Machine Learning Algorithms

Affinity Propagation

Affinity Propagation is a relatively new clustering technique that makes clusters based on graph distances between points. The clusters tend to be smaller and have uneven sizes. Strengths: The user doesn't need to specify the number of clusters (but does need to specify 'sample preference' and 'damping' hyperparameters). Weaknesses: The main disadvantage of Affinity Propagation is that it's quite slow and memory-heavy, making it difficult to scale to larger datasets. In addition, it also assumes the true underlying clusters are globular.

Autoencoders

Autoencoders are neural networks that are trained to reconstruct their original inputs. For example, image autoencoders are trained to reproduce the original images instead of classifying the image as a dog or a cat. So how is this helpful? Well, the key is to structure the hidden layer to have fewer neurons than the input/output layers. Thus, that hidden layer will learn to produce a smaller representation of the original image. Because you use the input image as the target output, autoencoders are considered unsupervised. They can be used directly (e.g. image compression) or stacked in sequence (e.g. deep learning). Strengths: Autoencoders are neural networks, which means they perform well for certain types of data, such as image and audio data. Weaknesses: Autoencoders are neural networks, which means they require more data to train. They are not used as general-purpose dimensionality reduction algorithms.

Classification

Classification is the supervised learning task for modeling and predicting categorical variables. Examples include predicting employee churn, email spam, financial fraud, or student letter grades. As you'll see, many regression algorithms have classification counterparts. The algorithms are adapted to predict a class (or class probabilities) instead of real numbers.

Feature Extraction

Feature extraction is for creating a new, smaller set of features that stills captures most of the useful information. Again, feature selection keeps a subset of the original features while feature extraction creates new ones. As with feature selection, some algorithms already have built-in feature extraction. The best example is Deep Learning, which extracts increasingly useful representations of the raw input data through each hidden neural layer. We covered this in Part 1. As a stand-alone task, feature extraction can be unsupervised (i.e. PCA) or supervised (i.e. LDA).

Hierarchical / Agglomerative

Hierarchical clustering, a.k.a. agglomerative clustering, is a suite of algorithms based on the same idea: (1) Start with each point in its own cluster. (2) For each cluster, merge it with another based on some criterion. (3) Repeat until only one cluster remains and you are left with a hierarchy of clusters. Strengths: The main advantage of hierarchical clustering is that the clusters are not assumed to be globular. In addition, it scales well to larger datasets. Weaknesses: Much like K-Means, the user must choose the number of clusters (i.e. the level of the hierarchy to "keep" after the algorithm completes).

Curse of dimensionality

In machine learning, "dimensionality" simply refers to the number of features (i.e. input variables) in your dataset. When the number of features is very large relative to the number of observations in your dataset, certain algorithms struggle to train effective models. This is called the "Curse of Dimensionality," and it's especially relevant for clustering algorithms that rely on distance calculations. "Let's say you have a straight line 100 yards long and you dropped a penny somewhere on it. It wouldn't be too hard to find. You walk along the line and it takes two minutes. Now let's say you have a square 100 yards on each side and you dropped a penny somewhere on it. It would be pretty hard, like searching across two football fields stuck together. It could take days. Now a cube 100 yards across. That's like searching a 30-story building the size of a football stadium. Ugh. The difficulty of searching through the space gets a lot harder as you have more dimensions."

K-Means

K-Means is a general purpose algorithm that makes clusters based on geometric distances (i.e. distance on a coordinate plane) between points. The clusters are grouped around centroids, causing them to be globular and have similar sizes. This is our recommended algorithm for beginners because it's simple, yet flexible enough to get reasonable results for most problems. Strengths: K-Means is hands-down the most popular clustering algorithm because it's fast, simple, and surprisingly flexible if you pre-process your data and engineer useful features. Weaknesses: The user must specify the number of clusters, which won't always be easy to do. In addition, if the true underlying clusters in your data are not globular, then K-Means will produce poor clusters.

(Regularized) Logistic Regression classification

Logistic regression is the classification counterpart to linear regression. Predictions are mapped to be between 0 and 1 through the logistic function, which means that predictions can be interpreted as class probabilities. The models themselves are still "linear," so they work well when your classes are linearly separable (i.e. they can be separated by a single decision surface). Logistic regression can also be regularized by penalizing coefficients with a tunable penalty strength. Strengths: Outputs have a nice probabilistic interpretation, and the algorithm can be regularized to avoid overfitting. Logistic models can be updated easily with new data using stochastic gradient descent. Weaknesses: Logistic regression tends to underperform when there are multiple or non-linear decision boundaries. They are not flexible enough to naturally capture more complex relationships.

