Noise reduction and data cleansing in machine learning, interpolation of missing values

Noise reduction and data cleansing in machine learning, interpolation of missing values

Noise removal and data cleansing and missing value interpolation in machine learning are important processes for improving data quality and the performance of predictive models.

Noise removal is a technique for removing unwanted information or random errors in data. Noise can be caused by a variety of factors, including sensor noise, measurement errors, and data entry errors. Noise can negatively impact the training and prediction of machine learning models, and the goal of noise removal is to obtain reliable data and improve model performance.

Data cleansing, or interpolation of missing values, is the process of cleaning a data set to resolve problems such as inaccuracies, incompleteness, duplicates, and missing values. The following techniques are used in data cleansing

• Missing value processing: A data set may contain missing values (missing data points). Methods for handling missing values include removing samples with missing values, supplementing missing values with the mean or median, or estimating missing values using a predictive model.
• Data de-duplication: When a dataset contains duplicate data, de-duplication can improve the quality of the data. Duplicate data can lead to model bias.
• Outlier handling: Data sets may contain abnormal values (outliers) that are outside the normal range. Outliers can distort model training and prediction. Methods for detecting and handling outliers include statistical methods, threshold-based methods, and replacing outliers with other values.
• Feature scaling: Features in a dataset may have different scales. These are feature scaling (normalization or standardization) to unify the scales of the features, which can speed up model convergence and facilitate comparison among features.

The algorithms used for them are described next.

Algorithms used for noise reduction, data cleansing, and missing value interpolation in machine learning

Various algorithms and methods are used for noise reduction, data cleansing, and missing value interpolation in machine learning. The following is a description of some of the most common algorithms.

• Missing value processing
  • Mean, median, and mode completion: replacing missing values with the mean, median, or mode in the data set.
  • K-Nearest Neighbors (KNN): Predicts missing values by using values of data points in the neighborhood of the data point with missing values.
  • Regression Model Prediction: This method predicts missing values using regression models (linear regression, decision trees, random forests, etc.) to predict features with missing values.
• De-duplication of data: by de-duplicating the data set.
  • Extraction of unique values: This method removes duplicate data in a dataset and extracts only unique data points.
  • Duplicate detection by hash values or identifiers: detects and removes duplicate data points by calculating hash values or unique identifiers of the data points.
• Outlier processing
  • Statistical methods: Statistical methods such as mean and standard deviation, median and absolute deviation, box plots, etc. are used to detect and remove outliers.
  • Robust statistical models: Statistical models that are robust to outliers (RANSAC, Tukey’s biweight, etc.) are used to detect and remove outliers.
• Denoising
  • Moving Average or Exponential Smoothing: Averages or weighted averages of data points over a period of time are calculated to smooth out the noise. See “Overview of Exponential Smoothing and Examples of Algorithms and Implementations” in detail.
  • Filtering methods: These methods use filtering techniques (low-pass filter, median filter, Kalman filter, etc.) to remove noise.

The following libraries and platforms are used to utilize these algorithms.

Libraries and platforms used for noise reduction, data cleansing, and missing value interpolation in machine learning

The following libraries and platforms are used for noise reduction, data cleansing, and missing value interpolation in machine learning.

• Python libraries:
  • NumPy: provides basic functionality for numerical computation and data manipulation, and is used to handle missing values and manipulate data.
  • pandas: provides data frames and series data structures, used for data cleansing, missing value processing, duplicate elimination, etc.
  • scikit-learn: a comprehensive library for machine learning that provides missing value processing, outlier detection, feature scaling, and more.
  • TensorFlow and PyTorch: major frameworks for deep learning, used for building and training models for noise reduction and data cleansing.
• R packages: R is the main framework for deep learning, used to build and train models for noise reduction and data cleansing.
  • tidyr: used for data organization and transformation, suitable for missing value processing and data cleansing.
  • dplyr: used for data manipulation, filtering and aggregation, useful for data cleansing and aggregation processes.
  • caret: a comprehensive package for machine learning, providing functions for data preprocessing, feature selection, and outlier handling.
• Visual programming tools:
  • KNIME: an open source platform for data mining and machine learning that allows users to build and visualize workflows for noise removal and data cleansing.
  • RapidMiner: a platform for machine learning and data mining that allows users to graphically perform data cleansing and preprocessing tasks.
• OpenRefine: an open source tool for data cleansing, data transformation, and data shaping that allows users to improve data quality and consistency while working with large data sets.

Finally, we will describe an example python implementation of denoising and data cleansing (including missing value interpolation).

