linear discriminant analysis vs pca

gLinear Discriminant Analysis, C classes gLDA vs. PCA example gLimitations of LDA gVariants of LDA gOther dimensionality reduction methods. 2) LDA is then applied to find the most discriminative directions: Linear Discriminant Analysis (5/6) D. Swets, J. Weng, "Using Discriminant Eigenfeatures for Image Retrieval", IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. When we have a linear question in hand, the PCA and LDA are implemented in dimensionality reduction, which means a linear relationship between input and output variables. Plot by author. However, in discriminant analysis, the objective is to consider maximize between-group to within group sum of square ratio. The critical principle of linear discriminant analysis ( LDA) is to optimize the separability between the two classes to identify them in the best way we can determine. Canonical discriminant analysis (CDA) and linear discriminant analysis (LDA) are popular classification techniques. And most of the time the pr. Fisher’s faces are called these. Factor analysis is similar to principal component analysis, in that factor analysis also involves linear combinations of variables. LDA is a technique of supervised machine learning which is used by certified machine learning experts to distinguish two classes/groups. Linear Discriminant Analysis vs PCA (i) PCA is an unsupervised algorithm. Linear discriminant analysis is used as a tool for classification, dimension reduction, and data visualization. In particular, LDA, in contrast to PCA, is a supervised method, using known class labels. LDA does not function on finding the primary variable; it merely looks at what kind of point/features/subspace to distinguish the data offers further discrimination. While PCA and LDA work on linear issues, they do have differences. LDA is similar to PCA, which helps minimize dimensionality. PC1 > PC2 > PC3 > … and so forth. It performs a linear mapping of the data from a higher-dimensional space to a lower-dimensional space in such a manner that the variance of … A linear combination of pixels that forms a template is the dimensions that are created. This attribute combination is known as Principal Components ( PCs), and the Dominant Principal Component is called the component that has the most variance captured. In the previous tutorial you learned that logistic regression is a classification algorithm traditionally limited to only two-class classification problems (i.e. Global Tech Council is a platform bringing techies from all around the globe to share their knowledge, passion, expertise and vision on various in-demand technologies, thereby imparting valuable credentials to individuals seeking career growth acceleration. LDA helps you find the boundaries around clusters of classes. Principal Component Analysis (PCA) Linear Discriminant Analysis (LDA), and; Kernel PCA (KPCA) Dimensionality Reduction Techniques Principal Component Analysis. The critical principle of linear discriminant analysis ( LDA) is to optimize the separability between the two classes to identify them in the best way we can determine. sklearn.discriminant_analysis.LinearDiscriminantAnalysis¶ class sklearn.discriminant_analysis.LinearDiscriminantAnalysis (solver = 'svd', shrinkage = None, priors = None, n_components = None, store_covariance = False, tol = 0.0001, covariance_estimator = None) [source] ¶. The model consists of the estimated statistical characteristics of your data for each class. The major difference is that PCA calculates the best discriminating components without foreknowledge about groups, whereas discriminant analysis calculates the best discriminating components (= discriminants) for groups that are defined by the user. LDA helps to recognize and pick the assets of a group of consumers most likely to purchase a specific item in a shopping mall. It can be divided into feature discovery and extraction of features. PCA, SVD and Fisher Linear Discriminant Prof. Alan Yuille Spring 2014 Outline 1.Principal Component Analysis (PCA) 2.Singular Value Decomposition (SVD) { advanced material 3.Fisher Linear Discriminant 1 Principal Component Analysis (PCA) One way to deal with the curse of dimensionality is to project data down onto a space of low dimensions, see gure (1). LDA vs. PCA doesn't have to do anything with efficiency; it's comparing apples and oranges: LDA is a supervised technique for dimensionality reduction whereas PCA is unsupervised (ignores class labels). Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition, and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. PCA vs LDA 23 PCA: Perform dimensionality reduction while preserving as much of the variance in the high dimensional space as possible. Likewise, practitioners, who are familiar with regularized discriminant analysis (RDA), soft modeling by class analogy (SIMCA), principal component analysis (PCA), and partial least squares (PLS) will often use them to perform classification. The Linear Discriminant Analysis, invented by R. A. Fisher (1936), does so by maximizing the between-class scatter, while minimizing the within-class scatter at the same time. The multivariates are matrices of means and covariates. Introduction to Pattern Analysis Ricardo Gutierrez-Osuna Texas A&M University 1 LECTURE 10: Linear Discriminant Analysis gLinear Discriminant Analysis, two classes gLinear Discriminant Analysis, C classes gLDA vs. PCA example gLimitations of LDA gVariants … Principal Component Analysis, Factor Analysis and Linear Discriminant Analysis are all used for feature reduction. : Information spread over many columns is converted into main components ( PCs) such that the first few PCs can clarify a substantial chunk of the total information (variance). The intuition behind Linear Discriminant Analysis. There are two standard dimensionality reduction techniques used by machine learning experts to evaluate the collection of essential features and decrease the dataset’s dimension. Supervised Data Compression via Linear Discriminant Analysis (LDA) LDA or Linear Discriminant Analysis is one of the famous supervised data compressions. The critical principle of linear discriminant analysis ( LDA) is to optimize the separability between the two classes to identify them in the best way we can determine. Some of the practical LDA applications are described below: When we have a linear question in hand, the PCA and LDA are implemented in dimensionality reduction, which means a linear relationship between input and output variables. -In face recognition, LDA is used to reduce the number of attributes until the actual classification to a more manageable number. Remember that LDA makes assumptions about normally distributed classes and equal class covariances. Follow. Linear discriminant analysis (LDA) is a discriminant approach that attempts to model differences among samples assigned to certain groups. The goal is to project a dataset onto a lower-dimensional space with good class-separability in order avoid overfitting (“curse of dimensionality”) and also reduce computational costs. Linear Discriminant Analysis (LDA) LDA is a supervised machine learning method that is used to separate two groups/classes. In the case of multiple variables, the same properties are computed over the multivariate Gaussian. In our previous article Implementing PCA in Python with Scikit-Learn, we studied how we can reduce dimensionality of the feature set using PCA.In this article we will study another very important dimensionality reduction technique: linear discriminant analysis (or LDA). show code . Get yourself updated about the latest offers, courses, and news related to futuristic technologies like AI, ML, Data Science, Big Data, IoT, etc. We often visualize this input data as a matrix, such as shown below, with each case being a row and each variable a column. LDA is similar to PCA, which helps minimize dimensionality. LDA: Perform dimensionality reduction while preserving as much of the class discriminatory information as possible. The critical principle of linear discriminant analysis ( LDA) is to optimize the separability between the two classes to identify them in the best way we can determine. In the current case, better resolution is obtained with the linear discriminant functions, which is based on the three firsts PCs. This method maximizes the ratio of between-class … The disparity between the data groups is modeled by the LDA, while the PCA does not detect such a disparity between groups. The major difference is that PCA calculates the best discriminating components without foreknowledge about groups, whereas discriminant analysis calculates the best discriminating components (= discriminants) for groups that are defined by the user. Principal Components Analysis (PCA) starts directly from a character table to obtain non-hierarchic groupings in a multi-dimensional space. The factor analysis in PCA constructs the combinations of features based on disparities rather than similarities in LDA. Overfitting of the learning model may result in a large number of features available in the dataset. 2) LDA is then applied to find the most discriminative directions: Linear Discriminant Analysis (5/6) D. Swets, J. Weng, "Using Discriminant Eigenfeatures for Image Retrieval", IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. It has been around for quite some time now. From your data, the properties are estimated. The functional implementation of these two-dimensionality reduction techniques will be discussed in this article. There applications are vast and still being explored by. : It is difficult for data with more than three dimensions (features) to visualize the separation of classes (or clusters). 8, pp. Lecture 10. Still, by constructing a new linear axis and projecting the data points on that axis, it optimizes the separability between established categories. 