Naive abates classification

Naive Bayes (NB) is a very simple algorithm based around conditional probability and counting. Essentially, your model is actually a probability table that gets updated through your training data. To predict a new observation, you'd simply "look up" the class probabilities in your "probability table" based on its feature values. It's called "naive" because its core assumption of conditional independence (i.e. all input features are independent from one another) rarely holds true in the real world. Strengths: Even though the conditional independence assumption rarely holds true, NB models actually perform surprisingly well in practice, especially for how simple they are. They are easy to implement and can scale with your dataset. Weaknesses: Due to their sheer simplicity, NB models are often beaten by models properly trained and tuned using the previous algorithms listed.

Regression

Regression is the supervised learning task for modeling and predicting continuous, numeric variables. Examples include predicting real-estate prices, stock price movements, or student test scores. Regression tasks are characterized by labeled datasets that have a numeric target variable. In other words, you have some "ground truth" value for each observation that you can use to supervise your algorithm.

Support Vector Machines classification

Support vector machines (SVM) use a mechanism called kernels, which essentially calculate distance between two observations. The SVM algorithm then finds a decision boundary that maximizes the distance between the closest members of separate classes. For example, an SVM with a linear kernel is similar to logistic regression. Therefore, in practice, the benefit of SVM's typically comes from using non-linear kernels to model non-linear decision boundaries. Strengths: SVM's can model non-linear decision boundaries, and there are many kernels to choose from. They are also fairly robust against overfitting, especially in high-dimensional space. Weaknesses: However, SVM's are memory intensive, trickier to tune due to the importance of picking the right kernel, and don't scale well to larger datasets. Currently in the industry, random forests are usually preferred over SVM's.

Deep Learning Classification

To continue the trend, deep learning is also easily adapted to classification problems. In fact, classification is often the more common use of deep learning, such as in image classification. Strengths: Deep learning performs very well when classifying for audio, text, and image data. Weaknesses: As with regression, deep neural networks require very large amounts of data to train, so it's not treated as a general-purpose algorithm.

Variance Thresholds

Variance thresholds remove features whose values don't change much from observation to observation (i.e. their variance falls below a threshold). These features provide little value. For example, if you had a public health dataset where 96% of observations were for 35-year-old men, then the 'Age' and 'Gender' features can be eliminated without a major loss in information. Because variance is dependent on scale, you should always normalize your features first. Strengths: Applying variance thresholds is based on solid intuition: features that don't change much also don't add much information. This is an easy and relatively safe way to reduce dimensionality at the start of your modeling process. Weaknesses: If your problem does require dimensionality reduction, applying variance thresholds is rarely sufficient. Furthermore, you must manually set or tune a variance threshold, which could be tricky. We recommend starting with a conservative (i.e. lower) threshold.

DBSCAN

DBSCAN is a density based algorithm that makes clusters for dense regions of points. There's also a recent new development called HDBSCAN that allows varying density clusters. Strengths: DBSCAN does not assume globular clusters, and its performance is scalable. In addition, it doesn't require every point to be assigned to a cluster, reducing the noise of the clusters (this may be a weakness, depending on your use case). Weaknesses: The user must tune the hyperparameters 'epsilon' and 'min_samples,' which define the density of clusters. DBSCAN is quite sensitive to these hyperparameters.

Classification Trees (Ensembles)

Classification trees are the classification counterparts to regression trees. They are both commonly referred to as "decision trees" or by the umbrella term "classification and regression trees (CART)." Strengths: As with regression, classification tree ensembles also perform very well in practice. They are robust to outliers, scalable, and able to naturally model non-linear decision boundaries thanks to their hierarchical structure. Weaknesses: Unconstrained, individual trees are prone to overfitting, but this can be alleviated by ensemble methods.

Clustering

Clustering is an unsupervised learning task for finding natural groupings of observations (i.e. clusters) based on the inherent structure within your dataset. Examples include customer segmentation, grouping similar items in e-commerce, and social network analysis. Because clustering is unsupervised (i.e. there's no "right answer"), data visualization is usually used to evaluate results. If there is a "right answer" (i.e. you have pre-labeled clusters in your training set), then classification algorithms are typically more appropriate.

Correlation Thresholds

Correlation thresholds remove features that are highly correlated with others (i.e. its values change very similarly to another's). These features provide redundant information. For example, if you had a real-estate dataset with 'Floor Area (Sq. Ft.)' and 'Floor Area (Sq. Meters)' as separate features, you can safely remove one of them. Which one should you remove? Well, you'd first calculate all pair-wise correlations. Then, if the correlation between a pair of features is above a given threshold, you'd remove the one that has larger mean absolute correlation with other features. Strengths: Applying correlation thresholds is also based on solid intuition: similar features provide redundant information. Some algorithms are not robust to correlated features, so removing them can boost performance. Weaknesses: Again, you must manually set or tune a correlation threshold, which can be tricky to do. Plus, if you set your threshold too low, you risk dropping useful information. Whenever possible, we prefer algorithms with built-in feature selection over correlation thresholds. Even for algorithms without built-in feature selection, Principal Component Analysis (PCA) is often a better alternative.