On an example implementation in python of noise reduction in machine learning

Below is an example of implementing noise removal in Python. In this example, a smoothing filter is used to remove noise.

import numpy as np
import matplotlib.pyplot as plt

def add_noise(signal, noise_level):
    noise = np.random.randn(len(signal)) * noise_level
    noisy_signal = signal + noise
    return noisy_signal

def moving_average_filter(signal, window_size):
    filtered_signal = np.zeros(len(signal))
    for i in range(len(signal)):
        start = max(0, i - window_size//2)
        end = min(len(signal), i + window_size//2 + 1)
        filtered_signal[i] = np.mean(signal[start:end])
    return filtered_signal

# Signal generation including noise
t = np.linspace(0, 1, 100)
signal = np.sin(2 * np.pi * 5 * t)  # 5Hz sine wave
noise_level = 0.2
noisy_signal = add_noise(signal, noise_level)

# Noise Reduction
window_size = 5
filtered_signal = moving_average_filter(noisy_signal, window_size)

# plot
plt.figure(figsize=(10, 6))
plt.plot(t, signal, label='Clean Signal')
plt.plot(t, noisy_signal, label='Noisy Signal')
plt.plot(t, filtered_signal, label='Filtered Signal')
plt.xlabel('Time')
plt.ylabel('Amplitude')
plt.legend()
plt.show()

In this example, noise is generated with the add_noise function, a moving average filter is applied with the moving_average_filter function, and finally, the original, noisy, and filtered signals are plotted.

On examples of python implementations of data cleansing and missing value interpolation in machine learning

Below is an example of data cleansing implemented in Python. In this example, missing values are processed and duplicate data are removed.

import pandas as pd

# Creation of sample data
data = {
    'Name': ['John', 'Alice', 'Bob', 'John', 'Alice'],
    'Age': [25, None, 30, 25, 28],
    'Gender': ['Male', 'Female', None, 'Male', 'Female'],
    'Salary': [50000, 60000, 70000, None, 60000]
}
df = pd.DataFrame(data)

# missing-value processing
df['Age'] = df['Age'].fillna(df['Age'].mean())
df['Gender'] = df['Gender'].fillna(df['Gender'].mode()[0])
df['Salary'] = df['Salary'].fillna(df['Salary'].median())

# Duplicate data removal
df = df.drop_duplicates()

# Data display after cleansing
print(df)

In this example, data cleansing is performed using the pandas library, first creating the sample data as a DataFrame object, and then processing the missing values. They use the fillna method to complete the missing values in the Age column with the mean value, the missing values in the Gender column with the mode value, and the missing values in the Salary column with the median value. They then remove duplicate data, using the drop_duplicates method to remove duplicate rows, and finally, they display the data after cleansing.

Reference Information and Reference Books

<Noise reduction and data cleansing>

• Noise Reduction by Statistical Processing

Actual images are subject to some kind of disturbance or noise, and if local features obtained from images affected by disturbances are used as they are, the expected weaving accuracy may not be achieved. Therefore, statistical feature extraction, which transforms the observed data into features that are advantageous to weaving based on the established statistical structure of the data, is necessary. Statistical feature extraction refers to further feature extraction based on the probabilistic statistical structure of the extracted local features to transform them into robust features that are less susceptible to noise and disturbance. Statistical feature extraction is applicable not only to local features but also to various features in image recognition.

• Noise reduction and normalization in speech recognition

Speech contains many features other than the phonological features required for speech recognition. Among them, features related to who is speaking, i.e., the speaker, are important. The separation of phonological and speaker features in speech has been a longstanding problem in speech engineering, but it has not yet been solved.

• Anomaly detection using support vector data description method -Biangulation problems and Lagrangian functions and data cleansing

In the classical method, Hotelling’s T2 method, the anomaly detection model was created assuming that all data followed a single normal distribution. On the other hand, the approaches using the mixture distribution model and Bayesian estimation gave up using a single distribution and focused on the local scatter of data around the point of interest to create an anomaly detection model. In this section, I will discuss an approach that takes the idea back to the world of Hotelling’s T2 method, but instead uses a technique called the “kernel trick” to indirectly represent the shading of the distribution.

• Data cleansing tool OpenRefine Data cleaning tool for natural language etc.

The method to process the data cleanly is called data cleansing. These data cleansing processes are necessary in the pre-processing of machine learning and post-processing of natural language processed data.

• Image Feature Extraction and Missing Value Inference with Linear Dimensionality Reduction Model in Bayesian Inference

Linear dimensionality reduction (linear dimensionality reduction) is a basic technique for reducing the amount of data, extracting feature patterns, and summarizing and visualizing data by mapping multidimensional data to a low-dimensional space. In fact, it is known empirically that, for many real data, a space of dimension M, which is much smaller than the dimension D of the observed data, is sufficient to represent the main trends of the data, so the idea of dimensionality reduction has been developed and utilized in various application fields, not limited to machine learning.

