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Locally weighted Linear Regression | Linear Regression Notion | Mar 14, 2023 | Alan Jo | Alan Jo | Apr 18, 2023 | [Non-parametric algorithm](https://texonom.com/non-parametric-algorithm-bc41f745a14c4837bd54368652da5982) |
### LWR
weights depend on the particular point x at which we're trying to evaluate x
| 6f405fcc12f64e0b9ec061c87d81e1e2 |
Ridge regression | Linear Regression Notion | Mar 14, 2023 | Alan Jo | Alan Jo | Apr 18, 2023 | [Regularized parameter](https://texonom.com/regularized-parameter-f3b208cdd37a4002a5d39ef990b8be33) [L2 Norm](https://texonom.com/l2-norm-38c15917350a4c82a11003474ac7d280) |
### bias ๋ํ๊ณ , variance ์ค์ด๋ ๋ฐฉ๋ฒ์ผ๋ก regulation ์ํ
[Regularization](https://texonom.com/regularization-c85433c8c0554eba8edf0035b7fd334c) concept is first adapted to Ridge Regression model
not like linear regression, focus on Regularizer too not only on Fitting error
$$J(\theta) = \frac{1}{2}(\theta\Phi - \vec{y})^T(\theta\Phi - \vec{y}) + \frac{\lambda}{2}\theta^T\theta$$
find 0 point in function derivation by $\theta$
- $\lambda$ controls the tradeoff between Fitting error, Regularizer (overfitting and underfitting)
**alpha, lamda, regularization parameter, penalty term is same**
> [Lasso, Ridge regularization - ํ๊ท์์ selection๊ณผ shrinkage](https://sosal.kr/1104)
> [Ridge regression (๋ฆฟ์ง ํ๊ท) python](https://signature95.tistory.com/46)
> [Ridge regression(๋ฆฟ์งํ๊ท)](https://velog.io/@zhenxi_23/Ridge-regression๋ฆฟ์งํ๊ท)
| 8520dc9911234f62bc6fa25976af0972 |
LMS with Kernel Trick | LMS Notion | Apr 6, 2023 | Alan Jo | Alan Jo | Apr 17, 2023 | [Kernel Trick](https://texonom.com/kernel-trick-a3d7cdc0b30d44efbb072a926b0d99aa) [Basis Function](https://texonom.com/basis-function-994de24f84dd437d9d563ca2a87652d6) [Polynomial Kernel](https://texonom.com/polynomial-kernel-aec7cc809f4546dab71c5bc92d176d7d) |
phi ํจ์์์ monomial๋ณ๋ก ๋คํญ์์ ๋ถ๋ฆฌํ๋ฉด, ๊ฐ๊ฐ์ monomial์ ๋ํ ๊ณ์ฐ๋ง ์ํํ๋ฉด ๋ฉ
$\beta$ is weight of Linear Regression and $\theta$ is weight of LMS
define Kernel $K(x, z) = <\phi(x), \phi(z)>$ ์ฆ ๋ฐ์ดํฐ x์ z์ฌ์ด ์ ์ฌ๋๋ฅผ ๊ณ์ฐํ์ฌ ๊ณ ์ฐจ์ ํน์ง ๊ณต๊ฐ์์ ์ ํ ๋ถ๋ฆฌ ๊ฐ๋ฅํ ๋ฌธ์ ๋ก ๋ฐ๊พธ๊ธฐ ์ํด์
์
๋ ฅ ๋ฐ์ดํฐ๊ฐ ์ ์ฌ๋๋ฅผ ๋ํ๋ด๋ ํ๋ ฌ
1. ์ปค๋๋ก ๋น์ ํ ํจํด์ ์
๋ ฅ ๋ฐ์ดํฐ๋ฅผ ์ ํ ํน์ง ๋ฒกํฐ๋ก ๋ณํ ํ
2. [Linear Regression](https://texonom.com/linear-regression-0137f4fba64746f6bc28e059d0aa6dd1) ์ผ๋ก ํ์ต
| b2130bc9ef1d41bbb779435512612157 |
Multi-Class Logistic Regression | Logistic Regression Notion | Mar 21, 2023 | Alan Jo | Alan Jo | Mar 21, 2023 | [Multi-Class Regression](https://texonom.com/multi-class-regression-b0971c1ace5240abb9d6032522766455) |
input features
weight vectors are optimized by maximizing the log-likelihood
use weight vectors โ classifier by [Bayes Decision Rule](https://texonom.com/bayes-decision-rule-6cbc2961ba31420184b0ea43fd01b862) (argmax) โ decision boundary
| 545d3a376a4d49dd8845111405909327 |
L0 Norm | Regularization Norms | May 11, 2023 | Alan Jo | Alan Jo | May 11, 2023 |
### size
๋ฒกํฐ์ 0์ด ์๋ ์์์ ์ด ๊ฐฏ์์ ํด๋น
| 47471a6f6dea484fbf30a4c46cde8152 |
|
L1 Norm | Regularization Norms | Mar 27, 2023 | Alan Jo | Alan Jo | Mar 27, 2023 |
### ****Manhattanย Distance, Taxicab geometry3****
| d316024c475e4eb691785783756bce57 |
|