Deep Learning regression

Deep learning refers to multi-layer neural networks that can learn extremely complex patterns. They use "hidden layers" between inputs and outputs in order to model intermediary representations of the data that other algorithms cannot easily learn. They have several important mechanisms, such as convolutions and drop-out, that allows them to efficiently learn from high-dimensional data. However, deep learning still requires much more data to train compared to other algorithms because the models have orders of magnitudes more parameters to estimate. Strengths: Deep learning is the current state-of-the-art for certain domains, such as computer vision and speech recognition. Deep neural networks perform very well on image, audio, and text data, and they can be easily updated with new data using batch propagation. Their architectures (i.e. number and structure of layers) can be adapted to many types of problems, and their hidden layers reduce the need for feature engineering. Weaknesses: Deep learning algorithms are usually not suitable as general-purpose algorithms because they require a very large amount of data. In fact, they are usually outperformed by tree ensembles for classical machine learning problems. In addition, they are computationally intensive to train, and they require much more expertise to tune (i.e. set the architecture and hyperparameters).

Feature Selection

Feature selection is for filtering irrelevant or redundant features from your dataset. The key difference between feature selection and extraction is that feature selection keeps a subset of the original features while feature extraction creates brand new ones. To be clear, some supervised algorithms already have built-in feature selection, such as Regularized Regression and Random Forests. Typically, we recommend starting with these algorithms if they fit your task. They're covered in Part 1. As a stand-alone task, feature selection can be unsupervised (e.g. Variance Thresholds) or supervised (e.g. Genetic Algorithms). You can also combine multiple methods if needed.

Genetic Algorithms

Genetic algorithms (GA) are a broad class of algorithms that can be adapted to different purposes. They are search algorithms that are inspired by evolutionary biology and natural selection, combining mutation and cross-over to efficiently traverse large solution spaces. Here's a great intro to the intuition behind GA's. In machine learning, GA's have two main uses. The first is for optimization, such as finding the best weights for a neural network. The second is for supervised feature selection. In this use case, "genes" represent individual features and the "organism" represents a candidate set of features. Each organism in the "population" is graded on a fitness score such as model performance on a hold-out set. The fittest organisms survive and reproduce, repeating until the population converges on a solution some generations later. Strengths: Genetic algorithms can efficiently select features from very high dimensional datasets, where exhaustive search is unfeasible. When you need to preprocess data for an algorithm that doesn't have built-in feature selection (e.g. nearest neighbors) and when you must preserve the original features (i.e. no PCA allowed), GA's are likely your best bet. These situations can arise in business/client settings that require a transparent and interpretable solution. Weaknesses: GA's add a higher level of complexity to your implementation, and they aren't worth the hassle in most cases. If possible, it's faster and simpler to use PCA or to directly use an algorithm with built-in feature selection.

Linear Discriminant Analysis (LDA)

Linear discriminant analysis (LDA) - not to be confused with latent Dirichlet allocation - also creates linear combinations of your original features. However, unlike PCA, LDA doesn't maximize explained variance. Instead, it maximizes the separability between classes. Therefore, LDA is a supervised method that can only be used with labeled data. So which is better: LDA and PCA? Well, results will vary from problem to problem, and the same "No Free Lunch" theorem from Part 1 applies. The LDA transformation is also dependent on scale, so you should normalize your dataset first. Strengths: LDA is supervised, which can (but doesn't always) improve the predictive performance of the extracted features. Furthermore, LDA offers variations (i.e. quadratic LDA) to tackle specific roadblocks. Weaknesses: As with PCA, the new features are not easily interpretable, and you must still manually set or tune the number of components to keep. LDA also requires labeled data, which makes it more situational.

(Regularized) Linear Regression

Linear regression is one of the most common algorithms for the regression task. In its simplest form, it attempts to fit a straight hyperplane to your dataset (i.e. a straight line when you only have 2 variables). As you might guess, it works well when there are linear relationships between the variables in your dataset. In practice, simple linear regression is often outclassed by its regularized counterparts (LASSO, Ridge, and Elastic-Net). Regularization is a technique for penalizing large coefficients in order to avoid overfitting, and the strength of the penalty should be tuned. Strengths: Linear regression is straightforward to understand and explain, and can be regularized to avoid overfitting. In addition, linear models can be updated easily with new data using stochastic gradient descent. Weaknesses: Linear regression performs poorly when there are non-linear relationships. They are not naturally flexible enough to capture more complex patterns, and adding the right interaction terms or polynomials can be tricky and time-consuming.

