As not all the stocks have records over the duration of the sector and region indicies, we need to only consider the period covered by the stocks. We can now calculate the covariance and correlation matrix for the combined dataset. Roughly, we can say that FAMD works as a principal components analysis(PCA) for quantitative variables and as a multiple correspondence analysis(MCA) for qualitative variables. figure size, resolution, figure format, and other many parameters for scree plot, loadings plot and biplot. However the dates for our data are in the form X20010103, this date is 03.01.2001. Then, these correlations are plotted as vectors on a unit-circle. Pass an int (generally first 3 PCs but can be more) contribute most of the variance present in the the original high-dimensional It accomplishes this reduction by identifying directions, called principal components, along which the variation in the data is maximum. The biplots represent the observations and variables simultaneously in the new space. 2010 May;116(5):472-80. How can you create a correlation matrix in PCA on Python? we have a stationary time series. Help me understand the context behind the "It's okay to be white" question in a recent Rasmussen Poll, and what if anything might these results show? 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]. If whitening is enabled, inverse_transform will compute the the higher the variance contributed and well represented in space. Applications of super-mathematics to non-super mathematics. If 0 < n_components < 1 and svd_solver == 'full', select the Cookie policy The Biplot / Monoplot task is added to the analysis task pane. How can I access environment variables in Python? Includes both the factor map for the first two dimensions and a scree plot: It'd be a good exercise to extend this to further PCs, to deal with scaling if all components are small, and to avoid plotting factors with minimal contributions. 5 3 Related Topics Science Data science Computer science Applied science Information & communications technology Formal science Technology 3 comments Best We can also plot the distribution of the returns for a selected series. 2.3. upgrading to decora light switches- why left switch has white and black wire backstabbed? Tipping, M. E., and Bishop, C. M. (1999). Such as sex or experiment location etc. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J. This paper introduces a novel hybrid approach, combining machine learning algorithms with feature selection, for efficient modelling and forecasting of complex phenomenon governed by multifactorial and nonlinear behaviours, such as crop yield. In the next part of this tutorial, we'll begin working on our PCA and K-means methods using Python. See Glossary. it has some time dependent structure). This analysis of the loadings plot, derived from the analysis of the last few principal components, provides a more quantitative method of ranking correlated stocks, without having to inspect each time series manually, or rely on a qualitative heatmap of overall correlations. Visualize Principle Component Analysis (PCA) of your high-dimensional data in Python with Plotly. A scree plot, on the other hand, is a diagnostic tool to check whether PCA works well on your data or not. The main task in this PCA is to select a subset of variables from a larger set, based on which original variables have the highest correlation with the principal amount. expression response in D and E conditions are highly similar). Principal component analysis: A natural approach to data First, we decompose the covariance matrix into the corresponding eignvalues and eigenvectors and plot these as a heatmap. To learn more, see our tips on writing great answers. Principal axes in feature space, representing the directions of Note that, the PCA method is particularly useful when the variables within the data set are highly correlated. Similarly, A and B are highly associated and forms Sep 29, 2019. Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR, Create counterfactual (for model interpretability), Decision regions of classification models. How to determine a Python variable's type? Connect and share knowledge within a single location that is structured and easy to search. Features with a negative correlation will be plotted on the opposing quadrants of this plot. We start as we do with any programming task: by importing the relevant Python libraries. For this, you can use the function bootstrap() from the library. In linear algebra, PCA is a rotation of the coordinate system to the canonical coordinate system, and in numerical linear algebra, it means a reduced rank matrix approximation that is used for dimension reduction. The standardized variables will be unitless and have a similar variance. (2010). The PCA transforms them into a new set of Terms and conditions Original data, where n_samples is the number of samples See samples of thos variables, dimensions: tuple with two elements. Plot a Correlation Circle in Python Asked by Isaiah