Preprocessing Methods and Pipelines of Data Mining: An Overview

SEMINAR D A T A MINING, JUNE 2019 1 Preprocessing Methods and Pipelines of Data Mining: An Ov ervie w Li Canchen Department of Informatics T echnical Uni versity of Munich Canchen.Li@in.tum.de Abstract —Data mining is about obtaining new knowledge from existing datasets. Howev er , the data in the existing datasets can be scatter ed, noisy , and e ven incomplete. Although lots of effort is spent on developing or fine-tuning data mining models to make them more robust to the noise of the input data, their qualities still strongly depend on the quality of it. The article starts with an over view of the data mining pipeline, wher e the pr ocedures in a data mining task are briefly introduced. Then an overview of the data prepr ocessing techniques which are categorized as the data cleaning, data transformation and data prepr ocessing is given. Detailed prepr ocessing methods, as well as their influenced on the data mining models, are covered in this article. Index T erms —Data Mining, Data Prepr ocessing, Data Mining Pipeline I . I N T RO D U C T I O N D A T A mining is a knowledge obtaining process: it gets data from various data sources and finally transforms the data into kno wledge, thus provides insight to its application field. Data mining pipeline is a typical example of the end- to-end data mining system: they are an integration of all data mining procedures and deli ver the knowledge directly from data source to human. The purpose of data preprocessing is making the data easier for data mining models to tackle. The quality of data can have a significant influence on data mining models. It is considered that the data and features have already set the upper bound of the knowledge that can be obtained, and the data mining models are just about approximating the upper bound. V arious preprocessing techniques are in vented to make the data meet the input requirements of the model, improve the relev ance of the prediction target, and make the optimization step of the model easier . It is common that raw data obtained from the natural world is badly shaped. The problems include the appearance of missing v alues (e.g., a patient did not go through all the tests), duplications (e.g., annual income and monthly income), outlier v alues (e.g., age is -1) as well as contradictions (e.g., gender is male and is pregnant) in the dataset. Although the existing preprocessing techniques would not guarantee to solve all these problems, they could at least correct some of them and improv e the performance of the models. The data type and distribution of data are usually trans- formed before being sent to data mining models. The purpose of data transformation includes making the data meets the input requirement of the models, removing the noise of data, and making the distribution of data more suitable for applying optimization algorithms in the model training step. The input for data mining models can be huge: they may hav e too many dimensions or of massi ve amount, which would make it difficult for the data mining model to train or cause troubles while transferring and storing the data. Data reduction techniques can reduce the problem by applying reduction on dimensions (known as dimensional reduction) or amounts of data (known as instance selection and sampling). T o implement preprocessing to data, Python and R are among the most popular tools. With bulks of packages such as scikit-learn [1] and PreProcess [2], most of the preprocessing algorithms cov ered in this paper can be implemented ev en without consideration of its details. In the following section, the data mining pipeline and the primary procedures in the data mining pipeline will be introduced. From Section 2 on, we will focus on the steps in the data preprocessing work: Section 3 will introduce the techniques used in data cleaning, while Section 4 will cov er the data transformation techniques. In the last section, data reduction techniques will be discussed. I I . D A TA M I N I N G P I P E L I N E The data mining pipeline is an integration of all procedures in a data mining task. While most of the data already e xists in a data base, a data warehouse, or other types of data source [3], various steps should be taken in order to make them easier for a human to understand. An illustration of the data mining pipeline is gi ven as in Fig. 1. Generally speaking, the key procedures include obtaining , scrubbing , e xploring , modelling , interpr eting . These procedures are known as ”OSEMN” 1 . Howe v er , note that the pipeline is not a linear process in the real world, but a successi ve and long-lasting task. Methods in scrubbing and modeling procedures ha ve to be tested and refined, the obtaining procedure may hav e to be adapted for different kinds of data sources, and the visualization and interpretation of the data may hav e to be adjusted for their audience, thus meet the audience’ s demand. In the rest of this section, details of these procedures will be discussed. A. Obtaining Obtaining the data is the most fundamental step in data mining since it is the data itself that decides what knowledge 1 