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

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

Overview

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

Noise reduction aims to remove unnecessary information such as sensor noise and measurement errors to obtain reliable data.

Data cleansing includes missing value completion (deletion, completion by mean and median, and estimation using predictive models), duplicate data removal, outlier handling (statistical and threshold-based methods), and feature scaling (normalization and standardization) to unify feature scales.

Various algorithms are utilized in these methods, including the following.

• Missing value processing includes completion by mean, median, and mode, estimation using the K nearest neighbor (KNN) method, and prediction using regression models.
• Data de-duplication uses extraction of unique values and duplicate detection using hash values and identifiers.
• Outlier processing utilizes statistical methods (mean/standard deviation, box plots) and robust statistical models such as RANSAC.
• For noise removal, smoothing by moving average or exponential smoothing and filtering methods such as low-pass filters, median filters, and Kalman filters are used.

The following libraries and tools are used to implement these methods.

Python Library

• NumPy: numerical computation and missing value processing
• pandas: data frame manipulation, data cleansing
• scikit-learn: missing value processing, outlier detection, feature scaling
• TensorFlow and PyTorch: model building for noise removal and data cleansing

R packages

• tidyr: data organization and missing value processing
• dplyr: data manipulation and filtering
• caret: preprocessing, outlier handling

Visual programming tools

• KNIME: workflow data processing and visualization
• RapidMiner: Graphical data cleansing
• OpenRefine: Shaping and quality improvement of large data sets

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.

Technical Topics

Noise reduction and data cleansing

Noise Reduction by Statistical Processing

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

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

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.

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

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 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 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

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

Sparse Modeling and Multivariate Analysis (10Use 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

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

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

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

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.