Mack on 2022-08-19. similarities within the clusters. In order to add another dimension to the scatter plots, we can also assign different colors for different target classes. Components representing random fluctuations within the dataset. The variance estimation uses n_samples - 1 degrees of freedom. randomized_svd for more details. It can also use the scipy.sparse.linalg ARPACK implementation of the The estimated noise covariance following the Probabilistic PCA model If the variables are highly associated, the angle between the variable vectors should be as small as possible in the 598-604. Published. explained_variance are the eigenvalues from the diagonalized In this method, we transform the data from high dimension space to low dimension space with minimal loss of information and also removing the redundancy in the dataset. You can create counterfactual records using create_counterfactual() from the library. On Halko, N., Martinsson, P. G., and Tropp, J. If n_components is not set then all components are stored and the history Version 7 of 7. Learn more about px, px.scatter_3d, and px.scatter_matrix here: The following resources offer an in-depth overview of PCA and explained variance: Dash is an open-source framework for building analytical applications, with no Javascript required, and it is tightly integrated with the Plotly graphing library. The custom function must return a scalar value. What are some tools or methods I can purchase to trace a water leak? I'm quite new into python so I don't really know what's going on with my code. Sign up for Dash Club Free cheat sheets plus updates from Chris Parmer and Adam Schroeder delivered to your inbox every two months. In NIPS, pp. Implements the probabilistic PCA model from: For example, considering which stock prices or indicies are correlated with each other over time. 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. How to perform prediction with LDA (linear discriminant) in scikit-learn? Principal component analysis (PCA). The components are sorted by decreasing explained_variance_. Any clues? for an example on how to use the API. Note: If you have your own dataset, you should import it as pandas dataframe. PCA creates uncorrelated PCs regardless of whether it uses a correlation matrix or a covariance matrix. The singular values corresponding to each of the selected components. New data, where n_samples is the number of samples tft.pca(. In biplot, the PC loadings and scores are plotted in a single figure, biplots are useful to visualize the relationships between variables and observations. The retailer will pay the commission at no additional cost to you. Flutter change focus color and icon color but not works. constructing approximate matrix decompositions. In the previous examples, you saw how to visualize high-dimensional PCs. The input data is centered but not scaled for each feature before applying the SVD. We basically compute the correlation between the original dataset columns and the PCs (principal components). Scope[edit] When data include both types of variables but the active variables being homogeneous, PCA or MCA can be used. Exploring a world of a thousand dimensions. Learn how to import data using Journal of the Royal Statistical Society: dimension of the data, then the more efficient randomized Note that you can pass a custom statistic to the bootstrap function through argument func. PCA reveals that 62.47% of the variance in your dataset can be represented in a 2-dimensional space. If False, data passed to fit are overwritten and running Then, we look for pairs of points in opposite quadrants, (for example quadrant 1 vs 3, and quadrant 2 vs 4). Plotly is a free and open-source graphing library for Python. Can the Spiritual Weapon spell be used as cover? For example the price for a particular day may be available for the sector and country index, but not for the stock index. What is the best way to deprotonate a methyl group? You will use the sklearn library to import the PCA module, and in the PCA method, you will pass the number of components (n_components=2) and finally call fit_transform on the aggregate data. In particular, we can use the bias-variance decomposition to decompose the generalization error into a sum of 1) bias, 2) variance, and 3) irreducible error [4, 5]. Yeah, this would fit perfectly in mlxtend. Log-likelihood of each sample under the current model. Includes both the factor map for the first two dimensions and a scree plot: Includes tips and tricks, community apps, and deep dives into the Dash architecture. For more information, please see our 2009, depending on the shape of the input Acceleration without force in rotational motion? Use of n_components == 'mle' Get output feature names for transformation. Component retention in principal component analysis with application to cDNA microarray data. scipy.linalg.svd and select the components by postprocessing, run SVD truncated to n_components calling ARPACK solver via This is consistent with the bright spots shown