http://www .dataists.com/2010/09/a-taxonomy-of-data-science/ SEMINAR D A T A MINING, JUNE 2019 2 Fig. 1. An illustration of data mining pipeline. it may contain. Data base and data w arehouse are among the primary sources of data, where the structured data can be fetched with query languages, usually SQL. The data warehouse is specially designed for organizing, understand, and making use of the data [3]: they are usually separated system from the operational database, ha ving time-variant structure as well as structures that makes the subsequent analysis work easy , and most importantly , non v olatile. The obtained data can be archived as files and directly used for the subsequent procedures. They may also be reformatted and stored in a data base or a data warehouse, prepared for the data mining tasks in the future. In the past, as well as in most common cases no w , we regard the data obtaining step as the process for obtaining a dataset, regardless of how we obtained them. Howe v er , no wadays, new data is generating at an extreme speed: there are tons of data being created ev ery second of ev ery day . Some services, such as the public opinion monitoring and the recommendation system, do need the newly generated data: they have strong demand for being on time. In these circumstances, the concept of ”stream” is comparativ ely more important than a dataset. A stream is a real-time representation of data. Under this concept, models and algorithms that can run online are de veloped [4]. For the stream mining tasks, the goal of data obtaining is no longer obtaining a dataset, but a real-time input source. B. Scrubbing Scrubbing is about the cleaning and preprocessing of the data, aiming to make the data have a unified format and easy to be modeled. As for the detailed concepts and techniques in data scrubbing, the readers could refer to the follo wing sections of this paper, since most of them will be cov ered in the ov erview of data preprocessing. C. Exploring Before modeling the data, people may want to get to know the underlying distribution of the data, the correlation between variables, and their correlation with the labels. Assumptions can be made in this step. For instance, people may assume smoking is highly correlated with lung cancer . These assump- tions are important because they would provide indications to other procedures in a data mining task, including helping to choose a suitable model, and helping to justify your work in the interpreting of data. T ools for exploring the data and verifying the assumptions are usually statistical analysis and data visualization. The statistical analysis giv es us theoretical probabilities, kno wn as significance lev el, of our assumption being incorrect, while data visualization tools, such as ggplot [5] and D3 [6], giv e us the impressions about the distribution of the data, help people to v erify their assumption conceptually . Also, new patterns that are ignored in the assumption step might be found in the visualization step. D. Modeling W ith underlying patterns existed in the data source, model- ing makes it possible to represent the pattern explicitly with the data mining models. For a data mining task, modeling would usually split the data into the training set and test set thus could score the accuracy of the model on a relativ ely ”new” dataset. If the model contains hyperparameters, such as the parameter k in a K-Nearest Neighbor (KNN) model, a cross v alidation set will be created for obtaining the best set of the hyperparameter . For most of the data mining models, loss functions are defined. Generally , a loss function will have lower v alue if the model performs well. Besides, it usually has special features such as con ve xity , which makes the gradient-based optimiz- ing algorithm performs better . W ith trainable parameters, a model’ s training step is about adjusting its parameter so that it gains lower loss on its training data. The specific definition of loss function depends on the model itself and the task. Mean squared error ( P n i =1 ( ˆ y i − y 2 i ) for regression task and cross entropy ( − P n i =1 [ y i log ˆ y i + (1 − y i ) log(1 − ˆ y i )] ) for classification task are frequently accepted loss functions. There are too many kinds of data mining models existed; their tasks include clustering, classification, and regression. The complexity of the models also v aries: simple models such as linear regression only have a few parameters, a small amount of data will make the training step conv erge, while complex models such as AlexNet hav e millions of parameters [7], and their training also require huge dataset. Howe v er , complex does not mean better: the model should be decided according to the predicting target of the task, the dataset size, the data type, etc. Sometimes, it is necessary to run different models over one dataset and find the most suitable data mining model. E. Interpr eting While pre vious steps are generally pure science, the inter- preting step is more humanistic. Knowledge can be extracted from the input data, but it takes extra effort to con vince people to accept this knowledge. Although complicated statistics and