L2 Norm | Regularization Norms | Mar 27, 2023 | Alan Jo | Alan Jo | Jul 6, 2023 |
### ****Euclideanย Distance | Euclidean Norm****
0์์ ๊ธฐ์ธ๊ธฐ๊ฐ 0์ด๋ผ์ ์์ ํ ์์์ฃผ๋ [Sparsity of the Model](https://texonom.com/sparsity-of-the-model-80d3dc9702704c03bf7bfd9074d19829) ๋ ๋ชป๋์ธ๋ค
### Matrix Norm
| 38c15917350a4c82a11003474ac7d280 |
|
Pattern | Geometry Notion | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 | 8d5100e53f024576ade60a2d880171d7 |
||
Polytope | Geometry Notion | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 |
### Polytopes
|Title|
|:-:|
|[Polygon](https://texonom.com/polygon-620d5cc274bb4a558a4efc1ade1239e9)|
|[Polyhedron](https://texonom.com/polyhedron-9aff2db4adca4dc1acbaf371eb4b7b73)|
### Polytope Notion
|Title|
|:-:|
|[Convex polytope](https://texonom.com/convex-polytope-8398c3f34fa549fd8a74f06be0476c89)|
> [Polytope](https://en.wikipedia.org/wiki/Polytope)
| 1f77e7cffb7b4609bcf549f9551c61be |
|
**Convex polytope** | Polytope Notion | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 |
> [Convex polytope](https://en.wikipedia.org/wiki/Convex_polytope)
| 8398c3f34fa549fd8a74f06be0476c89 |
|
Polygon | Polytopes | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 | 620d5cc274bb4a558a4efc1ade1239e9 |
||
Crystallography | Polyhedron Notion | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 |
### Crystallography Notion
|Title|
|:-:|
|[Bravais lattice](https://texonom.com/bravais-lattice-e0bad58061dd4df2bcfa8067878e1604)|
|[Crystal](https://texonom.com/crystal-448c038c71584bb193a10048b8af9193)|
> [Crystallography](https://en.wikipedia.org/wiki/Crystallography)
| 3c5c6dab988546959b1a085ba81ed676 |
|
**Bravais lattice** | Crystallography Notion | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 | [Quasicrystal](https://texonom.com/quasicrystal-34b0f812cdce430e89b8ba39857e76f1) [Regular Polyhedron](https://texonom.com/regular-polyhedron-90f91a9623f645c8906d4a904d754ff9) [Penrose tiling](https://texonom.com/penrose-tiling-1726e61c22aa4d388ba15acbb02fba5f) |
> [Bravais lattice](https://en.wikipedia.org/wiki/Bravais_lattice)
| e0bad58061dd4df2bcfa8067878e1604 |
Crystal | Crystallography Notion | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 |
### Crystal Types
|Title|
|:-:|
|[Quasicrystal](https://texonom.com/quasicrystal-34b0f812cdce430e89b8ba39857e76f1)|
> [Crystal](https://en.wikipedia.org/wiki/Crystal)
| 448c038c71584bb193a10048b8af9193 |
|
**Quasicrystal** | Crystal Types | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 | [Bravais lattice](https://texonom.com/bravais-lattice-e0bad58061dd4df2bcfa8067878e1604) [Penrose tiling](https://texonom.com/penrose-tiling-1726e61c22aa4d388ba15acbb02fba5f) |
> [Quasicrystal](https://en.wikipedia.org/wiki/Quasicrystal)
| 34b0f812cdce430e89b8ba39857e76f1 |
**Platonic solid** | Regular Polyhedrons | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 |
## [Convex polytope](https://texonom.com/convex-polytope-8398c3f34fa549fd8a74f06be0476c89)
> [The Infinite Pattern That Never Repeats](https://www.youtube.com/watch?v=48sCx-wBs34)
> [Platonic solid](https://en.wikipedia.org/wiki/Platonic_solid)
| e15de9735a2a48f7a7b1ad1d0c38ee96 |
|
Bayes Factor | Bayes Theorem Notion | Apr 18, 2023 | Alan Jo | Alan Jo | Apr 18, 2023 |
$$likelihood / data \; prior$$
| d73be6d93c004384b454957f98e13aad |