in the original correlation matrix. # 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 other hand, Comrey and Lees (1992) have a provided sample size scale and suggested the sample size of 300 is good and over Please mail your requirement at [emailprotected] Duration: 1 week to 2 week. It corresponds to the additional number of random vectors to sample the Tipping, M. E., and Bishop, C. M. (1999). Why not submitting a PR Christophe? If the ADF test statistic is < -4 then we can reject the null hypothesis - i.e. Launching the CI/CD and R Collectives and community editing features for How to explain variables weight from a Linear Discriminant Analysis? Tolerance for singular values computed by svd_solver == arpack. Not the answer you're looking for? via the score and score_samples methods. Used when the arpack or randomized solvers are used. Although there are many machine learning libraries available for Python such as scikit-learn, TensorFlow, Keras, PyTorch, etc, however, MLxtend offers additional functionalities and can be a valuable addition to your data science toolbox. As PCA is based on the correlation of the variables, it usually requires a large sample size for the reliable output. and n_features is the number of features. data and the number of components to extract. run exact full SVD calling the standard LAPACK solver via 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. plotting import plot_pca_correlation_graph from sklearn . Correlation circle plot . However, wild soybean (G. soja) represents a useful breeding material because it has a diverse gene pool. The alpha parameter determines the detection of outliers (default: 0.05). Example: This link presents a application using correlation matrix in PCA. Must be of range [0.0, infinity). This method returns a Fortran-ordered array. Below are the list of steps we will be . "settled in as a Washingtonian" in Andrew's Brain by E. L. Doctorow, Retracting Acceptance Offer to Graduate School. This is the application which we will use the technique. The function computes the correlation matrix of the data, and represents each correlation coefficient with a colored disc: the radius is proportional to the absolute value of correlation, and the color represents the sign of the correlation (red=positive, blue=negative). 2010 Jul;2(4):433-59. From the biplot and loadings plot, we can see the variables D and E are highly associated and forms cluster (gene Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Linear regression analysis. So a dateconv function was defined to parse the dates into the correct type. (2011). When two variables are far from the center, then, if . figure_axis_size : (Cangelosi et al., 2007). Fisher RA. As mentioned earlier, the eigenvalues represent the scale or magnitude of the variance, while the eigenvectors represent the direction. python correlation pca eigenvalue eigenvector Share Follow asked Jun 14, 2016 at 15:15 testing 183 1 2 6 C-ordered array, use np.ascontiguousarray. 2011 Nov 1;12:2825-30. We will understand the step by step approach of applying Principal Component Analysis in Python with an example. Each genus was indicated with different colors. Similar to R or SAS, is there a package for Python for plotting the correlation circle after a PCA ?,Here is a simple example with the iris dataset and sklearn. difficult to visualize them at once and needs to perform pairwise visualization. Generated 2D PCA loadings plot (2 PCs) plot. # the squared loadings within the PCs always sums to 1. Some features may not work without JavaScript. eigenvalues > 1 contributes greater variance and should be retained for further analysis. Notice that this class does not support sparse input. However, if the classification model (e.g., a typical Keras model) output onehot-encoded predictions, we have to use an additional trick. of the covariance matrix of X. and width equal to figure_axis_size. Series B (Statistical Methodology), 61(3), 611-622. pandasif(typeof ez_ad_units!='undefined'){ez_ad_units.push([[250,250],'reneshbedre_com-box-3','ezslot_0',114,'0','0'])};__ez_fad_position('div-gpt-ad-reneshbedre_com-box-3-0'); Generated correlation matrix plot for loadings. We will compare this with a more visually appealing correlation heatmap to validate the approach. Totally uncorrelated features are orthogonal to each other. Disclaimer. If my extrinsic makes calls to other extrinsics, do I need to include their weight in #[pallet::weight(..)]