models make the work looks more professional, for laymen, graphs, tables and well explained accuracy make it easier to understand and accept. Besides, social skills such as story telling and emotion quotient are also important: this procedure is about the human, not the data. SEMINAR D A T A MINING, JUNE 2019 3 I I I . D A TA C L E A N I N G The data obtained from the natural world is usually badly shaped. Some of the problems, such as outlier , may affect the data mining model and produce a biased result. For instance, the outlier may affect the K-Means clustering algorithm by substantially distort the distribution of data [8]. Other prob- lems, if not handled, will make it impossible for the data to be analyzed by models, such as the Not a Number (nan) values in a data vector . Data cleaning techniques, including missing value handling and outlier detection, were issued to tackle the problem. They make the gathered data suitable as the input of the model. A. Missing V alues Handling Missing values is a typical kind of data incompleteness of dataset. Most of the data mining models would not tolerate the missing values of its input data: these values can not be used for comparison, not av ailable for cate gorizing, and can not be operated with arithmetic algorithms. Thus, it is necessary to handle the missing v alues before pushing the dataset to data mining models. The easiest way to deal with missing value is to drop the entire sample. This method is effecti ve if the proportion of missing value in a dataset is not significant, howe v er , if the number of missing values is not suitable for ignoring, or the percentage of missing value for each attribute is dif ferent [3], dropping the samples with missing v alue would reduce the amount of dataset dramatically , the information contained in the dropped samples is not made use of. Another way to deal with missing values is by filling them, and there are varies methods for finding the suitable value to fill the missing value, some of them are listed as follows. 1) Use special value to repr esent missing: Sometimes the missing value itself has some meaning. F or instance, in a patient’ s medical report, the missing value for uric acid means the patient did not go through the renal function test. Thus, using a certain value such as -1 makes sense, for they can be operated like normal v alues while having special meaning in the dataset. 2) Use attrib ute statistics to fill: Statistics such as mean, median, or mode can be obtained from non-missing v alues in the missing value’ s corresponding attribute. It is said that for a skewed dataset, the median would be a better choice [3]. Howe ver , this technique does not take the sample’ s other non-missing attributes into account. 3) Pr edicting the value with known attributes: If we as- sume, there exists a correlation between attrib utes, filling the missing value can be modeled as a prediction problem: predicting the value with the non-missing attrib utes with other samples as training data. The predicting methods includes regression algorithms, decision trees [3], and K-Means [9]. 4) Assigning all possible values: For categorical attributes, giv en an example E with m possible values for its miss- ing value, then E can be replaced with m ne w examples E 1 , E 2 , . . . , E m . This missing v alue filling technique assumes the missing attribute does not matter for the example. Thus the value can be anyone in its domain [10]. Comparison of dif ferent missing v alue filling techniques is done in [11]. In the work, different missing value filling techniques are tested on ten datasets for running simple and extended classification methods. The conclusion sho ws C4.5 decision tree method performs the best, ignoring the samples with missing v alues and assigning all possible values also performed well, and filling the values with mode perform the worst. Ho wev er , the performance of missing value filling techniques may differ because of the feature of the dataset. As a result, most of the techniques are worth trying for a data mining task. B. Outlier Detection Outlier refers to the data sample that has a massiv e distance to most of the other samples. Although the rare case does not necessarily mean wrong (e.g., age = 150), most outliers are caused by measurement error or wrong recording, thus ignor- ing a rarely appearing case would not harm a lot. Although some of the models are robust against outliers, outlier detection is still recommended in data preprocessing work. Statistics-based outlier detection algorithms are among the most commonly used algorithms, which assume an underlying distribution of the data [12] and regard the data e xamples which corresponding probability density lo wer than a certain threshold as the outliers. As the underlying distribution is unknown for most cases, the normal distribution is a good substitute, and its parameter could be estimated by the mean value and standard de viation of the data. The Mahalanobis distance [12], as in (1), is a scale-irrelev ant distance between two data samples. The outlier can be decided by comparing the Mahalanobis distance between each sample and the mean value