|
Evidence | Bayes Theorem Notion | Apr 18, 2023 | Alan Jo | Alan Jo | Apr 18, 2023 |
์ฆ๊ฑฐ๋ ๋ฏฟ์์ ๊ฒฐ์ ํด์๋ ์๋๊ณ , ๋ฏฟ์์ ์
๋ฐ์ดํธํด์ผํ๋ค. ์ํ์ ์ผ๋ก
์ฆ ์ํฉ์ ํ๋จํ ๋ ์ฆ๊ฑฐ ์ด์ ์ ํ๋ฅ ๋ ๊ฐ์ด ๊ณ ๋ คํด์ผ ๋ ์ ํํ๋ค
๊ทธ๋ฆฌ๊ณ Subset์ Superset๋ณด๋ค ํญ์ ์๋ค ์ฆ ์ฌ๋ฌ ํ๋ฅ ์ด ๊ฒน์น๊ฒ ๋ ๋
> [Bayes theorem, the geometry of changing beliefs](https://www.youtube.com/watch?v=HZGCoVF3YvM)
| 80ff49d6ff4f44d8a0a212a75012908f |
|
Likelihood | Bayes Theorem Notion | Apr 18, 2023 | Alan Jo | Alan Jo | Apr 18, 2023 | [Marginal Probability](https://texonom.com/marginal-probability-ee22b391f7f44fab8b821400cf67e63d) |
### Evidence
| 7a4315f7502440cfbb93b4a469cfe55b |
Odds | Bayes Theorem Notion | Apr 18, 2023 | Alan Jo | Alan Jo | Apr 18, 2023 |
[Probability](https://texonom.com/probability-6b1e766c2c6442c7a599b558453300e4)
20% is 1/5 and 1:4 odds
$$O()$$
> [The medical test paradox, and redesigning Bayes' rule](https://www.youtube.com/watch?v=lG4VkPoG3ko)
| fc52380a1eb842c8b76a1089ae85311c |
|
Posterior | null | null | null | null | null | null |
### Posterior๋ ๋ฐ์ดํฐ๋ฅผ ๊ด์ธกํ ํ์ ๊ฒฐ์
๋ฐ์ดํฐ๋ฅผ ๊ด์ธกํ๊ธฐ ์ ์ ์ด๋ฏธ ์๊ณ ์๋ ์ ๋ณด๋ ๊ฒฝํ ๋ฑ์ ๋ฐํ์ผ๋ก ๊ฒฐ์
Posterior density is intractable due to the data likelihood (๋ถ๋ชจ)
Data likelihood is intractable due to the integral
updated probability of an event occurring after new evidence or information has been taken into account
$\theta$ probability
**๋ถํฌ ์ถ์ ์ Machine Learning์ ํต์ฌ ์ฌํญ**
posterior ์๊ฒ ๋๋ฉด ๋ฐ์ดํฐ๋ก label ์์์๋ค
> [Variational Inference ์์๋ณด๊ธฐ - MLE, MAP๋ถํฐ ELBO๊น์ง](https://modulabs.co.kr/blog/variational-inference-intro/)
| 87e0f5df288140c7ba475b0629bdda05 |
Prior Probability | null | null | null | null | null | null |
prior ์๋ฉด ์ด์์น ํ์ง, ๊ฒฐ์ธก์น ์ฑ์ฐ๊ธฐ, ๋ฒกํฐ ์์ํ ๊ฐ๋ฅ
| 34585174a5cd42bbae9094138713932b |
Stationary distribution | Markovย Chain | null | null | null | null | null |
๋ง๋ฅด์ฝํ ์ฒด์ธ์ ์ํ(State)๊ฐ ์ผ์ ํ ํ๋ฅ ๋ถํฌ๋ฅผ ๊ฐ์ง๋ ์ํ๋ฅผ ์๋ฏธ
[Transition Matrix](https://texonom.com/transition-matrix-ecaeb8f71cfa4443bbb2039c6a9569f5)
[https://kim-hjun.medium.com/markov-chain-stationary-distribution-5198941234f6](https://kim-hjun.medium.com/markov-chain-stationary-distribution-5198941234f6)
> [Stationary distribution](https://en.wikipedia.org/wiki/Stationary_distribution)
| 33dad1d30cb44491be6156020969c62c |
Transition Matrix | Stationary distribution | null | null | null | null | null | ecaeb8f71cfa4443bbb2039c6a9569f5 |
|
Indicator random variable | Random Variable Notion | Sep 14, 2023 | Alan Jo | Alan Jo | Sep 14, 2023 |
random 1 or 0
| cac27017b7ba4e0db0242d305884e37d |
|
Random number | Random Variable Notion | Sep 14, 2023 | Alan Jo | Alan Jo | Sep 17, 2023 |
### Random number generation
|Title|
|:-:|
|[Pseudorandom number generator](https://texonom.com/pseudorandom-number-generator-1fc10a07129d4a70b8c97e1a36bfce7e)|
> [Random number generation](https://en.wikipedia.org/wiki/Random_number_generation)
| 23cec3dc46b74275a70c50875d9708cc |
|
**Pseudorandom number generator** | Random number generation | Sep 14, 2023 | Alan Jo | Alan Jo | Sep 17, 2023 |
## **PRNG, deterministic random bit generator, DRBG**
> [Pseudorandom number generator](https://en.wikipedia.org/wiki/Pseudorandom_number_generator)
> [Hardware random number generator](https://en.wikipedia.org/wiki/Hardware_random_number_generator)