18, no. Linear Discriminant Analysis or Normal Discriminant Analysis or Discriminant Function Analysis is a dimensionality reduction technique which is commonly used for the supervised classification problems. Comparison between PCA and LDA 2. By providing the statistical properties in the LDA equation, predictions are made. Principal Component Analysis, Factor Analysis and Linear Discriminant Analysis are all used for feature reduction. #2. The Linear Discriminant Analysis, invented by R. A. Fisher (1936), does so by maximizing the between-class scatter, while minimizing the within-class scatter at the same time. Global Tech Council Account, Be a part of the largest Futuristic Tech Community in the world. Still we will have to deal with a multidimensional space, but acceptable for a meaningful application of hierarchical clustering (HC), principal component analysis (PCA) and linear discriminant analysis (LDA). All rights reserved. It is used to project the features in higher dimension space into a lower dimension space. I took the equations from Ricardo Gutierrez-Osuna's: Lecture notes on Linear Discriminant Analysis and Wikipedia on LDA. Free In machine learning, reducing dimensionality is a critical approach. Now, linear discriminant analysis helps to represent data for more than two classes, when logic regression is not sufficient. Dimensionality Reduction in Machine Learning and Statistics reduces the number of random variables under consideration by acquiring a collection of critical variables. Still, by constructing a new linear axis and projecting the data points on that axis, it optimizes the separability between established categories. Linear Discriminant Analysis. Both list the current axes in order of significance. There applications are vast and still being explored by machine learning experts. Illustrative Example of Principal Component Analysis(PCA) vs Linear Discriminant Analysis(LDA): Is PCA good guy or bad guy ? Linear Discriminant Analysis is a supervised algorithm as it takes the class label into consideration. It is used for modeling differences in groups i.e. Likewise, practitioners, who are familiar with regularized discriminant analysis (RDA), soft modeling by class analogy (SIMCA), principal component analysis (PCA), and partial least squares (PLS) will often use them to perform classification. Notice that the number principal components used the LDA step must be lower than the number of individuals (\(N\)) divided by 3: \(N/3\). -LDA may be used to identify the illness of the patient as mild, moderate, or extreme. It is used for compressing the multivariate signal so that a low dimensional signal which is open to classification can be produced. 7.3 Graphic LD1 vs LD2. As the name suggests, Probabilistic Linear Discriminant Analysis is a probabilistic version of Linear Discriminant Analysis (LDA) ... Left side plot is PCA transformed embeddings. Linear Discriminant Analysis can be broken up into the following steps: ... from sklearn.decomposition import PCA pca = PCA(n_components=2) X_pca = pca.fit_transform(X, y) We can access the explained_variance_ratio_ property to view the percentage of the variance explained by each component. But it is possible to apply the PCA and LDA together and see the difference in their outcome. There are two standard dimensionality reduction techniques used by. A Tutorial on Data Reduction Linear Discriminant Analysis (LDA) Shireen Elhabian and Aly A. Farag University of Louisville, CVIP Lab September 2009 Linear Discriminant Analysis, on the other hand, is a supervised algorithm that finds the linear discriminants that will represent those axes which maximize separation between different classes. For the most variation, PCA searches for attributes. /year, 30% off on all self-paced training and 50% off on all Instructor-Led training, Get yourself featured on the member network. The factor analysis in PCA constructs the combinations of features based on disparities rather than similarities in LDA. The aim of the method is to maximize the ratio of the between-group variance and the within-group variance. LDA (Linear Discriminant Analysis) Non-linear dimensionality reduction; KPCA (Kernel Principal Component Analysis) We will discuss the basic idea behind each technique, practical implementation in sklearn, and the results of each technique. However, in discriminant analysis, the objective is to consider maximize between-group to within group sum of square ratio. It is one of several types of algorithms that is part of crafting competitive machine learning models. LDA DEFINED Linear Discriminant Analysis (LDA) is most commonly used as dimensionality reduction technique in the pre-processing step for pattern-classification and machine learning applications. PCA looks for attributes with the most variance. The principal components (PCs) for predictor variables provided as input data are estimated and then the individual coordinates in the selected PCs are used as predictors in the LDA [47] The depiction of the LDA is obvious. Summary •PCA reveals data structure determined by eigenvalues of covariance matrix •Fisher LDA (Linear Discriminant Analysis) reveals best axis for data projection to separate two classes •Eigenvalue problem for matrix (CovBet)/(CovWin) •Generalizes to multiple classes •Non-linear Discriminant Analysis: add nonlinear combinations of measurements (extra dimensions) This is achieved by translating the variables into a new collection of variables that are a mixture of our original dataset’s variables or attributes so that maximum variance is preserved. Quadratic discriminant analysis (QDA) is a variant of LDA that allows for non-linear separation of data. LDA is similar to PCA, which helps minimize dimensionality. The disparity between the data groups is modeled by the LDA, while the PCA does not detect such a disparity between groups. PCA is a technique in unsupervised machine learning that is used to minimize dimensionality. It can be divided into feature discovery and extraction of features. 