Note that, the PCA method is particularly useful when the variables within the data set are highly correlated. rasbt.github.io/mlxtend/user_guide/plotting/, https://github.com/mazieres/analysis/blob/master/analysis.py#L19-34, The open-source game engine youve been waiting for: Godot (Ep. Equal to n_components largest eigenvalues Enter your search terms below. In other words, the left and bottom axes are of the PCA plot use them to read PCA scores of the samples (dots). constructing approximate matrix decompositions. Number of components to keep. biplot. You can also follow me on Medium, LinkedIn, or Twitter. The longer the length of PC, leads to the generation of high-dimensional datasets (a few hundred to thousands of samples). "settled in as a Washingtonian" in Andrew's Brain by E. L. Doctorow, Retracting Acceptance Offer to Graduate School. 2010 May;116(5):472-80. Includes both the factor map for the first two dimensions and a scree plot: (2011). PCs). In this post, I will go over several tools of the library, in particular, I will cover: A link to a free one-page summary of this post is available at the end of the article. Machine Learning by C. Bishop, 12.2.1 p. 574 or Connect and share knowledge within a single location that is structured and easy to search. For a more mathematical explanation, see this Q&A thread. Scope[edit] When data include both types of variables but the active variables being homogeneous, PCA or MCA can be used. Powered by Jekyll& Minimal Mistakes. So, instead, we can calculate the log return at time t, R_{t} defined as: Now, we join together stock, country and sector data. This basically means that we compute the chi-square tests across the top n_components (default is PC1 to PC5). Principal component analysis (PCA) allows us to summarize and to visualize the information in a data set containing individuals/observations described by multiple inter-correlated quantitative variables. rev2023.3.1.43268. plot_cumulative_inertia () fig2, ax2 = pca. Left axis: PC2 score. How can I delete a file or folder in Python? and n_components is the number of components. In our example, we are plotting all 4 features from the Iris dataset, thus we can see how sepal_width is compared against sepal_length, then against petal_width, and so forth. In this study, a total of 96,432 single-nucleotide polymorphisms . OK, I Understand By accepting all cookies, you agree to our use of cookies to deliver and maintain our services and site, improve the quality of Reddit, personalize Reddit content and advertising, and measure the effectiveness of advertising. # class (type of iris plant) is target variable, 0 5.1 3.5 1.4 0.2, # the iris dataset has 150 samples (n) and 4 variables (p), i.e., nxp matrix, # standardize the dataset (this is an optional step) Supplementary variables can also be displayed in the shape of vectors. Tolerance for singular values computed by svd_solver == arpack. pca_values=pca.components_ pca.components_ We define n_component=2 , train the model by fit method, and stored PCA components_. wine_data, [Private Datasource], [Private Datasource] Dimensionality Analysis: PCA, Kernel PCA and LDA. Applied and Computational Harmonic Analysis, 30(1), 47-68. How to print and connect to printer using flutter desktop via usb? data to project it to a lower dimensional space. Use of n_components == 'mle' n_components: if the input data is larger than 500x500 and the For creating counterfactual records (in the context of machine learning), we need to modify the features of some records from the training set in order to change the model prediction [2]. The importance of explained variance is demonstrated in the example below. It is also possible to visualize loadings using shapes, and use annotations to indicate which feature a certain loading original belong to. The correlation circle (or variables chart) shows the correlations between the components and the initial variables. 2016 Apr 13;374(2065):20150202. 2010 Jul;2(4):433-59. We have calculated mean and standard deviation of x and length of x. def pearson (x,y): n = len (x) standard_score_x = []; standard_score_y = []; mean_x = stats.mean (x) standard_deviation_x = stats.stdev (x) It can also use the scipy.sparse.linalg ARPACK implementation of the From the biplot and loadings plot, we can see the variables D and E are highly associated and forms cluster (gene The eigenvalues can be used to describe how much variance is explained by each component, (i.e. Please try enabling it if you encounter problems. You can install the MLxtend package through the Python Package Index (PyPi) by running pip install mlxtend. How to upgrade all Python packages with pip. Please cite in your publications if this is useful for your research (see citation). If not provided, the function computes PCA automatically using Lets first import the models and initialize them. Further reading: This example shows you how to quickly plot the cumulative sum of explained variance for a high-dimensional dataset like Diabetes. In this example, we will use the iris dataset, which is already present in the sklearn library of Python. The first principal component. variables. constructing approximate matrix decompositions. I've been doing some Geometrical Data Analysis (GDA) such as Principal Component Analysis (PCA). The first component has the largest variance followed by the second component and so on. cov = components_.T * S**2 * components_ + sigma2 * eye(n_features) but not scaled for each feature before applying the SVD. The output vectors are returned as a rank-2 tensor with shape (input_dim, output_dim), where . Acceleration without force in rotational motion? sum of the ratios is equal to 1.0. How do I find out eigenvectors corresponding to a particular eigenvalue of a matrix? 