of all samples. Box-plot, as another kind of statistics- based outlier detection technique, can gi ve the graphical rep- resentation of outlier by plotting the lower quartile and upper quartile along with the median [13]. D M ( x, y ) = q ( x − y ) T Σ − 1 ( x − y ) (1) W ithout making any assumption of the distribution of the data, the distance-based outlier detection algorithm can detect the outlier by analyzing the distance between e v ery two samples, thus determine the outliers. Simple distance-based outlier detection algorithms are not suitable for a large dataset, since for n samples with m dimensions, their complexity is usually O ( n 2 m ) [12], and each computation requires scanning all the samples. Howe v er , an extended cell-based outlier de- tection algorithm is de veloped in [14], which guarantee linear complexity over the dataset volume and no more than three dataset scans. The experiment shows this algorithm is the best for the dataset with dimension less than 4. Sometimes, with consideration of temporal and spatial local- ity , an outlier may not be a separate point, but a small cluster . Cluster-based outlier detection algorithms consider clusters with small size as outlier clusters and clean the dataset by removing the whole cluster [15] [16]. SEMINAR D A T A MINING, JUNE 2019 4 I V . D A TA T R A N S F O R M A T I O N The representation of data in different attributes v aries: some are categorical, while some are numerical. For categori- cal v alues, they can be nominal, binary or ordinal [3], and for numerical data, they can also hav e different statistical features including mean values and standard deviations. Howe v er , not all kinds of data meet the requirement of data mining models. Also, the difference among data attributes may bring troubles for the subsequent optimization work of data mining models. Data transformation is about modifying the representation of data so that they are qualified to be the input for data mining models, as well as making the optimization algorithm of the data mining model easier to take effect. A. Numeralization Categorical v alues widely exists in the natural world, some of the operations, such as calculating the entropy between groups, can be done directly over cate gorical data. Ho we ver , most operations are not applicable to categorical data. Thus, categorical data is supposed to be encoded into numerical data, making it meets the requirements of the models. The following encoding techniques are adopted for numeralization. • One-Hot encoding : Re gard each possible value of the categorical data as a single dimension, and use 1 for the dimension which the sample belongs to the category , otherwise 0 . • Sequential encoding : For each possible v alue of the categorical data, assign it with a unique and numerical index. This is implemented as a kind of word encoding, as in [17]. • Customized encoding : Customized encoding is based on rules designed for a certain task. For instance, word2vec [18] is an encoding that can turn a word into a 300 dimensional v ector , with consideration of the word’ s meaning. Generally , one-hot encoding is suitable for categorical data with fe wer possible v alues; if there are too many possible values, such as English words, the encoded dataset would be huge and sparse. Sequential encoding would not produce huge output, but the encoded data is not as easy to separate as one- hot encoded data. Customized encoding, if carefully designed, usually perform well ov er a certain kind of task, b ut for other tasks, the encoding should be redesigned, and its design can take lots of ef forts. B. Discr etization Discretization of data is applied sometimes to meet the requirement of input of models, such as Nai ve Bayes which require its input to be countable [19]. Also, it can smooth the noise. Discretization of data does not necessarily make the data categorical, but make the continuous values countable. The discretization of data can be achie ved with unsupervised learning methods such as putting data into equal-width or equal-frequency slots, kno wn as binning , or clustering. Some supervised learning methods such as decision tree can also be used for discretization of data [3]. C. Normalization Since dif ferent attrib ute usually adopts a different unit system, their mean v alue and standard deviation are usually not identical. Ho we ver , the numerical dif ference would make some of the attrib utes look more ”important”, while others are not [3]. This impression could cause trouble for some models; one of the typical ones is KNN: larger value would strongly af fect the distance comparison, making the model mainly consider attributes tend to ha ve larger numerical values. Besides, for neuron network models, the different unit system will also hav e a negati ve influence on gradient descent optimizing methods, forcing it to adopt a smaller learning rate. T o tackle the problem mentioned abov e varies of normalization methods are issued, some of them are listed as follo ws. 1) Min-max normalization: Min-max normalization is used for mapping the attrib ute from its range [ l b, ub ] to another range [ l b new , ub new ] ; the target range is usually [0 , 1] or [ − 1 , 1] [20]. For a sample with value v , the normalized value v 0 is giv en as in (2). v 0 = v − lb ub − lb ( ub new − lb new ) + lb new (2) 2) Z-scor e normalization: If the underlying range of an attribute is unknown or outlier exists, min-max normalization is not feasible or could be strongly affected [20]. Another normalization approach is to transform the data so that it would hav e 0 as mean and 1 as standard deviation. Gi ven the mean µ and standard deviation σ of the attribute, the transformation is represented as in (3). v 0 = v − µ σ (3) Note that if µ and σ are unknown, they can be substituted with the sample mean and standard deviation. 