High level missing value imputation operators.
High level missing value imputation operators. The NaN values in the input data are treated as missing values and will be replaced with imputed values after the processing.
Impute missing values with the average of other attributes in the instance.
Impute missing values with the average of other attributes in the instance. Assume the attributes of the dataset are of same kind, e.g. microarray gene expression data, the missing values can be estimated as the average of non-missing attributes in the same instance. Note that this is not the average of same attribute across different instances.
the data set with missing values.
Missing value imputation by K-Means clustering.
Missing value imputation by K-Means clustering. First cluster data by K-Means with missing values and then impute missing values with the average value of each attribute in the clusters.
the data set.
the number of clusters.
the number of runs of K-Means algorithm.
Missing value imputation by k-nearest neighbors.
Missing value imputation by k-nearest neighbors. The KNN-based method selects instances similar to the instance of interest to impute missing values. If we consider instance A that has one missing value on attribute i, this method would find K other instances, which have a value present on attribute i, with values most similar (in term of some distance, e.g. Euclidean distance) to A on other attributes without missing values. The average of values on attribute i from the K nearest neighbors is then used as an estimate for the missing value in instance A.
the data set with missing values.
the number of neighbors.
Local least squares missing value imputation.
Local least squares missing value imputation. The local least squares imputation method represents a target instance that has missing values as a linear combination of similar instances, which are selected by k-nearest neighbors method.
the data set.
the number of similar rows used for imputation.
Missing value imputation with singular value decomposition.
Missing value imputation with singular value decomposition. Given SVD A = U Σ V^{T}, we use the most significant eigenvectors of V^{T} to linearly estimate missing values. Although it has been shown that several significant eigenvectors are sufficient to describe the data with small errors, the exact fraction of eigenvectors best for estimation needs to be determined empirically. Once k most significant eigenvectors from V^{T} are selected, we estimate a missing value j in row i by first regressing this row against the k eigenvectors and then use the coefficients of the regression to reconstruct j from a linear combination of the k eigenvectors. The j th value of row i and the j th values of the k eigenvectors are not used in determining these regression coefficients. It should be noted that SVD can only be performed on complete matrices; therefore we originally fill all missing values by other methods in matrix A, obtaining A'. We then utilize an expectation maximization method to arrive at the final estimate, as follows. Each missing value in A is estimated using the above algorithm, and then the procedure is repeated on the newly obtained matrix, until the total change in the matrix falls below the empirically determined threshold (say 0.01).
the data set.
the number of eigenvectors used for imputation.
the maximum number of iterations.
Missing value imputation. In statistics, missing data, or missing values, occur when no data value is stored for the variable in the current observation. Missing data are a common occurrence and can have a significant effect on the conclusions that can be drawn from the data.
Data are missing for many reasons. Missing data can occur because of nonresponse: no information is provided for several items or no information is provided for a whole unit. Some items are more sensitive for nonresponse than others, for example items about private subjects such as income.
Dropout is a type of missingness that occurs mostly when studying development over time. In this type of study the measurement is repeated after a certain period of time. Missingness occurs when participants drop out before the test ends and one or more measurements are missing.
Sometimes missing values are caused by the device failure or even by researchers themselves. It is important to question why the data is missing, this can help with finding a solution to the problem. If the values are missing at random there is still information about each variable in each unit but if the values are missing systematically the problem is more severe because the sample cannot be representative of the population.
All of the causes for missing data fit into four classes, which are based on the relationship between the missing data mechanism and the missing and observed values. These classes are important to understand because the problems caused by missing data and the solutions to these problems are different for the four classes.
The first is Missing Completely at Random (MCAR). MCAR means that the missing data mechanism is unrelated to the values of any variables, whether missing or observed. Data that are missing because a researcher dropped the test tubes or survey participants accidentally skipped questions are likely to be MCAR. If the observed values are essentially a random sample of the full data set, complete case analysis gives the same results as the full data set would have. Unfortunately, most missing data are not MCAR.
At the opposite end of the spectrum is Non-Ignorable (NI). NI means that the missing data mechanism is related to the missing values. It commonly occurs when people do not want to reveal something very personal or unpopular about themselves. For example, if individuals with higher incomes are less likely to reveal them on a survey than are individuals with lower incomes, the missing data mechanism for income is non-ignorable. Whether income is missing or observed is related to its value. Complete case analysis can give highly biased results for NI missing data. If proportionally more low and moderate income individuals are left in the sample because high income people are missing, an estimate of the mean income will be lower than the actual population mean.
In between these two extremes are Missing at Random (MAR) and Covariate Dependent (CD). Both of these classes require that the cause of the missing data is unrelated to the missing values, but may be related to the observed values of other variables. MAR means that the missing values are related to either observed covariates or response variables, whereas CD means that the missing values are related only to covariates. As an example of CD missing data, missing income data may be unrelated to the actual income values, but are related to education. Perhaps people with more education are less likely to reveal their income than those with less education.
A key distinction is whether the mechanism is ignorable (i.e., MCAR, CD, or MAR) or non-ignorable. There are excellent techniques for handling ignorable missing data. Non-ignorable missing data are more challenging and require a different approach.
If it is known that the data analysis technique which is to be used isn't content robust, it is good to consider imputing the missing data. Once all missing values have been imputed, the dataset can then be analyzed using standard techniques for complete data. The analysis should ideally take into account that there is a greater degree of uncertainty than if the imputed values had actually been observed, however, and this generally requires some modification of the standard complete-data analysis methods. Many imputation techniques are available.
Imputation is not the only method available for handling missing data. The expectation-maximization algorithm is a method for finding maximum likelihood estimates that has been widely applied to missing data problems. In machine learning, it is sometimes possible to train a classifier directly over the original data without imputing it first. That was shown to yield better performance in cases where the missing data is structurally absent, rather than missing due to measurement noise.