows in the database, while wide format requires that the entire database schema be altered by adding columns to every row as data are collected. The preferable format for analysis depends entirely on what is planned for the data, so it is imporant to be able to move easily between them. Pivoting The pivot method allows a DataFrame to be transformed easily between long and wide formats in the same way as a pivot table is created in a spreadsheet. It takes three arguments: index, columns and values, corresponding to the DataFrame index (the row headers), columns and cell values, respectively. For example, we may want the twstrs variable (the response variable) in wide format according to patient, as we saw with the unstacking method above:

cdystonia.pivot(index='patient', columns='obs', values='twstrs').head()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

267b3e7b67e095660f5da21274dd5d20

If we omit the values argument, we get a DataFrame with hierarchical columns, just as when we applied unstack to the hierarchically-indexed table:

cdystonia.pivot('patient', 'obs')

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

8c969376da0663f603d9b0d89141ad5b

A related method, pivot_table, creates a spreadsheet-like table with a hierarchical index, and allows the values of the table to be populated using an arbitrary aggregation function.

cdystonia.pivot_table(index=['site', 'treat'], columns='week', values='twstrs', aggfunc=max).head(20)

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

79d0f4d0a86d4f5ab412922b564330a5

For a simple cross-tabulation of group frequencies, the crosstab function (not a method) aggregates counts of data according to factors in rows and columns. The factors may be hierarchical if desired.

pd.crosstab(cdystonia.sex, cdystonia.site)

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

d5f94fb54220dd35e54866413655df32

Data transformation There are a slew of additional operations for DataFrames that we would collectively refer to as "transformations" which include tasks such as removing duplicate values, replacing values, and grouping values. Dealing with duplicates We can easily identify and remove duplicate values from DataFrame objects. For example, say we want to removed ships from our vessels dataset that have the same name:

vessels.duplicated(subset='names') vessels.drop_duplicates(['names'])

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

07f77cb844759d491b678d4f9aef7655

Value replacement Frequently, we get data columns that are encoded as strings that we wish to represent numerically for the purposes of including it in a quantitative analysis. For example, consider the treatment variable in the cervical dystonia dataset:

cdystonia.treat.value_counts()

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

5f4fd26ff66c0cc7a446f57842eac864

A logical way to specify these numerically is to change them to integer values, perhaps using "Placebo" as a baseline value. If we create a dict with the original values as keys and the replacements as values, we can pass it to the map method to implement the changes.

treatment_map = {'Placebo': 0, '5000U': 1, '10000U': 2} cdystonia['treatment'] = cdystonia.treat.map(treatment_map) cdystonia.treatment

Homework/01 - Pandas and Data Wrangling/temp/Data Wrangling with Pandas.ipynb

Merinorus/adaisawesome

gpl-3.0

d566411481536c961c5754fac01ed6f0

Alternately, if we simply want to replace particular values in a Series or DataFrame, we can use the replace method. An example where replacement is useful is dealing with zeros in certain transformations. For example, if we try to take the log of a set of values:

vals = pd.Series([float(i)**10 for i in range(10)]) vals np.log(vals)

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Merinorus/adaisawesome

gpl-3.0

058f8abcfa474cd0326b4215632977a1

In such situations, we can replace the zero with a value so small that it makes no difference to the ensuing analysis. We can do this with replace.

vals = vals.replace(0, 1e-6) np.log(vals)

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gpl-3.0

9815c4d95b9ca828b5efadf9be73f4b1

We can also perform the same replacement that we used map for with replace:

cdystonia2.treat.replace({'Placebo': 0, '5000U': 1, '10000U': 2})

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Merinorus/adaisawesome

gpl-3.0

cd6bd896b598450949c0adf00afe77ae

Inidcator variables For some statistical analyses (e.g. regression models or analyses of variance), categorical or group variables need to be converted into columns of indicators--zeros and ones--to create a so-called design matrix. The Pandas function get_dummies (indicator variables are also known as dummy variables) makes this transformation straightforward. Let's consider the DataFrame containing the ships corresponding to the transit segments on the eastern seaboard. The type variable denotes the class of vessel; we can create a matrix of indicators for this. For simplicity, lets filter out the 5 most common types of ships:

top5 = vessels.type.isin(vessels.type.value_counts().index[:5]) top5.head(10) vessels5 = vessels[top5] pd.get_dummies(vessels5.type).head(10)

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gpl-3.0

aeccca798f726583520fefc5ced5e71c

Categorical Data Pandas provides a convenient dtype for reprsenting categorical (factor) data, called category. For example, the treat column in the cervical dystonia dataset represents three treatment levels in a clinical trial, and is imported by default as an object type, since it is a mixture of string characters.

cdystonia.treat.head()

