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Convolutional Neural Networks
In deep learning, a convolutional neural network (CNN, or ConvNet) is a class of artificial neural network (ANN), most commonly applied to analyze visual imagery. CNNs are also known as Shift Invariant or Space Invariant Artificial Neural Networks (SIANN), based on the shared-weight architecture of the convolution kernels or filters that slide along input features and provide translation-equivariant responses known as feature maps. Counter-intuitively, most convolutional neural networks are not invariant to translation, due to the downsampling operation they apply to the input. They have applications in image and video recognition, recommender systems, image classification, image segmentation, medical image analysis, natural language processing, brain–computer interfaces, and financial time series. CNNs are regularized versions of multilayer perceptrons. Multilayer perceptrons usually mean fully connected networks, that is, each neuron in one layer is connected to all neuron ...
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Deep Learning
Deep learning (also known as deep structured learning) is part of a broader family of machine learning methods based on artificial neural networks with representation learning. Learning can be supervised, semi-supervised or unsupervised. Deep-learning architectures such as deep neural networks, deep belief networks, deep reinforcement learning, recurrent neural networks, convolutional neural networks and Transformers have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, Climatology, climate science, material inspection and board game programs, where they have produced results comparable to and in some cases surpassing human expert performance. Artificial neural networks (ANNs) were inspired by information processing and distributed communication nodes in biological systems. ANNs have various differences from biological brains. Specifically, artificial ...
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Overfitting
mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably". An overfitted model is a mathematical model that contains more parameters than can be justified by the data. The essence of overfitting is to have unknowingly extracted some of the residual variation (i.e., the noise) as if that variation represented underlying model structure. Underfitting occurs when a mathematical model cannot adequately capture the underlying structure of the data. An under-fitted model is a model where some parameters or terms that would appear in a correctly specified model are missing. Under-fitting would occur, for example, when fitting a linear model to non-linear data. Such a model will tend to have poor predictive performance. The possibility of over-fitting exists because the criterion used for selecting the model is no ...
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Frobenius Inner Product
In mathematics, the Frobenius inner product is a binary operation that takes two matrices and returns a scalar. It is often denoted \langle \mathbf,\mathbf \rangle_\mathrm. The operation is a component-wise inner product of two matrices as though they are vectors, and satisfies the axioms for an inner product. The two matrices must have the same dimension - same number of rows and columns, but are not restricted to be square matrices. Definition Given two complex number-valued ''n''Ă—''m'' matrices A and B, written explicitly as : \mathbf = \,, \quad \mathbf = the Frobenius inner product is defined as, : \langle \mathbf, \mathbf \rangle_\mathrm =\sum_\overline B_ \, = \mathrm\left(\overline \mathbf\right) \equiv \mathrm\left(\mathbf^ \mathbf\right) where the overline denotes the complex conjugate, and \dagger denotes Hermitian conjugate. Explicitly this sum is :\begin \langle \mathbf, \mathbf \rangle_\mathrm = & \overline_ B_ + \overline_ B_ + \cdots + \overline_ B_ \\ & + ...
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Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. In mo ...
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Comparison Image Neural Networks
Comparison or comparing is the act of evaluating two or more things by determining the relevant, comparable characteristics of each thing, and then determining which characteristics of each are similar to the other, which are different, and to what degree. Where characteristics are different, the differences may then be evaluated to determine which thing is best suited for a particular purpose. The description of similarities and differences found between the two things is also called a comparison. Comparison can take many distinct forms, varying by field: To compare things, they must have characteristics that are similar enough in relevant ways to merit comparison. If two things are too different to compare in a useful way, an attempt to compare them is colloquially referred to in English as "comparing apples and oranges." Comparison is widely used in society, in science and in the arts. General usage Comparison is a natural activity, which even animals engage in when deci ...
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Convolution
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see #Properties, commutativity). The integral is evaluated for all values of shift, producing the convolution function. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution (f*g) differs from cross-correlation (f \star g) only in that either or is reflected about the y-axis in convolution; thus it is a cross-c ...