Nearest Neighbors regression

Nearest neighbors algorithms are "instance-based," which means that that save each training observation. They then make predictions for new observations by searching for the most similar training observations and pooling their values. These algorithms are memory-intensive, perform poorly for high-dimensional data, and require a meaningful distance function to calculate similarity. In practice, training regularized regression or tree ensembles are almost always better uses of your time.

Principal Component Analysis (PCA)

Principal component analysis (PCA) is an unsupervised algorithm that creates linear combinations of the original features. The new features are orthogonal, which means that they are uncorrelated. Furthermore, they are ranked in order of their "explained variance." The first principal component (PC1) explains the most variance in your dataset, PC2 explains the second-most variance, and so on. Therefore, you can reduce dimensionality by limiting the number of principal components to keep based on cumulative explained variance. For example, you might decide to keep only as many principal components as needed to reach a cumulative explained variance of 90%. You should always normalize your dataset before performing PCA because the transformation is dependent on scale. If you don't, the features that are on the largest scale would dominate your new principal components. Strengths: PCA is a versatile technique that works well in practice. It's fast and simple to implement, which means you can easily test algorithms with and without PCA to compare performance. In addition, PCA offers several variations and extensions (i.e. kernel PCA, sparse PCA, etc.) to tackle specific roadblocks. Weaknesses: The new principal components are not interpretable, which may be a deal-breaker in some settings. In addition, you must still manually set or tune a threshold for cumulative explained variance.

Decision Trees (Ensembles) regression

Regression trees (a.k.a. decision trees) learn in a hierarchical fashion by repeatedly splitting your dataset into separate branches that maximize the information gain of each split. This branching structure allows regression trees to naturally learn non-linear relationships. Ensemble methods, such as Random Forests (RF) and Gradient Boosted Trees (GBM), combine predictions from many individual trees. We won't go into their underlying mechanics here, but in practice, RF's often perform very well out-of-the-box while GBM's are harder to tune but tend to have higher performance ceilings. Strengths: Decision trees can learn non-linear relationships, and are fairly robust to outliers. Ensembles perform very well in practice, winning many classical (i.e. non-deep-learning) machine learning competitions. Weaknesses: Unconstrained, individual trees are prone to overfitting because they can keep branching until they memorize the training data. However, this can be alleviated by using ensembles.

Stepwise-Search

Stepwise search is a supervised feature selection method based on sequential search, and it has two flavors: forward and backward. For forward stepwise search, you start without any features. Then, you'd train a 1-feature model using each of your candidate features and keep the version with the best performance. You'd continue adding features, one at a time, until your performance improvements stall. Backward stepwise search is the same process, just reversed: start with all features in your model and then remove one at a time until performance starts to drop substantially. We note this algorithm purely for historical reasons. Despite many textbooks listing stepwise search as a valid option, it almost always underperforms other supervised methods such as regularization. Stepwise search has many documented flaws, one of the most fatal being that it's a greedy algorithm that can't account for future effects of each change. We don't recommend this method.

Normalization techniques in Machine Learning

The most widely used types of normalization in machine learning are: Min-Max Scaling - Subtract the minimum value from each column's highest value and divide by the range. Each new column has a minimum value of 0 and a maximum value of 1. Standardization Scaling - The term "standardization" refers to the process of centering a variable at zero and standardizing the variance at one. Subtracting the mean of each observation and then dividing by the standard deviation is the procedure: The features will be rescaled so that they have the attributes of a typical normal distribution with standard deviations.

When to use normalization and standardization

When you don't know the distribution of your data or when you know it's not Gaussian, normalization is a smart approach to apply. Normalization is useful when your data has variable scales and the technique you're employing, such as k-nearest neighbors and artificial neural networks, doesn't make assumptions about the distribution of your data. The assumption behind standardization is that your data follows a Gaussian (bell curve) distribution. This isn't required, however, it helps the approach work better if your attribute distribution is Gaussian. When your data has variable dimensions and the technique you're using (like logistic regression, linear regression, linear discriminant analysis) standardization is useful. Consider a data collection that includes two characteristics: age and income. Where the age spans from 0 to 80 years old, and the income extends from 0 to 80,000 dollars and up. Income is roughly 1,000 times that of age. As a result, the ranges of these two characteristics are vastly different. Because of its bigger value, the attributed income will organically influence the conclusion more when we undertake further analysis, such as multivariate linear regression. However, this does not necessarily imply that it is a better predictor. As a result, we normalize the data so that all of the variables are in the same range. We normalize training data to solve the model learning challenge. We make sure that the various features have similar value ranges (feature scaling) so that gradient descents can converge faster.