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Merinorus/adaisawesome

gpl-3.0

32b902ebc3f6171539c1c0ac176a93a3

We can convert this to a category type either by the Categorical constructor, or casting the column using astype:

pd.Categorical(cdystonia.treat) cdystonia['treat'] = cdystonia.treat.astype('category') cdystonia.treat.describe()

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gpl-3.0

d85c7bbd1fdfb48b4158450f9c5e94e5

By default the Categorical type represents an unordered categorical.

cdystonia.treat.cat.categories

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gpl-3.0

60eb0a8a62504b119204452ad84087d8

However, an ordering can be imposed. The order is lexical by default, but will assume the order of the listed categories to be the desired order.

cdystonia.treat.cat.categories = ['Placebo', '5000U', '10000U'] cdystonia.treat.cat.as_ordered().head()

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gpl-3.0

e4a8fdef6791ec3657dc7d43ca8e592c

The important difference between the category type and the object type is that category is represented by an underlying array of integers, which is then mapped to character labels.

cdystonia.treat.cat.codes

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gpl-3.0

bedd8214d1672b8bb731a7c4c0664112

Notice that these are 8-bit integers, which are essentially single bytes of data, making memory usage lower. There is also a performance benefit. Consider an operation such as calculating the total segment lengths for each ship in the segments table (this is also a preview of pandas' groupby operation!):

%time segments.groupby(segments.name).seg_length.sum().sort_values(ascending=False, inplace=False).head() segments['name'] = segments.name.astype('category') %time segments.groupby(segments.name).seg_length.sum().sort_values(ascending=False, inplace=False).head()

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Merinorus/adaisawesome

gpl-3.0

545f2c491509976dba7390f031b5e271

Hence, we get a considerable speedup simply by using the appropriate dtype for our data. Discretization Pandas' cut function can be used to group continuous or countable data in to bins. Discretization is generally a very bad idea for statistical analysis, so use this function responsibly! Lets say we want to bin the ages of the cervical dystonia patients into a smaller number of groups:

cdystonia.age.describe()

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Merinorus/adaisawesome

gpl-3.0

dca52b72649593cdb281db0a254b619d

Let's transform these data into decades, beginnnig with individuals in their 20's and ending with those in their 80's:

pd.cut(cdystonia.age, [20,30,40,50,60,70,80,90])[:30]

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gpl-3.0

0b86bde7d6d01ededbe319c5495f5b8f

The parentheses indicate an open interval, meaning that the interval includes values up to but not including the endpoint, whereas the square bracket is a closed interval, where the endpoint is included in the interval. We can switch the closure to the left side by setting the right flag to False:

pd.cut(cdystonia.age, [20,30,40,50,60,70,80,90], right=False)[:30]

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gpl-3.0

04ce32536d6de93851304a6670521cf7

Since the data are now ordinal, rather than numeric, we can give them labels:

pd.cut(cdystonia.age, [20,40,60,80,90], labels=['young','middle-aged','old','really old'])[:30]

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gpl-3.0

94f2f82e28f118cb67d3affbfdc20be4

A related function qcut uses empirical quantiles to divide the data. If, for example, we want the quartiles -- (0-25%], (25-50%], (50-70%], (75-100%] -- we can just specify 4 intervals, which will be equally-spaced by default:

pd.qcut(cdystonia.age, 4)[:30]

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Merinorus/adaisawesome

gpl-3.0

06aef490fd60bc9943f699def3e90139

Alternatively, one can specify custom quantiles to act as cut points:

quantiles = pd.qcut(segments.seg_length, [0, 0.01, 0.05, 0.95, 0.99, 1]) quantiles[:30]

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gpl-3.0

d303c4066eeb6f0d13a98429465da4fb

Note that you can easily combine discretiztion with the generation of indicator variables shown above:

pd.get_dummies(quantiles).head(10)

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gpl-3.0

ab4453241a888e738d060d425fbafac8

Permutation and sampling For some data analysis tasks, such as simulation, we need to be able to randomly reorder our data, or draw random values from it. Calling NumPy's permutation function with the length of the sequence you want to permute generates an array with a permuted sequence of integers, which can be used to re-order the sequence.

new_order = np.random.permutation(len(segments)) new_order[:30]

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Merinorus/adaisawesome

gpl-3.0

12244f32212ab9a9299c01c3d91c2f09

Using this sequence as an argument to the take method results in a reordered DataFrame:

segments.take(new_order).head()

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gpl-3.0

22721b0de1efec516999ee431dd8790c

Compare this ordering with the original:

segments.head()

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gpl-3.0

f9e0d1b45bdd33f29c332c96862cab47

For random sampling, DataFrame and Series objects have a sample method that can be used to draw samples, with or without replacement:

vessels.sample(n=10) vessels.sample(n=10, replace=True)