The methods described here are closely related to techniques called probabilistic principal component analysis, factor analysis, or probabilistic matrix factorization. Although closely related to techniques such as probabilistic principal component analysis, factor analysis, or probabilistic matrix factorization, we will focus here on simpler models that are simpler than commonly used methods.

In addition, as a specific application here, we will also conduct simple experiments on image data compression and interpolation of missing values using the linear dimensionality reduction model. The ideas of dimensionality reduction and missing value interpolation are common to models such as nonnegative matrix factorization and tensor decomposition.

• Robust Principal Component Analysis Overview and Implementation Examples

Robust Principal Component Analysis (RPCA) is a method for finding a basis in data, and is characterized by its robustness to data containing outliers and noise. This paper describes various applications of RPCA and its concrete implementation using pyhton.

• Statistical Hypothesis Testing and Machine Learning Techniques

Statistical Hypothesis Testing is a method in statistics that probabilistically evaluates whether a hypothesis is true or not, and is used not only to evaluate statistical methods, but also to evaluate the reliability of predictions and to select and evaluate models in machine learning. It is also used in the evaluation of feature selection as described in “Explainable Machine Learning,” and in the verification of the discrimination performance between normal and abnormal as described in “Anomaly Detection and Change Detection Technology,” and is a fundamental technology. This section describes various statistical hypothesis testing methods and their specific implementations.

<missing-value interpolation>

• Application of Variational Bayesian Algorithm to Defective Value Matrix Decomposition Models

When all components of the observation matrix are unobserved, the same policy can be used to age the variational Bayesian learning algorithm, but the posterior covariance of A and B is a little more complicated due to the missing effects. In this article, we will discuss the derivation of those algorithms.

• Sparse Modeling and Multivariate Analysis (10) Use of matrix data decomposition

Although there are innumerable possible factorizations of a matrix, a decomposition that gives an expansion in terms of a normal orthogonal basis for each row vector of the original matrix, and that approximates the original data in the least squared error sense when the expansion is terminated in the middle, can be obtained by singular value decomposition as described in “Overview of Singular Value Decomposition (SVD) and examples of algorithms and implementations“.

Low-rank approximation through such decomposition has been applied not only to the data of customer x products, but also to various other data. For example, if X is the data of document x words, the method of decomposing the matrix into singular values is called latent semantic analysis (LSA) or latent semantic indexing (LSI).

By decomposing this matrix into singular values, we can obtain a new basis for representing the meaning of a sentence (a concept such as a weighted combination of multiple word meanings = topic) and a representation of the document using the new basis. For example, if we look at the shopping example as a document x word matrix, we can interpret that the topic of bread and the topic of fruit are extracted from the data of documents about bread and documents about fruit.

• Image Feature Extraction and Missing Value Inference with Linear Dimensionality Reduction Model in Bayesian Inference

Linear dimensionality reduction (linear dimensionality reduction) is a basic technique for reducing the amount of data, extracting feature patterns, and summarizing and visualizing data by mapping multidimensional data to a low-dimensional space. In fact, it is known empirically that, for many real data, a space of dimension M, which is much smaller than the dimension D of the observed data, is sufficient to represent the main trends of the data, so the idea of dimensionality reduction has been developed and utilized in various application fields, not limited to machine learning.

The methods described here are closely related to techniques called probabilistic principal component analysis, factor analysis, or probabilistic matrix factorization. Although closely related to techniques such as probabilistic principal component analysis, factor analysis, or probabilistic matrix factorization, we will focus here on simpler models that are simpler than commonly used methods.

In addition, as a specific application here, we will also conduct simple experiments on image data compression and interpolation of missing values using the linear dimensionality reduction model. The ideas of dimensionality reduction and missing value interpolation are common to models such as nonnegative matrix factorization and tensor decomposition.

• EM Algorithm and Examples of Various Application Implementations

The EM algorithm (Expectation-Maximization Algorithm) is an iterative optimization algorithm widely used in statistical estimation and machine learning. In particular, it is often used for parameter estimation of stochastic models with latent variables.

Here, we provide an overview of the EM algorithm, the flow of applying the EM algorithm to mixed models, HMMs, missing value estimation, and rating prediction, respectively, and an example implementation in python.

• Overview of DBSCAN (Density-Based Spatial Clustering of Applications with Noise) and Examples of Applications and Implementations

DBSCAN is a popular clustering algorithm in data mining and machine learning that aims to discover clusters based on the spatial density of data points rather than assuming the shape of the clusters. This section provides an overview of this DBSCAN, its algorithm, various application examples, and a concrete implementation in python.

• Solving Constraint Satisfaction Problems Using the EM Algorithm

The EM (Expectation Maximization) algorithm can also be used as a method for solving the Constraint Satisfaction Problem. This approach is particularly useful when there is incomplete information, such as missing or incomplete data. This paper describes various applications of the constraint satisfaction problem using the EM algorithm and its implementation in python.