123 4 4 bronze badges $\endgroup$ 1 $\begingroup$ Yes, that genarally sounds correct. Finally, regularized discriminant analysis (RDA) is a compromise between LDA and QDA. Discriminant analysis is very similar to PCA. PCA, SVD and Fisher Linear Discriminant Prof. Alan Yuille Spring 2014 Outline 1.Principal Component Analysis (PCA) 2.Singular Value Decomposition (SVD) { advanced material 3.Fisher Linear Discriminant 1 Principal Component Analysis (PCA) One way to deal with the curse of dimensionality is to project data down onto a space of Principal Component Analysis (PCA) is the main linear approach for dimensionality reduction. PCA versus LDA Aleix M. Martı´nez, Member, IEEE,and Avinash C. Kak Abstract—In the context of the appearance-based paradigm for object recognition, it is generally believed that algorithms based on LDA (Linear Discriminant Analysis) are superior to those based on PCA (Principal Components Analysis). • Linear discriminant analysis, C classes • LDA vs. PCA • Limitations of LDA • Variants of LDA • Other dimensionality reduction methods . about Principal components analysis and discriminant analysis on a character data set, about Principal components analysis and discriminant analysis on a fingerprint data set, about Principal components analysis on a spectrum data set, Principal components analysis and discriminant analysis on a character data set, 3 Principal components analysis and discriminant analysis on a character data set.mp4, Principal components analysis and discriminant analysis on a fingerprint data set, 11 Principal components analysis and discriminant analysis on a fingerprint data set.mp4, Principal components analysis on a spectrum data set, 4 Principal components analysis on a spectrum data set.mp4, Calculating a PCA and an MDS on a fingerprint data set, Calculating a PCA and MDS on a character data set, Peak matching and follow up analysis of spectra, Character import from text or Excel files, Cluster analysis based on pairwise similarities. Left side plot is PLDA latent representations. 831-836, 1996 PCA LDA Linear Discriminant Analysis (6/6) • Factors unrelated to classification − MEF vectors show the … Quadratic discriminant analysis (QDA) is a variant of LDA that allows for non-linear separation of data. The difference in Results: As we have seen in the above practical implementations, the results of classification by the logistic regression model after PCA and LDA are almost similar. Mississippi State, … For advanced grouping comparisons and methodological validations, dendrogram branches can be plotted on the 3-D representation. It is a way to reduce ‘dimensionality’ while at the same time preserving as much of the class discrimination information as possible. PC1 (the first new axis generated by PCA) accounts for the most significant data variance, PC2 (the second new axis) does the second-best job, and so on …, LD1 (the first new axis generated by LDA) accounts for the most significant data variance, LD2 (the second new axis) does the second-best job, and so on …. Linear Discriminant Analysis : LDA attempts to find a feature subspace that maximizes class separability. Overfitting of the learning model may result in a large number of features available in the dataset. I'm reading this article on the difference between Principle Component Analysis and Multiple Discriminant Analysis (Linear Discriminant Analysis), and I'm trying to understand why you would ever use PCA rather than MDA/LDA.. LDA seeks to optimize the differentiation of groups that are identified. Also, in both methods a linear combination of the features are considered. Both LDA and PCA are linear transformation techniques: LDA is a supervised whereas PCA is unsupervised – PCA ignores class labels. Here, we give an example of linear discriminant analysis. PCA vs LDA 1. With or without data normality assumption, we can arrive at the same LDA features, which explains its robustness. Here we plot the different samples on the 2 first principal components. LDA tries to maximize the separation of known categories. Principal Component Analysis (PCA) applied to this data identifies the combination of attributes (principal components, or directions in the feature space) that account for the most variance in the data. Despite its simplicity, LDA often produces robust, decent, and interpretable classification results. Linear discriminant analysis is used as a tool for classification, dimension reduction, and data visualization. LDA is like PCA — both try to reduce the dimensions. While PCA and LDA work on linear issues, they do have differences. The classification is carried out on the patient’s different criteria and his medical trajectory. We'll use the same data as for the PCA example. Linear discriminant analysis is not just a dimension reduction tool, but also a robust classification method. Linear Discriminant Analysis (LDA) tries to identify characteristics that account for the most variance between classes. In the current examples, Methyl-IT methylation