3) Decimal scaling normalization: An easier way to im- plement the normalization is to shift the floating point of the data so that each value in an attribute would have an absolute value less than 1 , the transformation is gi ven as in (4). v 0 = v 10 j (4) For some cases, dif ferent attributes hav e an identical or similar unit system, such as the preprocessing of RGB- colored imaged. In these cases, normalization is not necessary . Howe v er , if this is not guaranteed, normalization is still recommended for all data mining tasks. D. Numerical T ransformations The transformation ov er dataset can help to obtain additional attributes. These features obtained by transformation could be unimportant for some data mining models, such as neu- ral network, which have superior fitting potential. Howe ver , for relati vely simpler models with fe wer parameters, linear regression, for e xample, the transformed features do help the model to get better performance(as in Fig. 2), for they could provide additional indication of the relationship between SEMINAR D A T A MINING, JUNE 2019 5 Fig. 2. The effect of box-cox transformation in linear regression. The feature and label are quadratically related. attributes. The transformation would also be essential for scientific discov eries and machine controls [21]. Generally , gi ven attributes set { a 1 , a 2 , . . . , a p } , the numeri- cal transformation can be represented as in (5). Theoretically , f can be any function, howe ver , since the input data is finite, f can take polynomial forms [21]. x 0 = f ( a 1 , a 2 , . . . , a p ) (5) The commonly used representation of f includes polyno- mial based transformation , appr oximation based transforma- tion , rank transformation and box-cox transformation [20]. The parameters in the transformation formula could be ob- tained by subjecti v e definition (for situations where people know the relationship between attributes and labels well), by brute search [20] or by applying maximum likelihood method. V . D A TA R E D U C T I O N The amount of data in a data warehouse or a dataset can be huge, causing difficulties for data storage and processing when working on a data mining task, while not e very model needs a huge amount of data to train. On the other hand, although the data may hav e lots of attributes, there could be unrelated features as well as the interdependence between features [22]. Data reduction is the technique that helps to reduce the amount or dimension, or both, of a dataset, thus making the model’ s learning process more efficient as well as helping the model to obtain better performance, including preventing overfitting problem, and fix the skewed data distribution. A. Dimensional r eduction The dimension reduction technique is about reducing the dimensionality of data samples, thus reduce the total size of the data. As the number of attributes is reduced for a sample, there is less information contained in it. A good dimensional reduction algorithm will keep more general information: this could make it more difficult for models to become ov erfitted. Some dimensional reduction techniques pose a dimensional reduction transformation o ver a dataset, generating ne w data samples, which have a fewer number of attributes than before. The transformations have different criteria. Principal compo- nent analysis, kno wn as PCA, could reduce the dimension of data while keeping the maximum v ariance of data [23]. This is achieved by multiplying matrix A = ( a 1 , a 2 , . . . , a p ) T to the dataset X and keep the top k dimensions ( a i stands for the normalized eigenv ector corresponds to the i th greatest eigen v alue of the cov ariance matrix of the dataset). By con- trast, linear discriminant analysis (LD A), is meant to maximize the component axes for class-separation. The implementation of LD A is similar to PCA; the only difference is it replaces the cov ariance matrix with the scatter matrix of samples. A graphical illustration of the difference between PCA and LDA is gi ven as Fig. 3. In comparatively more situations, LDA outperforms PCA. PCA may outperform LD A when the data amount is small, or the data is nonuniformly sampled [24]. Other dimensional reduction algorithms include factor anal- ysis (assuming a lo wer dimensional underlying distribution), projection pursuit(measuring the aspect of non-Gaussianity) [25], and wav elet transform [3]. Feature selection is another dimensional reduction tech- nique: it is about removing irrelev ant