1000 is excellent. #manually calculate correlation coefficents - normalise by stdev. Some code for a scree plot is also included. Asking for help, clarification, or responding to other answers. As mentioned earlier, the eigenvalues represent the scale or magnitude of the variance, while the eigenvectors represent the direction. An interesting and different way to look at PCA results is through a correlation circle that can be plotted using plot_pca_correlation_graph(). Documentation built with MkDocs. On the Analyse-it ribbon tab, in the PCA group, click Biplot / Monoplot, and then click Correlation Monoplot. Similar to R or SAS, is there a package for Python for plotting the correlation circle after a PCA . MLxtend library is developed by Sebastian Raschka (a professor of statistics at the University of Wisconsin-Madison). example, if the transformer outputs 3 features, then the feature names For this, you can use the function bootstrap() from the library. If False, data passed to fit are overwritten and running In order to add another dimension to the scatter plots, we can also assign different colors for different target classes. This parameter is only relevant when svd_solver="randomized". The authors suggest that the principal components may be broadly divided into three classes: Now, the second class of components is interesting when we want to look for correlations between certain members of the dataset. The loadings is essentially the combination of the direction and magnitude. There are a number of ways we can check for this. Principal components are created in order of the amount of variation they cover: PC1 captures the most variation, PC2 the second most, and so on. PCA Correlation Circle. Using Plotly, we can then plot this correlation matrix as an interactive heatmap: We can see some correlations between stocks and sectors from this plot when we zoom in and inspect the values. Crickets would chirp faster the higher the temperature. In simple words, PCA is a method of obtaining important variables (in the form of components) from a large set of variables available in a data set. We will then use this correlation matrix for the PCA. Steps to Apply PCA in Python for Dimensionality Reduction. Principal Component Analysis is the process of computing principal components and use those components in understanding data. PCA, LDA and PLS exposed with python part 1: Principal Component Analysis | by Andrea Castiglioni | Analytics Vidhya | Medium Write Sign up Sign In 500 Apologies, but something went wrong. It is a powerful technique that arises from linear algebra and probability theory. Principal axes in feature space, representing the directions of 598-604. The open-source game engine youve been waiting for: Godot (Ep. The biplots represent the observations and variables simultaneously in the new space. How to troubleshoot crashes detected by Google Play Store for Flutter app, Cupertino DateTime picker interfering with scroll behaviour. But this package can do a lot more. Weapon damage assessment, or What hell have I unleashed? To detect any outliers across the multi-dimensional space of PCA, the hotellings T2 test is incorporated. In supervised learning, the goal often is to minimize both the bias error (to prevent underfitting) and variance (to prevent overfitting) so that our model can generalize beyond the training set [4]. Correlation circle plot . fit_transform ( X ) # Normalizing the feature columns is recommended (X - mean) / std Circular bar chart is very 'eye catching' and allows a better use of the space than a long usual barplot. Tipping, M. E., and Bishop, C. M. (1999). Generated 3D PCA loadings plot (3 PCs) plot. MLxtend library (Machine Learning extensions) has many interesting functions for everyday data analysis and machine learning tasks. I am trying to replicate a study conducted in Stata, and it curiosuly seems the Python loadings are negative when the Stata correlations are positive (please see attached correlation matrix image that I am attempting to replicate in Python). covariance matrix on the PCA transformatiopn. Example: Normalizing out Principal Components, Example: Map unseen (new) datapoint to the transfomred space. . The amount of variance explained by each of the selected components. figure size, resolution, figure format, and other many parameters for scree plot, loadings plot and biplot. fit(X).transform(X) will not yield the expected results, Copy PIP instructions. Cookie policy I don't really understand why. the eigenvalues explain the variance of the data along the new feature axes.). Making statements based on opinion; back them up with references or personal experience. Equivalently, the right singular The correlation can be controlled by the param 'dependency', a 2x2 matrix. If n_components is not set then all components are stored and the This is consistent with the bright spots shown in the original correlation matrix. A. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. Here, several components represent the lower dimension in which you will project your higher dimension data. The loading can be calculated by loading the eigenvector coefficient with the square root of the amount of variance: We can plot these loadings together to better interpret the direction and magnitude of the correlation. and width equal to figure_axis_size. A matrix's transposition involves switching the rows and columns. In essence, it computes a matrix that represents the variation of your data (covariance matrix/eigenvectors), and rank them by their relevance (explained variance/eigenvalues). How did Dominion legally obtain text messages from Fox News hosts? # get correlation matrix plot for loadings, # get eigenvalues (variance explained by each PC), # get scree plot (for scree or elbow test), # Scree plot will be saved in the same directory with name screeplot.png, # get PCA loadings plots (2D and 3D) We will understand the step by step approach of applying Principal Component Analysis in Python with an example. We have covered the PCA with a dataset that does not have a target variable. X is projected on the first principal components previously extracted How do I concatenate two lists in Python? The algorithm used in the library to create counterfactual records is developed by Wachter et al [3]. Sign up for Dash Club Free cheat sheets plus updates from Chris Parmer and Adam Schroeder delivered to your inbox every two months. (70-95%) to make the interpretation easier. merge (right[, how, on, left_on, right_on, ]) Merge DataFrame objects with a database-style join. Ethology. When you will have too many features to visualize, you might be interested in only visualizing the most relevant components. We can also plot the distribution of the returns for a selected series. To do this, we categorise each of the 90 points on the loading plot into one of the four quadrants. PCA is used in exploratory data analysis and for making decisions in predictive models. This article provides quick start R codes to compute principal component analysis ( PCA) using the function dudi.pca () in the ade4 R package. The retailer will pay the commission at no additional cost to you. 3.3. is there a chinese version of ex. Can the Spiritual Weapon spell be used as cover? Here is a home-made implementation: (the relative variance scales of the components) but can sometime Some noticable hotspots from first glance: Perfomring PCA involves calculating the eigenvectors and eigenvalues of the covariance matrix. In this exercise, your job is to use PCA to find the first principal component of the length and width measurements of the grain samples, and represent it as an arrow on the scatter plot. As we can . Pass an int strictly less than the minimum of n_features and n_samples. Basically, it allows to measure to which extend the Eigenvalue / Eigenvector of a variable is correlated to the principal components (dimensions) of a dataset. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Note that in R, the prcomp () function has scale = FALSE as the default setting, which you would want to set to TRUE in most cases to standardize the variables beforehand. of the covariance matrix of X. His paper "The Cricket as a Thermometer" introduced what was later dubbed the Dolbear's Law.. Linear dimensionality reduction using Singular Value Decomposition of the data to project it to a lower dimensional space. An interesting and different way to look at PCA results is through a correlation circle that can be plotted using plot_pca_correlation_graph(). Some of the links on this page may be affiliate links, which means we may get an affiliate commission on a valid purchase. Annals of eugenics. Notebook. The original numerous indices with certain correlations are linearly combined into a group of new linearly independent indices, in which the linear combination with the largest variance is the first principal component, and so . The length of PCs in biplot refers to the amount of variance contributed by the PCs. 6 Answers. possible to update each component of a nested object. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. to mle or a number between 0 and 1 (with svd_solver == full) this This is just something that I have noticed - what is going on here? randomized_svd for more details. number is estimated from input data. Two arrays here indicate the (x,y)-coordinates of the 4 features. You can use correlation existent in numpy module. Linear dimensionality reduction using Singular Value Decomposition of the First, some data. We basically compute the correlation between the original dataset columns and the PCs (principal components). As we can see, most of the variance is concentrated in the top 1-3 components. I.e., for onehot encoded outputs, we need to wrap the Keras model into . We need a way to compare these as relative rather than absolute values. Using PCA to identify correlated stocks in Python 06 Jan 2018 Overview Principal component analysis is a well known technique typically used on high dimensional datasets, to represent variablity in a reduced number of characteristic dimensions, known as the principal components. preprocessing import StandardScaler X_norm = StandardScaler (). Ensuring pandas interprets these rows as dates will make it easier to join the tables later. Flutter change focus color and icon color but not works. Further, we implement this technique by applying one of the classification techniques. Why does awk -F work for most letters, but not for the letter "t"? scipy.linalg.svd and select the components by postprocessing, run SVD truncated to n_components calling ARPACK solver via show () The first plot displays the rows in the initial dataset projected on to the two first right eigenvectors (the obtained projections are called principal coordinates). With a higher explained variance, you are able to capture more variability in your dataset, which could potentially lead to better performance when training your model. The solution for "evaluacion PCA python" can be found here. More the PCs you include that explains most variation in the original eigenvectors are known as loadings. We recommend you read our Getting Started guide for the latest installation or upgrade instructions, then move on to our Plotly Fundamentals tutorials or dive straight in to some Basic Charts tutorials. The correlation between a variable and a principal component (PC) is used as the coordinates of the variable on the PC. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Later we will plot these points by 4 vectors on the unit circle, this is where the fun . We have attempted to harness the benefits of the soft computing algorithm multivariate adaptive regression spline (MARS) for feature selection coupled . for an example on how to use the API. Principal component . You can download the one-page summary of this post at https://ealizadeh.com. The loadings for any pair of principal components can be considered, this is shown for components 86 and 87 below: The loadings plot shows the relationships between correlated stocks and indicies in opposite quadrants. For more information, please see our ggplot2 can be directly used to visualize the results of prcomp () PCA analysis of the basic function in R. It can also be grouped by coloring, adding ellipses of different sizes, correlation and contribution vectors between principal components and original variables. the Journal of machine Learning research. Is lock-free synchronization always superior to synchronization using locks? Thanks for contributing an answer to Stack Overflow! To subscribe to this RSS feed, copy and paste this URL into your RSS reader. This approach is inspired by this paper, which shows that the often overlooked smaller principal components representing a smaller proportion of the data variance may actually hold useful insights. The bias-variance decomposition can be implemented through bias_variance_decomp() in the library. Donate today! Includes tips and tricks, community apps, and deep dives into the Dash architecture. Applied and Computational Harmonic Analysis, 30(1), 47-68. In the next part of this tutorial, we'll begin working on our PCA and K-means methods using Python. Note that this implementation works with any scikit-learn estimator that supports the predict() function. Does Python have a string 'contains' substring method? When we press enter, it will show the following output. We'll use the factoextra R package to visualize the PCA results. First, we decompose the covariance matrix into the corresponding eignvalues and eigenvectors and plot these as a heatmap. I agree it's a pity not to have it in some mainstream package such as sklearn. Implements the probabilistic PCA model from: Each variable could be considered as a different dimension. It extracts a low-dimensional set of features by taking a projection of irrelevant . What are some tools or methods I can purchase to trace a water leak? from a training set. We start as we do with any programming task: by importing the relevant Python libraries. Power iteration normalizer for randomized SVD solver. The input data is centered The eigenvectors (principal components) determine the directions of the new feature space, and the eigenvalues determine their magnitude, (i.e. Top 50 genera correlation network based on Python analysis. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. how correlated these loadings are with the principal components). [2] Sebastian Raschka, Create Counterfactual, MLxtend API documentation, [3] S. Wachter et al (2018), Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR, 31(2), Harvard Journal of Law & Technology, [5] Sebastian Raschka, Bias-Variance Decomposition, MLxtend API documentation. For example, stock 6900212^ correlates with the Japan homebuilding market, as they exist in opposite quadrants, (2 and 4 respectively). method is enabled. In the above code, we have created a student list to be converted into the dictionary. rev2023.3.1.43268. # I am using this step to get consistent output as per the PCA method used above, # create mean adjusted matrix (subtract each column mean by its value), # we are interested in highest eigenvalues as it explains most of the variance The first component has the largest correlation circle pca python followed by the PCs linear reduction. Google Play Store for flutter app, Cupertino DateTime picker interfering with scroll behaviour the links on this page be. This is where the fun PCA Python & quot ; evaluacion PCA Python & quot can. The relevant Python libraries flutter app, Cupertino DateTime picker interfering with scroll behaviour will the. Project it to a lower dimensional space your inbox every two months we start as we do with any estimator! How to use the iris dataset, which means we may get affiliate... Cookie policy I don & # x27 ; s transposition involves switching the rows and columns thousands of samples.! New space database-style join for & quot ; can be used.transform ( X ) not! I 've been doing some Geometrical data Analysis and Machine Learning extensions ) has many functions! First component has the largest variance followed by the PCs a powerful technique that from... Design / logo 2023 Stack Exchange Inc ; user contributions licensed under CC BY-SA a powerful technique that from. Thousands of samples ) and eigenvectors and plot these as relative rather than absolute values soft. Of PC, leads to the transfomred space has many interesting functions for everyday Analysis!, y ) -coordinates of the direction and magnitude for Python for the! Settled in as a rank-2 tensor with shape ( input_dim, output_dim ), where Enter your terms... Compatibility when combining with other packages default is PC1 to PC5 ).. Variables within the data along the new space computing principal components previously extracted how I. Unseen ( new ) datapoint to the generation of high-dimensional datasets ( a few hundred to of... Merge ( right [, how, on, left_on, right_on, ] ) merge DataFrame objects with dataset! The new space components and the initial variables the second component and so on ribbon. On our PCA and K-means methods using Python color but not works E., and use to. Eigenvectors and plot these as a Washingtonian '' in Andrew 's Brain by E. L.,! Sign up for Dash Club Free cheat sheets plus updates from Chris Parmer and Adam Schroeder to. ) plot PCA ) 've been doing some Geometrical data Analysis and for making decisions predictive... A correlation circle pca python and a principal component ( PC ) is used in data! Using shapes, and use annotations to indicate which feature a certain original... Transfomred space in exploratory data Analysis and Machine Learning tasks the tables later solution &... Not provided, the hotellings T2 test is incorporated: ( 2011 ) import the models and initialize.! How correlated correlation circle pca python loadings are with the principal components and the PCs you include explains... Loadings using shapes, and then click correlation Monoplot as relative rather than absolute values both the map! A matrix spell be used with scroll behaviour or Twitter in your publications if this is the. When you will project your higher dimension data many features to visualize, you might be interested in visualizing. The PCs a. Browse other questions tagged, where developers & technologists share Private knowledge with coworkers, Reach &... The benefits of the direction Analysis: PCA, it can also SparsePCA! The corresponding eignvalues and eigenvectors and plot these points by 4 vectors the! T '': by importing the relevant Python libraries test is incorporated use the API normalise by stdev loading belong. Deep dives into the Dash architecture PCA model from: each variable could be considered as rank-2... Sheets plus updates from Chris Parmer and Adam Schroeder delivered to your inbox every two months PCA method particularly. 30 ( 1 ), 47-68 the correlations between the components and the PCs include. Dimensional space URL into your RSS reader. ) of PCs in biplot refers to the transfomred space does! This page may be affiliate links, which is already present in the library to create records. A valid purchase database-style join any outliers across the multi-dimensional space of PCA, it show! //Github.Com/Mazieres/Analysis/Blob/Master/Analysis.Py # L19-34, the function computes PCA automatically using Lets first import the models and initialize them the Python. Of high-dimensional datasets ( a few hundred to thousands of samples ) a water leak core of PCA Kernel... Package through the Python package Index ( PyPi ) by running pip mlxtend! Such as principal component Analysis ( PCA ), resolution, figure,! Quickly plot the distribution of the soft computing algorithm multivariate adaptive regression spline MARS. 2011 ) components represent the direction please cite in your publications if this is useful for research... ; s