Noisy data

Jaimei Han and Micheline Kamber

Real-world data tends to be incomplete, noisy, and inconsistent. Data cleaning routines attempt to fill in missing values, smooth out noise while identifying outliers, and correct inconsistencies in the data. This tip, from Jiawei Han and Micheline Kamber's book "Data Mining Concepts and Techniques," concentrates on how to smooth out noise:

First of all, what is noise? Noise is random error or variance in a measured variable. Given a numeric such as, say price, how can we "smooth" out the data to remove the noise? Let's look at the following data smoothing techniques:

1. Binning: Binning methods smooth a sorted data value by consulting its "neighborhood," this is, the values around it. The sorted values are distributed into a number of "buckets," or bins. Because binning methods consult the neighborhood of values, they perform local smoothing. Here are several common binning techniques:

Sorted data for price (in dollars):
4, 8, 15, 21, 21, 24, 25, 28, 34

Partition into (equidepth) bins:
Bin 1: 4, 8, 15
Bin 2: 21, 21, 24
Bin 3: 25, 28, 34

Smoothing by bin means:
Bin 1: 9, 9, 9
Bin 2: 22, 22, 22
Bin 3: 29, 29, 29

Smoothing by bin boundaries:
Bin 1: 4, 4, 15
Bin 2: 21, 21, 24
Bin 3: 25, 25, 34

In these examples, the data for price are first sorted and then partitioned into equidepth bins of depth 3 (i.e., each bin contains

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three values). In smoothing by bin means, each value in a bin is replaced by the mean value of the bin. For example, the mean of the values 4, 8, and 15 in Bin 1 is 9. Therefore, each original value in this bin is replaced by the value 9. Similarly, smoothing by bin medians can be employed, in which each bin value is replaced by the bin median. In smoothing by bin boundaries, the minimum and maximum values in a given bin are identified as the bin boundaries. Each bin value is then replaced by the closest boundary value. In general, the larger the width, the greater the effect of the smoothing. Alternatively, bins may be equiwidth, where the interval range of values in each bin is constant. Binning is also used as a discretization technique.

2. Clustering: Outliers may be detected by clustering, where similar values are organized into groups, or "clusters." Intuitively, values that fall outside of the set of clusters may be considered outliers.

3. Combined computer and human inspection: Outliers may be identified through a combination of computer and human inspection. In one application, for example, an information-theoretic measure was used to help identify outlier patterns in a handwritten character database for classification. The measure's value reflected the "surprise" content of the predicted character label with respect to the known label. Outlier patterns may be informative (e.g., identifying useful data exceptions, such as different versions of the characters "0" or "7") or "garbage" (e.g., mislabeled characters). Patterns whose surprise content is above a threshold are output to a list. A human can then sort through the patterns in the list to identify the actual garbage ones. This is much faster than having to manually search though the entire database. The garbage patterns can then be excluded from use in subsequent data mining.

4. Regression: Data can be smoothed by fitting the data to a function, such as with regression. Linear regression involves finding the "best" line to fit two variables, so that one variable can be used to predict the other. Multiple linear regression is an extension of linear regression, where more than two variables are involved and the data are fit to a multidimensional surface. Using regression to find a mathematical equation to fit the data helps smooth out the noise.

Many methods for data smoothing are also methods for data reduction involving discretization. For example, the binning techniques described above reduce the number of distinct values per attribute. This acts as a form of data reduction for logic-based data mining methods, such as decision tree induction, which repeatedly make values comparisons on sorted data. Concept hierarchies are a form of data discretization that can also be sued for data smoothing. A concept hierarchy for price, for example, may map real price values into inexpensive, moderately_priced, and expensive, thereby reducing the number of data values to be handled by the mining process. Some methods of classification, such as neural networks, have built-in data smoothing mechanisms.

This was first published in February 2001

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