Analyzing Facial Characteristics Via Non-Negative Matrix Factorization from Basics in R Programming Software
Non-negative Matrix Factorization (NMF) Simplifies Object Recognition
Non-negative Matrix Factorization (NMF) is a computer vision technique that has proven to be a simple and effective tool for image and text mining. This method, introduced in 1994 by Paatero and Tapper and further popularized in 1999 by Daniel D Lee and H Sebastian Seung, learns a parts-based representation of objects.
In simple terms, NMF breaks down complex objects or data into additive parts, a process that corresponds to combining parts to form a whole, rather than subtracting. This approach is in line with psychological, physiological, and computational studies that support the idea of part-based representation in the brain.
The process begins with a nonnegative data matrix, (X), which is factorized into two lower-rank nonnegative matrices: (W) (basis matrix) and (H) (coefficient matrix). Each column of (H) corresponds to a column in the data matrix (X). The image pixels are then clipped to range [0,1] to allow nonnegativity.
The objective of NMF is to approximate (X) as (W H) with minimal error. The factors are constrained to be nonnegative, ensuring that each original data vector (e.g., an image) is approximated as an additive combination of parts (the columns of (W)) weighted by coefficients from (H).
This optimization problem is typically solved iteratively because it is NP-Hard. The resulting representation is additive and parts-based, allowing NMF to extract interpretable components. For example, in image processing, NMF can identify parts like eyes, noses, or mouths in faces; in topic modeling, it can group words representing topics.
The LFW (Labeled Faces in the Wild) dataset, containing over 13,000 facial images collected from the web, is often used for learning facial features in NMF. Each facial image is scaled to 150 x 150 pixels and then standardized so that the mean and standard deviation become equal to 0.25.
In the implementation, only 500 randomly selected images are used. Each image pixel is flattened to become a column vector, and combining all the flattened images as columns results in the data matrix (V). NMF is performed over (V) with an iterative algorithm that learns both a set of basis images and infers values for the hidden variables from the visible variables.
Although NMF can learn facial parts, it may not be successful in learning parts from databases containing images of objects viewed from extremely different angles or highly articulated objects. Furthermore, it's important to note that NMF does not learn about the "syntactic" relationships between parts and makes no further assumptions about their statistical dependencies.
In summary, NMF provides a powerful tool for image and text mining by learning a parts-based representation of complex objects or data. The non-negativity constraints in NMF are compatible with the intuitive notion of combining parts to form a whole, making it an attractive choice for applications seeking interpretable and additive decompositions. However, it's crucial to consider the limitations of NMF when dealing with objects viewed from various angles or highly articulated objects.
Data-and-cloud-computing technology can be used to store and process the large-scale data generated during the learning process of Non-negative Matrix Factorization (NMF), a technique used in education-and-self-development for understanding object recognition.
This technology can facilitate the rapid and scalable deployment of NMF algorithms, allowing researchers and practitioners to efficiently analyze and interpret complex objects or data, thereby enhancing their knowledge in data-and-cloud-computing and education-and-self-development.