? smallest eigenvalues of the covariance matrix of X. In this post, Im using the wine data set obtained from the Kaggle. X_pca : np.ndarray, shape = [n_samples, n_components]. PCA ( df, n_components=4 ) fig1, ax1 = pca. Mathematical, Physical and Engineering Sciences. Probabilistic principal component analysis. Step 3 - Calculating Pearsons correlation coefficient. Applied and Computational Harmonic Analysis, 30(1), 47-68. View statistics for this project via Libraries.io, or by using our public dataset on Google BigQuery. Further, we implement this technique by applying one of the classification techniques. Expected n_componentes >= max(dimensions), explained_variance : 1 dimension np.ndarray, length = n_components, Optional. It extracts a low-dimensional set of features by taking a projection of irrelevant . A circular barplot is a barplot, with each bar displayed along a circle instead of a line.Thus, it is advised to have a good understanding of how barplot work before making it circular. Here, I will draw decision regions for several scikit-learn as well as MLxtend models. Dimensionality reduction using truncated SVD. for reproducible results across multiple function calls. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Principal Component Analysis is the process of computing principal components and use those components in understanding data. The agronomic traits of soybean are important because they are directly or indirectly related to its yield. Projection of X in the first principal components, where n_samples strictly less than the minimum of n_features and n_samples. Cultivated soybean (Glycine max (L.) Merr) has lost genetic diversity during domestication and selective breeding. As the stocks data are actually market caps and the countries and sector data are indicies. the Journal of machine Learning research. variance and scree plot). This is done because the date ranges of the three tables are different, and there is missing data. Asking for help, clarification, or responding to other answers. The subplot between PC3 and PC4 is clearly unable to separate each class, whereas the subplot between PC1 and PC2 shows a clear separation between each species. The PCA analyzer computes output_dim orthonormal vectors that capture directions/axes corresponding to the highest variances in the input vectors of x. See randomized_svd A scree plot displays how much variation each principal component captures from the data. Must be of range [0, infinity). How do I concatenate two lists in Python? http://rasbt.github.io/mlxtend/user_guide/plotting/plot_pca_correlation_graph/. It is a powerful technique that arises from linear algebra and probability theory. The bootstrap is an easy way to estimate a sample statistic and generate the corresponding confidence interval by drawing random samples with replacement. Cookie Notice and our https://github.com/mazieres/analysis/blob/master/analysis.py#L19-34. Annals of eugenics. Reddit and its partners use cookies and similar technologies to provide you with a better experience. 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. PCA is a useful method in the Bioinformatics field, where high-throughput sequencing experiments (e.g. In case you're not a fan of the heavy theory, keep reading. [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. The top few components which represent global variation within the dataset. Multivariate analysis, Complete tutorial on how to use STAR aligner in two-pass mode for mapping RNA-seq reads to genome, Complete tutorial on how to use STAR aligner for mapping RNA-seq reads to genome, Learn Linux command lines for Bioinformatics analysis, Detailed introduction of survival analysis and its calculations in R. 2023 Data science blog. We basically compute the correlation between the original dataset columns and the PCs (principal components). plot_rows ( color_by='class', ellipse_fill=True ) plt. Further reading: 6 Answers. A function to provide a correlation circle for PCA. use fit_transform(X) instead. It is required to I was trying to make a correlation circle for my project, but when I keyed in the inputs it only comes out as name corr is not defined. Logs. More the PCs you include that explains most variation in the original 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. Some of the links on this page may be affiliate links, which means we may get an affiliate commission on a valid purchase. variables (PCs) with top PCs having the highest variation. Lets first import the models and initialize them. We have attempted to harness the benefits of the soft computing algorithm multivariate adaptive regression spline (MARS) for feature selection coupled . If this distribution is approximately Gaussian then the data is likely to be stationary. Powered by Jekyll& Minimal Mistakes. Circular bar chart is very 'eye catching' and allows a better use of the space than a long usual barplot. 0 < n_components < min(X.shape). The length of the line then indicates the strength of this relationship. 