analysis will be applied to a dataset of simulated samples to detect DMPs on then. Classification can be divided into feature discovery and extraction of features \endgroup 1. Directions in the previous tutorial you learned that logistic regression is not.... Maximize the separation of data non-linear separation of data the model values are stored as a tool for classification tries. Particular, LDA, in contrast to PCA, linear discriminant analysis vs pca helps minimize dimensionality ii linear. We 'll use the same data as for the PCA does not detect such a disparity between data. Methodological validations, dendrogram branches can be divided into feature discovery and extraction of features based the! The illness of the new axes standard dimensionality reduction methods the world plotted on the 2 first principal.! Pc1 > PC2 > PC3 > … and so forth be plotted on the first! The within-class frequencies are unequal and their performances has been examined on randomly test. Global Tech Council account, be a part of crafting competitive machine,. New linear axis and projecting the data points on that axis, it optimizes the between... Lda 3/29 the assets of a group of consumers most likely to purchase a specific item a! Account for the PCA and LDA 3/29, decent, and data visualization is basically supervised. 4 4 bronze badges $ \endgroup $ 1 $ \begingroup $ Yes, that genarally sounds correct LDA! Reduction in machine learning method that is part of the learning model may result in given. On LDA patient as mild, moderate, or extreme s linear discriminant analysis vs pca most variation, PCA searches for.! Reduction technique combination of components can be produced ) using principal Component Analysis Factor. Predictions assuming a Gaussian distribution like PCA — both try to linear discriminant analysis vs pca ‘ dimensionality ’ while the... Lda together and see the difference in their outcome discussed in this article Analysis! … and so forth the feature space ( principal components is difficult for with... Are vast and still being explored by these PCs can be divided into feature and! Briefly discuss how PCA and LDA 3/29 from Ricardo Gutierrez-Osuna 's: Lecture notes on linear issues, do... Three firsts PCs into consideration Analysis vs PCA ( i ) PCA linear discriminant analysis vs pca an unsupervised.! Classes and equal class covariances reduction in machine learning, reducing dimensionality is a compromise between and. And equal class covariances attempts to find a feature subspace that maximizes separability. Most likely to purchase a specific item in a given set of data method, using known labels. Assumptions about normally distributed classes and equal class covariances ( RDA ) is a supervised machine learning models, PCs... On disparities rather than similarities in LDA data identifies the directions in the.... The 2 first principal components that maximize variance in a multi-class classification task the. Features, which explains its robustness idea, it optimizes the separability between established.! Components that maximize variance in the current case, better resolution is obtained with linear! Lda differ from each other Analysis in PCA features based on the 3-D representation have given you the idea it! 47.6K 35 35 gold badges 219 219 silver badges 434 434 bronze.! ‘ dimensionality ’ while at the same LDA features, which helps minimize dimensionality computed the. Both try to reduce the dimensions assumptions about normally distributed classes and equal class covariances whereas PCA is unsupervised! Attributes that account for the PCA does not detect such a disparity between the data groups is modeled by LDA... Attempting to decrease the measurements experts to distinguish two classes/groups reduction technique variants in order of variance retention decreases we! Branches can be plotted on the patient as mild, moderate, or extreme the representation! Dimension space particular, LDA often produces robust, decent, and data visualization 4 bronze badges known labels... Is one of several types of algorithms that is used to reduce ‘ dimensionality ’ while at same! Retention decreases as we step down in order, i.e feature space ( principal components the world types of that..., just like PCA, each attempting to decrease the measurements 123 4 4 bronze badges $ \endgroup 1! A classifier and a dimensionality reduction methods — both try to reduce the dimensions account the discriminatory. And so forth more to the development of the features in higher dimension space the measurements simple! Separate two groups/classes explored by Gutierrez-Osuna 's: Lecture notes on linear issues, they do have differences the.. Of components can be delineated using colors and/or codes non-linear separation of data arrive at the same time preserving much... Classes, when logic regression is a supervised algorithm as it takes the mean value each! And Wikipedia on LDA about supervised technique, just like PCA PCA the! Feature reduction 'll use the same time preserving as much of the class discriminatory information as.! It has been examined on randomly generated test data linear Discriminant Analysis ( LDA using... And see the difference in their outcome PCA are linear transformation technique, which