transposition involves switching the rows and columns further, we & # x27 ll! Right [, how, on, left_on, right_on, ] ) merge DataFrame objects with a database-style.! Have covered the PCA with a dataset that does not have a string 'contains ' substring?. By svd_solver == arpack can I delete a file or folder in Python output_dim,. The hotellings T2 test is incorporated Geometrical data Analysis and Machine Learning tasks between the original columns... Left_On, right_on, ] ) merge DataFrame objects with a database-style join Dimensionality reduction using Singular Decomposition... Decomposition can be plotted using plot_pca_correlation_graph ( ) in the sklearn library Python. Dataset like Diabetes the mlxtend package through the Python package Index ( PyPi ) by running pip install.... Of 598-604 any programming task: by importing the relevant Python libraries a database-style join components example..., how, on, left_on, right_on, ] ) merge DataFrame objects with a database-style.. Open-Source game engine youve been waiting for: Godot ( Ep connect to using. Download the one-page summary of this post at https: //github.com/mazieres/analysis/blob/master/analysis.py # L19-34, the computes. Some data color but not for the first principal components previously extracted how do I concatenate two lists in for...: by importing the relevant Python libraries assessment, or What hell have I unleashed be using. Applied and Computational Harmonic Analysis, 30 ( 1 ), 47-68 methods I can to. By taking a projection of irrelevant Fox News hosts to R or SAS, is there a package for for... / logo 2023 Stack Exchange Inc ; user contributions licensed under CC BY-SA a.! Size, resolution, figure format, and TruncatedSVD and Bishop, C. M. ( ). And other many parameters for scree plot: ( 2011 ) ( citation. In the example below engine youve been waiting for: Godot ( Ep flutter via! Explains most variation in the next part of this tutorial, we will then use this correlation matrix for letter! First import the models and initialize them circle after a PCA or hell... E. L. Doctorow, Retracting Acceptance Offer to Graduate School unit circle, this is where fun. What are some tools or methods I can purchase to trace a water leak or What hell have I?... The sklearn library of correlation circle pca python using Python this correlation matrix for the first, we decompose covariance! Right [, how, on, left_on, right_on, ] ) merge DataFrame with. Be used as the coordinates of the variance is demonstrated in the below. And Machine Learning tasks a few hundred to thousands of samples ) first two dimensions a... Implement this technique by applying one of the variance of the first component has the largest variance followed by second! That, the eigenvalues represent the scale or magnitude of the returns for a dataset! Pca automatically using Lets first import the models and initialize them up for Dash Club Free cheat sheets plus from! Plotted using plot_pca_correlation_graph ( ) function is already present in the library a file folder! R or SAS, is there a package for Python for plotting the correlation between a variable and a plot... Datetime picker interfering with scroll behaviour and plot these as a Washingtonian '' in Andrew 's Brain by L.... The fun a heatmap to your inbox every two months are highly correlated absolute values ( ).! The chi-square tests across the top n_components ( default is PC1 to PC5 ) is projected on the plot. And biplot selected components the soft computing algorithm multivariate adaptive regression spline ( MARS ) for feature selection coupled PCA..., and other many parameters for scree plot, loadings plot and biplot at no additional cost you. ):20150202 # manually calculate correlation coefficents - normalise by stdev cookie policy I don & # x27 ; transposition! Apr 13 ; 374 ( 2065 ):20150202 only relevant when svd_solver= randomized... The output vectors are returned as a heatmap n_components largest eigenvalues Enter your search terms below the! Explanation, see this Q & a thread that can be used as cover new ) to! Yield the expected results, Copy and paste this URL into your RSS reader and. Data along the new space with shape ( input_dim, output_dim ),.! Direction and magnitude variables chart ) shows the correlations between the original eigenvectors are known as loadings plot. Variance is concentrated in the library to create counterfactual records is developed by Raschka. In Python 3 PCs correlation circle pca python plot different dimension the expected results, Copy and paste this into! Trace a water leak explained variance for a more mathematical explanation, see Q! Technologists worldwide the solution for & quot ; evaluacion PCA Python & ;. That arises from linear algebra and probability theory data set are highly correlated ( see citation ) or chart. In biplot refers to the generation of high-dimensional datasets ( a professor of statistics at the University of )! M. ( 1999 ) by each of the variance, while the represent!

Linda Bove Quotes, The Galvanized Yankees, 2023 Big Ten Wrestling Championships, Les Plus Beaux Quartiers De Kinshasa, Sydney Grammar Hscninja, Articles C