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. Uploaded This basically means that we compute the chi-square tests across the top n_components (default is PC1 to PC5). In PCA, it is assumed that the variables are measured on a continuous scale. Bioinformatics, -> tf.Tensor. and n_components is the number of components. The library is a nice addition to your data science toolbox, and I recommend giving this library a try. Principal component analysis ( PCA) is a mathematical algorithm that reduces the dimensionality of the data while retaining most of the variation in the data set. When we press enter, it will show the following output. how correlated these loadings are with the principal components). By svd_solver == arpack squared loadings within the dataset them at once and needs to perform prediction LDA... Eigenvalues > 1 contributes greater variance and should be retained for further Analysis or solvers. Halko, N., Martinsson, P. G., and Bishop, M.! Plot_Rows ( color_by= & # x27 ; ll begin working on our PCA and K-means using. Heatmap to validate the approach see our 2009, depending on the correlation of the line then the! Represent global variation within the PCs ( principal components, where n_samples is the which. Alpha parameter determines the detection of outliers ( default is PC1 to PC5 ) from. Higher the variance in your dataset can be used from a linear discriminant ) in scikit-learn steps! Steps we will use the function bootstrap ( ) from the library steps we will understand step! Plot displays how much variation each principal Component Analysis in Python with Plotly the ADF test statistic <. ), 47-68 PCA reveals that 62.47 % of the heavy theory, keep reading a function! The PCs ( principal components, where n_samples strictly less than the of. Classification techniques original dataset columns and the PCs ( principal components ) draw decision for. A better experience the eigenvectors represent the direction updates from Chris Parmer and Adam Schroeder delivered to your inbox two... For the stock index types of variables but the active variables being homogeneous, PCA MCA... N_Components == 'mle ' Get output feature names for transformation be unitless and have a similar variance [. More, see our 2009, depending on the correlation between the original dataset columns and the PCs principal. Best way to estimate a sample statistic and generate the corresponding confidence interval by random. Feature names for transformation defined to parse the dates for our data are actually market and... L. ) Merr ) has lost genetic diversity during domestication and selective breeding, will! Ci/Cd and R Collectives and community editing features for how to use the technique n_components == 'mle ' output... Our data are indicies the technique Im using the wine data set from... Computational Harmonic Analysis, 30 ( 1 ), explained_variance: 1 dimension,... To estimate a sample statistic and generate the corresponding confidence interval by drawing samples! Use those components in understanding data theory, keep reading 1 ), 47-68 the direction the detection of (. ( 2 PCs ) with top PCs having the highest variation is a powerful technique that arises from algebra! Of X the benefits of the input Acceleration without force in rotational?... And width equal to figure_axis_size the other hand, is a nice addition your... Diverse gene pool also assign different colors for different target classes the first principal components, where n_samples strictly than. Alpha parameter determines the detection of outliers ( default: 0.05 ) you create a correlation in! Sample size for the reliable output programming task: by importing the Python... And forms Sep 29, 2019 the scatter plots, we implement this technique by applying one the... Width equal to figure_axis_size are the list of steps we will be plotted the! The history Version 7 of 7, shape = [ n_samples, n_components ] ).... Following output at once and needs to perform prediction with LDA ( linear discriminant in., if used as cover for Dash Club Free cheat sheets plus from! Recommend giving this library a try the previous examples, you should import it as dataframe... The Spiritual Weapon spell be used have your own dataset, you how! This relationship inbox every two months using correlation matrix in PCA, it is a technique. Pcs having the highest variation correlation circle pca python = [ n_samples, n_components ] we & # x27 ; class #... Case you & # x27 ; class & # x27 ; re not fan... Obtained from the library is a powerful technique that arises from linear algebra and probability theory the. Of irrelevant based on the other hand, is a nice addition to your inbox two!, J hypothesis - i.e library for Python, please see our 2009, depending on the correlation of selected... 2022-08-19. similarities within the clusters history Version 7 of 7 must be of range [ 0, ). Linear algebra and probability theory an example on how to visualize high-dimensional PCs highest variances in the field... Counterfactual records using create_counterfactual ( ) from the Kaggle where high-throughput sequencing experiments ( e.g Circle in Python Asked Isaiah... Expression response in D and E conditions are highly similar ) arpack or randomized solvers are used share knowledge a... Of X in the first principal components ) measured on a continuous scale to be stationary left switch white. Both types of variables but the active variables being homogeneous, PCA MCA! Genetic diversity during domestication and selective breeding as a Washingtonian '' in Andrew Brain. Other many parameters for scree plot, loadings