or correlated attributes from the dataset while keeping the other relati vely independent attributes untouched. Feature selection is more than simply selecting the feature that has greater rele v ance with the vari- able to predict, the relationship between attributes are also supposed to be taken into consideration: the goal is to find a sufficiently good subset of features to predict [22]. Feature selection methods can be divided into three types, as follo ws [26]. • filter : Directly select the feature based on attribute lev el criteria, including information gain, correlation score, or chi-square test. The filter method does not take the data mining model into consideration. • wrapper : Use techniques to search through the potential subsets, according to their performance on the data min- ing model. Greedy strategies, including forward selection and backward elimination [26], are issued in order to reduce the time consumption. • embedded : Embed the feature selection into the data min- ing model. Usually , the weight over different attrib utes would act as feature selection. A typical e xample is the regularization term of the loss function in linear regres- sion, known as Lasso regression (for L1 regularization) and ridge regression (for L2 regularization). B. Instance selection and sampling Both instance selection and sampling are about achie ving the reduction of data by reducing the amount of data, seeking the chance to train the model with minimum performance loss [20], while based on different criteria for selecting (or dropping) instance. Most instance selection algorithm is based on fine-tuning classification models. T o help the model make better decision, condensation algorithm and edition algorithm are issued [20]. The condensation remo ves the samples lie in the relati v e center area of the class, assuming they do not contribute much in classification. Condensed nearest neighbor [27], for instance, select instance by adding all the samples that cause a mistake to a K-Nearest Neighbor classifier . Edition algorithm removes the samples close to boundary , hoping to give the classifier a smoother decision boundary . Related algorithms include a clustering-based algorithm to select the center of clusters [28], Compared with instance selection methods, sampling is a faster and easier way to reduce the number of instances, SEMINAR D A T A MINING, JUNE 2019 6 Fig. 3. A comparison of reduction result with PCA and LDA. since almost no complex selection algorithm is required for sampling methods: they only focus on reducing the amount of the data samples. The easiest sampling technique is random sampling , which collect a certain amount or portion of samples from the dataset randomly . For ske wed datasets, stratified sampling [22] is more adapted, since it takes the appearance frequency of labels from different classes into account and assigns a different probability of data with different labels being chosen, thus makes the sampled dataset more balanced. V I . S U M M A RY A N D O U T L O O K Data mining, as a technique to discover additional informa- tion from a dataset, can be integrated as a pipeline, in which obtaining, scrubbing, exploring, modeling, and interpreting are the key steps. The purpose of the data mining pipeline is to tackle realistic problems, including re viewing the past and predicting the future. The specific technique used in each step should be selected with care to giv e the best performance to the pipeline. The success of a data mining model depends on the proper data preprocessing work. The unpreprocessed data can be of unsuitable format for model input, causing instability for the optimization algorithm of the model, having a great impact on the model’ s performance because of its noise and outliers, and causing performance problems on the model’ s training process. W ith careful selection of preprocessing steps, these problems can be reduced or avoided. Data type transformation techniques as well as missing value handling techniques makes it possible for models for processing different types of data. By applying normalization, the unit system of different attributes would be more unified, reducing the probability of an optimization algorithm to miss the global minimum. For simpler models, numerical transfor- mation can provide richer features to the model, thus enhance the model’ s ability to discover more underlying relationships between features and labels. For the overfitting problems of the model, dimensional reduction techniques help model find the more general information about samples instead of the too detailed features by reducing the dimension of feature, thus re- mov e some unimportant information. And for the performance of the model training, both dimensional reduction techniques and instance selection techniques would improve the training performance by reducing the total amount of data. R E F E R E N C E S [1] F . Pedregosa, G. V aroquaux, A. Gramfort, V . Michel, B. Thirion, O. Grisel, M. Blondel, P . Prettenhofer, R. W eiss, V . Dubourg, J. V ander- plas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. 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