There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.

/pdf/robust-face-recognition-via-sparse-representation-4bfqv6y74o.pdf

Robust Face Recognition via Sparse Representation

As one of the most successful applications of image analysis and understanding, face recognition has recently received significant attention, especially during the past several years. At least two reasons account for this trend: the first is the wide range of commercial and law enforcement applications, and the second is the availability of feasible technologies after 30 years of research. Even though current machine recognition systems have reached a certain level of maturity, their success is limited by the conditions imposed by many real applications. For example, recognition of face images acquired in an outdoor environment with changes in illumination and/or pose remains a largely unsolved problem. In other words, current systems are still far away from the capability of the human perception system.This paper provides an up-to-date critical survey of still- and video-based face recognition research. There are two underlying motivations for us to write this survey paper: the first is to provide an up-to-date review of the existing literature, and the second is to offer some insights into the studies of machine recognition of faces. To provide a comprehensive survey, we not only categorize existing recognition techniques but also present detailed descriptions of representative methods within each category. In addition, relevant topics such as psychophysical studies, system evaluation, and issues of illumination and pose variation are covered.

Face recognition: A literature survey

The AR face database

In the context of the appearance-based paradigm for object recognition, it is generally believed that algorithms based on LDA (linear discriminant analysis) are superior to those based on PCA (principal components analysis). In this communication, we show that this is not always the case. We present our case first by using intuitively plausible arguments and, then, by showing actual results on a face database. Our overall conclusion is that when the training data set is small, PCA can outperform LDA and, also, that PCA is less sensitive to different training data sets.

PCA versus LDA

The classical way of attempting to solve the face (or object) recognition problem is by using large and representative data sets. In many applications, though, only one sample per class is available to the system. In this contribution, we describe a probabilistic approach that is able to compensate for imprecisely localized, partially occluded, and expression-variant faces even when only one single training sample per class is available to the system. To solve the localization problem, we find the subspace (within the feature space, e.g., eigenspace) that represents this error for each of the training images. To resolve the occlusion problem, each face is divided into k local regions which are analyzed in isolation. In contrast with other approaches where a simple voting space is used, we present a probabilistic method that analyzes how "good" a local match is. To make the recognition system less sensitive to the differences between the facial expression displayed on the training and the testing images, we weight the results obtained on each local area on the basis of how much of this local area is affected by the expression displayed on the current test image.

Recognizing imprecisely localized, partially occluded, and expression variant faces from a single sample per class

It is commonly assumed that a person’s emotional state can be readily inferred from his or her facial movements, typically called emotional expressions or facial expressions. This assumption influences legal judgments, policy decisions, national security protocols, and educational practices; guides the diagnosis and treatment of psychiatric illness, as well as the development of commercial applications; and pervades everyday social interactions as well as research in other scientific fields such as artificial intelligence, neuroscience, and computer vision. In this article, we survey examples of this widespread assumption, which we refer to as the common view, and we then examine the scientific evidence that tests this view, focusing on the six most popular emotion categories used by consumers of emotion research: anger, disgust, fear, happiness, sadness, and surprise. The available scientific evidence suggests that people do sometimes smile when happy, frown when sad, scowl when angry, and so on, as proposed by the common view, more than what would be expected by chance. Yet how people communicate anger, disgust, fear, happiness, sadness, and surprise varies substantially across cultures, situations, and even across people within a single situation. Furthermore, similar configurations of facial movements variably express instances of more than one emotion category. In fact, a given configuration of facial movements, such as a scowl, often communicates something other than an emotional state. Scientists agree that facial movements convey a range of information and are important for social communication, emotional or otherwise. But our review suggests an urgent need for research that examines how people actually move their faces to express emotions and other social information in the variety of contexts that make up everyday life, as well as careful study of the mechanisms by which people perceive instances of emotion in one another. We make specific research recommendations that will yield a more valid picture of how people move their faces to express emotions and how they infer emotional meaning from facial movements in situations of everyday life. This research is crucial to provide consumers of emotion research with the translational information they require.

https://journals.sagepub.com/doi/pdf/10.1177/1529100619832930

Emotional Expressions Reconsidered: Challenges to Inferring Emotion From Human Facial Movements:

Understanding the different categories of facial expressions of emotion regularly used by us is essential to gain insights into human cognition and affect as well as for the design of computational models and perceptual interfaces. Past research on facial expressions of emotion has focused on the study of six basic categories—happiness, surprise, anger, sadness, fear, and disgust. However, many more facial expressions of emotion exist and are used regularly by humans. This paper describes an important group of expressions, which we call compound emotion categories. Compound emotions are those that can be constructed by combining basic component categories to create new ones. For instance, happily surprised and angrily surprised are two distinct compound emotion categories. The present work defines 21 distinct emotion categories. Sample images of their facial expressions were collected from 230 human subjects. A Facial Action Coding System analysis shows the production of these 21 categories is different but consistent with the subordinate categories they represent (e.g., a happily surprised expression combines muscle movements observed in happiness and surprised). We show that these differences are sufficient to distinguish between the 21 defined categories. We then use a computational model of face perception to demonstrate that most of these categories are also visually discriminable from one another.

https://www.pnas.org/content/pnas/111/15/E1454.full.pdf

Aleix M. Martinez

Papers

The AR face database

PCA versus LDA

Recognizing imprecisely localized, partially occluded, and expression variant faces from a single sample per class

Emotional Expressions Reconsidered: Challenges to Inferring Emotion From Human Facial Movements:

Compound facial expressions of emotion.