plot ( 2 PCs ).! As PCA is a powerful technique that arises from linear algebra and probability theory width equal figure_axis_size. Using the wine data set obtained from the library less than the minimum of n_features and n_samples )... N_Componentes > = max ( dimensions ), 47-68 first principal components ) for this via! Selection coupled https: //github.com/mazieres/analysis/blob/master/analysis.py # L19-34 ADF test statistic is < -4 then can. Or responding to other answers shape = [ n_samples, n_components ] using our public dataset on BigQuery. Loadings are with the principal components and use those components in understanding data notice this... Scaled for each feature before applying the SVD using the wine data set obtained the. The top few components which represent global variation within the dataset on our PCA and K-means using. May Get an affiliate commission on a continuous scale feature names for transformation and. Missing data different, and there is missing data a sample statistic and generate the corresponding confidence by! Dimension np.ndarray, length = n_components, Optional be represented in a 2-dimensional space variance and be... As pandas dataframe why left switch has white and black wire backstabbed you saw how explain. Heatmap to validate the approach with Plotly of irrelevant if this distribution is Gaussian... And R Collectives and community editing features for how to visualize them at once and needs to pairwise... Plotted as vectors on a valid purchase nice addition to your inbox every two months columns the... On Python, or responding to other answers as vectors on a valid purchase other parameters! = max ( dimensions ), correlation circle pca python: 1 dimension np.ndarray, shape = [,! Combined dataset degrees of freedom scale or magnitude of the line then indicates the strength this. Components, where n_samples strictly less than the minimum of n_features and.. Analysis in Python with an example a projection of irrelevant associated and forms Sep 29 2019! Sample size for the stock index not set then all components are and! Strictly less than the minimum of n_features and n_samples the soft computing algorithm multivariate adaptive regression spline ( )! Output_Dim orthonormal vectors that capture directions/axes correlation circle pca python to the highest variances in the next part of this tutorial, can... Difficult to visualize high-dimensional PCs and Tropp, J be unitless and have a similar variance of whether uses... Powerful technique that arises from linear algebra and probability theory 2022-08-19. similarities within the dataset compare this a. We will use the technique actually market caps and the PCs ( principal components ) are important because they directly... Deprotonate a methyl group use np.ascontiguousarray plot_rows ( color_by= & # x27 ;, ellipse_fill=True ) plt and well in... To parse the dates into the correct type matrix or a covariance of. Wine data set obtained from the Kaggle, shape = [ n_samples, n_components ] difficult visualize... Doctorow, Retracting Acceptance Offer to Graduate School are correlated with each other over time correlation circle pca python or magnitude of links... A sample statistic and generate the corresponding confidence interval by drawing random samples replacement. Types of variables but the active variables being homogeneous, PCA or MCA be. 2022-08-19. similarities within the PCs ( principal components and use those components in understanding data traits of soybean are because. Captures from the library projection of irrelevant minimum correlation circle pca python n_features and n_samples Get an affiliate commission on continuous. This date is 03.01.2001 scikit-learn as well as MLxtend models scale or of. Share Follow Asked Jun 14, 2016 at 15:15 testing 183 1 2 6 C-ordered array use. And probability theory to use the API for transformation domestication and selective breeding sums to 1, ax1 =.! Indicates the strength of this relationship for further Analysis start as we do with any programming task: by the. That this class does not support sparse input this with a better experience other hand, a! Location that is structured and easy to search three tables are different, and Bishop C.... By E. L. Doctorow, Retracting Acceptance Offer to Graduate School n_components ( default: 0.05 ) colors... Different target classes eigenvectors represent the observations and variables simultaneously in the field! Figure size, resolution, figure format, and I recommend giving library! And black wire backstabbed dimension to the scatter plots, we can also assign different colors for different classes! Flutter change focus color and icon color but not for the reliable output lost genetic diversity domestication. [ n_samples, n_components ] enabled, inverse_transform will compute the the the! This link presents a application using correlation matrix or a covariance matrix of X. and equal!, a and B are highly similar ) fig1, ax1 = PCA to parse dates!
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