What are some advanced methods of exploratory data analysis?

Additional techniques include : Non-negative Matrix Factorization (NMF) is a powerful method for dimensionality reduction. Multiplicative update rule improved NMF, making it stable and capable of preserving more information than PCA. Linear Discriminant Analysis (LDA) finds a linear combination of features that maximizes class separability. Generalized Discriminant Analysis (GDA) extends LDA into a nonlinear framework using kernel functions. The Low Variance Filter eliminates constant variables. High Correlation Filter identifies and removes highly correlated features. Backward Feature Elimination and Forward Feature Construction are for feature selection. Random Forests offer classification and feature selection capabilities.

EDA (Exploratory Data Analysis) is basically an "Art of Storytelling" created from Sample dataset(s) for evaluating Population Parameters for analyzing a given Business Case Study. It forms a mix of ingredients like - Data, Statistics, Visualization & Story for further processing and actionable outcomes. EDA incorporates techniques as follows: a) Descriptive Statistics Measures of Central Tendency, Dispersion & Shape b) Inferential Statistics Confidence Intervals & Hypothesis c) Data Visualization-Data distribution & insights d) Outliers & their treatment e) Missing Values & their Imputation f) Domain Knowledge Application on given Business Case Study g) Sampling h) Feature Engineering - creating meaningful variables for analysis

1. Clearly define the objectives of your analysis to choose the most appropriate dimensionality reduction technique. Understand the nature of your data. Therefore plotting the data helps to see correlation 2. Preprocessing Steps Normalization and Scaling: Ensure that your data is properly scaled and normalized, as dimensionality reduction techniques can besensitive to the scale. PCA: Useful for linear relationships and when you want to preserve as much variance as possible. SVD: Often used in text data and recommendation systems. t-SNE: Ideal for visualizing clusters in high-dimensional data. UMAP (Uniform Manifold Approximation and Projection): A newer method that can often outperform t-SNE (speed & data structure preservation)

In handling outliers, merging statistical techniques - like z-score, IQR, and isolation forest - with 'domain expertise' is key. Understanding outliers in the context of specific industries or scenarios is vital. Sometimes, outliers carry crucial insights rather than just statistical anomalies. This understanding leads to a more refined approach, better decision-making in areas like finance, healthcare, and anomaly detection across industries. Integrating domain insights enhances outlier handling, ensuring more informed data-driven decisions.

Additional techniques include: Prophet based predictions and comparison with uncertainty and acceptable upper and lower bounds. Local Outlier Factor (LOF) calculates the density of data points compared to their neighboring points. Points with significantly lower density are considered outliers. One-Class SVM uses a support vector machine to detect outliers by classifying data points as belonging to a single class or being outliers. Histogram-based Outlier Score (HBOS) uses histograms to calculate outlier scores based on the frequency of data points within each bin. Autoencoders are neural networks used for unsupervised feature learning. Unusual data points that are poorly reconstructed by the autoencoder are flagged as outliers.

Outlier detection in exploratory data analysis include statistical methods such as ??-??????????, ?????? and ?????????????????????? ????????????????. Machine learning algorithms like ???????????? and ?????????????????? ?????????????? are also used for detecting anomalies. Visual techniques such as ?????? ??????????, ?????????????? ??????????, and ???????????????????? can be useful too. Lastly, techniques based on proximity or density based approaches like ?????????? ?????????????? ???????????? (??????) can be employed to identify outliers in a dataset.

Because of the way these processes work, it's best to tackle outlier detection before diving into dimensionality reduction. Dimensionality reduction techniques are all about finding patterns and relationships in the data, and outliers can mess with these patterns, making the reduced dimensions harder to interpret accurately.

The foremost reason to conduct an EDA is to understand the data, features and the values within the features. Understanding the data in conjunction with business knowledge will help formulate analysis and extracting patterns in the data. Feature engineering will help us in identifying the patterns as well as get the data ready to be used in the algorithm itself. For example, a column with age is useful by itself but sometimes binning can identify the age generation and thereby correlate the age with other features. And sometimes using the feature as it is will not give better performance in a particular algorithm. For example converting text features to numerical values will improve the usability and performance of the model.

Before jumping straight into feature engineering, no matter domain knowledge, it's better to organize your analysis: 1. Understand data distribution 2. Detect outliers and missing values 3. Detect correlations 4. Build new features More often than not steps 1-3 will tell you what type of feature engineering you need. Do you need to have bins for values like age or duration, or maybe combine them in a sort of an index (age and economic status, distance and time), if you are going to work in linear models then sth like age-physical activity "term" can be useful. If you are working with survey data then PCA can be very helpful as LSA with text data. There are more approaches here, but this is why following some basic steps is important.

Feature engineering primarily serves model building. EDA focuses on data exploration and understanding. While they can overlap (e.g., PCA for dimension reduction), high-quality data is essential for effective feature engineering.

Network analysis helps you see the big picture by uncovering hidden connections between things. Imagine your data as a web of interconnected points. This approach can be a game-changer in fields like biology, where understanding how tiny organisms interact can lead to breakthroughs. By mapping out these relationships, you can spot key players, improve processes, and even predict what might happen next. However you need a corresponding complex dataset to do network analysis.

Sometimes, I'm short of ideas on what to do for exploratory data analysis or tuning/optimizing my models. When this happens, I like to just reverse engineer solutions; instead of putting pressure on myself for trying to come up with a creative solution. I do that by first identifying and clarifying the problem. Oftentimes, that's a lot easier than trying to conjure up a creative solution. Once I'm sure I've clearly defined the problem I want to solve, I start to work backwards. What would I need in the ideal scenario to solve that problem? I take one step back and then I ask, what would I need to get this information? And then I take another step back and ask: Ok, well, what I need to get that information?

Another advanced tool is factor analysis (FA). FA is a statistical method used to explore underlying relationships among sets of complex variables or items, reducing them to a smaller number of factors. This technique simplifies the correlation matrices, making it easier for researchers to understand how variables relate and cluster, thereby supporting the construct validity of instruments. FA is commonly used for developing and refining measurement tools in research, helping identify dimensions or constructs that explain data patterns. Its applications include Exploratory Factor Analysis (EFA) for developing new measures and Confirmatory Factor Analysis (CFA) for testing established factor structures against new data.

Often overlooked, creating a clear roadmap before diving into data analysis is crucial. Outline your goals, the steps to achieve them, and how your analysis aligns with your hypothesis(es). This structured approach will keep you focused. Since EDA can be iterative, thorough documentation is essential to maintain clarity and avoid getting lost in the process.