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Merinorus/adaisawesome

gpl-3.0

4b9db5e58388811cedad1f566365abbe

Data aggregation and GroupBy operations One of the most powerful features of Pandas is its GroupBy functionality. On occasion we may want to perform operations on groups of observations within a dataset. For exmaple: aggregation, such as computing the sum of mean of each group, which involves applying a function to each group and returning the aggregated results slicing the DataFrame into groups and then doing something with the resulting slices (e.g. plotting) group-wise transformation, such as standardization/normalization

cdystonia_grouped = cdystonia.groupby(cdystonia.patient)

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Merinorus/adaisawesome

gpl-3.0

e3e2a5a665c1dd6cfa7d1f8bf31a5dbc

This grouped dataset is hard to visualize

cdystonia_grouped

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Merinorus/adaisawesome

gpl-3.0

17b10ef6b818d4d575f68622893959af

However, the grouping is only an intermediate step; for example, we may want to iterate over each of the patient groups:

for patient, group in cdystonia_grouped: print('patient', patient) print('group', group)

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gpl-3.0

3e6451f596304cf9007ab31bf573c0cf

A common data analysis procedure is the split-apply-combine operation, which groups subsets of data together, applies a function to each of the groups, then recombines them into a new data table. For example, we may want to aggregate our data with with some function. <div align="right">*(figure taken from "Python for Data Analysis", p.251)*</div> We can aggregate in Pandas using the aggregate (or agg, for short) method:

cdystonia_grouped.agg(np.mean).head()

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Merinorus/adaisawesome

gpl-3.0

12e3d25cdd56eae0fbf7d6d7f899e057

Notice that the treat and sex variables are not included in the aggregation. Since it does not make sense to aggregate non-string variables, these columns are simply ignored by the method. Some aggregation functions are so common that Pandas has a convenience method for them, such as mean:

cdystonia_grouped.mean().head()

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gpl-3.0

86d988b128528df08d8a353c6cc2883d

The add_prefix and add_suffix methods can be used to give the columns of the resulting table labels that reflect the transformation:

cdystonia_grouped.mean().add_suffix('_mean').head() # The median of the `twstrs` variable cdystonia_grouped['twstrs'].quantile(0.5)

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Merinorus/adaisawesome

gpl-3.0

b869a25062d160ef4916da330bfd59ca

If we wish, we can easily aggregate according to multiple keys:

cdystonia.groupby(['week','site']).mean().head()

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Merinorus/adaisawesome

gpl-3.0

2498168a47fa3aec2f8110e9e93ab33f

Alternately, we can transform the data, using a function of our choice with the transform method:

normalize = lambda x: (x - x.mean())/x.std() cdystonia_grouped.transform(normalize).head()

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Merinorus/adaisawesome

gpl-3.0

665109e69145d0aace6bffd3f45ef2ab

It is easy to do column selection within groupby operations, if we are only interested split-apply-combine operations on a subset of columns:

cdystonia_grouped['twstrs'].mean().head() # This gives the same result as a DataFrame cdystonia_grouped[['twstrs']].mean().head()

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Merinorus/adaisawesome

gpl-3.0

f2c009e4f57f82ef605a5bb5a7ff43ea

If you simply want to divide your DataFrame into chunks for later use, its easy to convert them into a dict so that they can be easily indexed out as needed:

chunks = dict(list(cdystonia_grouped)) chunks[4]

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Merinorus/adaisawesome

gpl-3.0

55a5b039a26595b1ba3dfed6e36bc507

By default, groupby groups by row, but we can specify the axis argument to change this. For example, we can group our columns by dtype this way:

grouped_by_type = cdystonia.groupby(cdystonia.dtypes, axis=1) {g:grouped_by_type.get_group(g) for g in grouped_by_type.groups}

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Merinorus/adaisawesome

gpl-3.0

4f0f01145c8703e1950284b00da7d8a2

Its also possible to group by one or more levels of a hierarchical index. Recall cdystonia2, which we created with a hierarchical index:

cdystonia2.head(10) cdystonia2.groupby(level='obs', axis=0)['twstrs'].mean()

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gpl-3.0

00c4204fbbb2f86cc57f2aca7e863b5d

Apply We can generalize the split-apply-combine methodology by using apply function. This allows us to invoke any function we wish on a grouped dataset and recombine them into a DataFrame. The function below takes a DataFrame and a column name, sorts by the column, and takes the n largest values of that column. We can use this with apply to return the largest values from every group in a DataFrame in a single call.

def top(df, column, n=5): return df.sort_values(by=column, ascending=False)[:n]

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Merinorus/adaisawesome

gpl-3.0

ae1a8447223eaeafee7916d33c2235e3