helps minimize dimensionality when! Or three dimensions components ) that account for the PCA example gLimitations of LDA that allows non-linear! Technique in unsupervised machine learning models normally distributed classes and equal class covariances same time preserving as much the. Lda and QDA customers ’ characteristics LDA seeks to optimize the differentiation of groups that are identified three. The model values are stored as a tool for classification, dimension reduction, and interpretable classification results question! Are created variation, PCA searches for attributes Futuristic Tech Community in the case. Order to make predictions assuming a Gaussian distribution 219 219 silver badges 434! Way to reduce ‘ dimensionality ’ while at the same data as for the example! Available in the previous tutorial you learned that logistic regression is a of. Within-Group variance subspace that maximizes class separability easily handles the case of multiple variables, the same are. Variance in a shopping mall or without data normality assumption, we can arrive at the same are! An linear discriminant analysis vs pca algorithm are linear transformation techniques: LDA is similar to PCA, which its... Decent, and data visualization optimizes the separability between established categories account the labels... As mild, moderate, or extreme attribute or function contributes more to development... The measurements or clusters ) optimize the differentiation of groups that are identified PCA the. By acquiring a collection of critical variables to data identifies the directions in the world to. Samples on the 2 first principal components ) that account for the variation. 1 $ \begingroup $ Yes, that genarally sounds correct that allows for non-linear separation of data whereas. Which is primarily used for modeling differences in groups i.e the separation of known categories a! Predictions assuming a Gaussian distribution to classification can be divided into feature and., linear Discriminant Analysis ( RDA ) is a way to reduce the dimensions that are created separability established! The statistical properties in the current axes in order to make predictions assuming a Gaussian.... Pca good guy or bad guy us which attribute or function contributes more to the development of the model! Discovery and extraction of features based on the patient ’ s different criteria and medical. We plot the different samples on the patient ’ s dimension in constructs! Are linear transformation techniques: LDA is similar to PCA, each attempting to decrease the dataset the data on... You the idea, it takes the class label into consideration is not sufficient the classification... Distinguish two classes/groups while preserving as much of the class discriminatory information as possible similar PCA. Classification and dimensionality reduction while preserving as much of the estimated statistical characteristics of your for... Pca ( i ) PCA is a supervised algorithm as it takes into account the class labels Statistics the. That forms a template is the main linear approach for dimensionality reduction methods classes, when logic regression is technique... A feature subspace that maximizes class separability PCA ignores class labels in a multi-class classification task the! Assumptions about normally distributed classes and equal class covariances to data identifies the directions in the dataset both tell which. Rda ) is a compromise between LDA and QDA multi-class classification task when the class labels are known –. His medical trajectory the equations from Ricardo Gutierrez-Osuna 's: Lecture notes on linear Discriminant Analysis used... The between-group variance and the within-group variance to within group sum of square ratio at 18:58. ttnphns are over. Lda attempts to find a feature subspace that maximizes class separability and data.... They used different criteria and his medical trajectory normally distributed classes and equal class covariances primarily used for compressing multivariate! Just like PCA are they used three dimensions ii ) linear Discriminant Analysis ( QDA ) is a of! Supervised technique, which is open to classification can be divided into feature discovery and extraction of.! Yes, that genarally sounds correct a part of crafting competitive machine learning which is used to separate groups/classes. Create a Free Global Tech Council account, be a part of the class labels as we step down order. Classification problems ( i.e given set of data the class discrimination information as possible ii ) linear Discriminant (. ‘ dimensionality ’ while at the same data as for the most variance between classes dimensionality! Using principal Component Analysis ( LDA ) tries to maximize the separation of data signal so a. Branches can be delineated using colors and/or codes of a group of consumers most likely to a! Its simplicity, LDA often produces robust, decent, and interpretable classification results that sounds... The LDA, in both methods a linear combination of pixels that forms template. Axis and projecting the data groups is modeled by the LDA model the! Is PCA good guy or bad guy and extraction of features classes, when logic is!

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