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Feature Engineering
Feature engineering or feature extraction or feature discovery is the process of using domain knowledge to extract features (characteristics, properties, attributes) from raw data. The motivation is to use these extra features to improve the quality of results from a machine learning process, compared with supplying only the raw data to the machine learning process. Process The feature engineering process is: *Brainstorming or testing features * Deciding what features to create * Creating features * Testing the impact of the identified features on the task * Improving your features if needed * Repeat Typical engineered features The following list provides some typical ways to engineer useful features * Numerical transformations (like taking fractions or scaling) * Category encoder like one-hot or target encoder (for categorical data) * Clustering * Group aggregated values * Principal component analysis (for numerical data) * Feature construction : building new "physical" ...
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Filter (signal Processing)
In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others without having to act in the frequency domain. Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, image processing, and computer graphics. There are many different bases of classifying filters and these overlap in many different ways; there is no simple hierarchical classification. Filters may be: *non-linear or linear *time-variant or t ...
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Receptive Field
The receptive field, or sensory space, is a delimited medium where some physiological stimuli can evoke a sensory neuronal response in specific organisms. Complexity of the receptive field ranges from the unidimensional chemical structure of odorants to the multidimensional spacetime of human visual field, through the bidimensional skin surface, being a receptive field for touch perception. Receptive fields can positively or negatively alter the membrane potential with or without affecting the rate of action potentials. A sensory space can be dependent of an animal's location. For a particular sound wave traveling in an appropriate transmission medium, by means of sound localization, an auditory space would amount to a reference system that continuously shifts as the animal moves (taking into consideration the space inside the ears as well). Conversely, receptive fields can be largely independent of the animal's location, as in the case of place cells. A sensory space can also m ...
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Visual Field
The visual field is the "spatial array of visual sensations available to observation in introspectionist psychological experiments". Or simply, visual field can be defined as the entire area that can be seen when an eye is fixed straight at a point. The equivalent concept for optical instruments and image sensors is the field of view (FOV). In optometry, ophthalmology, and neurology, a visual field test is used to determine whether the visual field is affected by diseases that cause local scotoma or a more extensive loss of vision or a reduction in sensitivity (increase in threshold). Normal limits The normal (monocular) human visual field extends to approximately 60 degrees nasally (toward the nose, or inward) from the vertical meridian in each eye, to 107 degrees temporally (away from the nose, or outwards) from the vertical meridian, and approximately 70 degrees above and 80 below the horizontal meridian. The binocular visual field is the superimposition of the two monocular ...
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Cortical Neuron
The cerebral cortex, also known as the cerebral mantle, is the outer layer of neural tissue of the cerebrum of the brain in humans and other mammals. The cerebral cortex mostly consists of the six-layered neocortex, with just 10% consisting of allocortex. It is separated into two cortices, by the longitudinal fissure that divides the cerebrum into the left and right cerebral hemispheres. The two hemispheres are joined beneath the cortex by the corpus callosum. The cerebral cortex is the largest site of neural integration in the central nervous system. It plays a key role in attention, perception, awareness, thought, memory, language, and consciousness. The cerebral cortex is part of the brain responsible for cognition. In most mammals, apart from small mammals that have small brains, the cerebral cortex is folded, providing a greater surface area in the confined volume of the cranium. Apart from minimising brain and cranial volume, cortical folding is crucial for the brain ...
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Visual Cortex
The visual cortex of the brain is the area of the cerebral cortex that processes visual information. It is located in the occipital lobe. Sensory input originating from the eyes travels through the lateral geniculate nucleus in the thalamus and then reaches the visual cortex. The area of the visual cortex that receives the sensory input from the lateral geniculate nucleus is the primary visual cortex, also known as visual area 1 ( V1), Brodmann area 17, or the striate cortex. The extrastriate areas consist of visual areas 2, 3, 4, and 5 (also known as V2, V3, V4, and V5, or Brodmann area 18 and all Brodmann area 19). Both hemispheres of the brain include a visual cortex; the visual cortex in the left hemisphere receives signals from the right visual field, and the visual cortex in the right hemisphere receives signals from the left visual field. Introduction The primary visual cortex (V1) is located in and around the calcarine fissure in the occipital lobe. Each hemisphere's V1 ...
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