| 1fc10a07129d4a70b8c97e1a36bfce7e |
|
ANOVA | Variance Usages | Mar 16, 2023 | Alan Jo | Alan Jo | Jul 13, 2023 | [law of total variance](https://texonom.com/law-of-total-variance-481cd44bdfde4e069f7f5f6913e17eb8) [F Distribution](https://texonom.com/f-distribution-491a1836300446499b51b79e388b9e80) [t-value](https://texonom.com/t-value-4f1e6fb2b0034235910718dd48de8096) |
### **ANalysis Of VAriance**
๋ค์์ ์ง๋จ์ ๋น๊ตํ ๋ ์ฌ์ฉํ๋ ๊ฐ์ค๊ฒ์ ๋ฐฉ๋ฒ
powerful tool for comparing means and understanding the variation in data
$$variance\;between\;groups / variance\; within\; group$$
[One-way ANOVA](https://texonom.com/one-way-anova-e42ed10ed8994cb883312cb7e26ee2b8)
[Two-way ANOVA](https://texonom.com/two-way-anova-def7597116cc485e87f495bf9413ebd8)
[MANOVA](https://texonom.com/manova-acdfd43476bd43c090f8464550c9154f)
[ANCOVA](https://texonom.com/ancova-4ccb7c6887fa4c50b686d194f8c815db)
[Post-Hoc analysis](https://texonom.com/post-hoc-analysis-938b6bbc73ec43519f247a735155e11a)
> [Analysis of variance](https://en.wikipedia.org/wiki/Analysis_of_variance)
> [๋ถ์ฐ ๋ถ์ (ANOVA)](https://bioinformaticsandme.tistory.com/198)
| aad04dffd648401c8c44525003c6f083 |
law of total variance | Variance Usages | Jul 13, 2023 | Alan Jo | Alan Jo | Jul 13, 2023 |
### **variance decomposition formula, conditional variance formulas**ย orย **law of iterated variances**ย also known asย **Eve's law**
decomposes the variance of two random variables on the same probability space into "explained" and "unexplained" components
$$Var(Y) = E[Var(Y|X)] + Var(E[Y|X])$$
EVPV(expected value of the process variance) + VHM (variance of the hypothetical means)
**Eve's law**, from the initials EV VE for "expectation of variance" and "variance of expectation".
| 481cd44bdfde4e069f7f5f6913e17eb8 |
|
**ANCOVA** | ANOVA | null | null | null | null | null |
**analysis of covariance** | 4ccb7c6887fa4c50b686d194f8c815db |
**MANOVA** | ANOVA | null | null | null | null | null |
**multiple analysis of variance** | acdfd43476bd43c090f8464550c9154f |
**One-way ANOVA** | ANOVA | null | null | null | null | null | e42ed10ed8994cb883312cb7e26ee2b8 |
|
**Post-Hoc analysis** | ANOVA | null | null | null | null | null | 938b6bbc73ec43519f247a735155e11a |
|
**Two-way ANOVA** | ANOVA | null | null | null | null | null | def7597116cc485e87f495bf9413ebd8 |
|
numpy.memmap | numpy Usages | Aug 19, 2023 | Alan Jo | Alan Jo | Aug 19, 2023 |
### save as binary file
```typearr = np.memmap(filename, dtype=dtype, mode='w+', shape=(arr_len,))arr.flush()```
> [numpy.memmap โ NumPy v1.25 Manual](https://numpy.org/doc/stable/reference/generated/numpy.memmap.html)
| a26cd2ad2e4f49338d8d5d1d5cdd1d31 |
|
***Kronecker***ย Delta | Tensor | null | null | null | null | null |
[Identity Diversity](https://texonom.com/identity-diversity-025eac70a756437db814e1d0eae61830)
| 5e1b070c308841eb831b512ef64664f3 |
Linear Dependent | Linear Independent notion | Sep 13, 2023 | Alan Jo | Alan Jo | Sep 13, 2023 | 895c1bc53e2f48b494ef2e2837c16bbf |
||
Orthogonality | null | null | null | null | null | null |
### Subset of linearly independent
independent
> [์ง๊ต์ฑ(orthogonality)์ ๊ณตํ์ ์๋ฏธ](https://satlab.tistory.com/37)
| d694f04a603d46f18da03a4dc737ca51 |
**Exponentiation** | Arithmetic Notion | Aug 29, 2023 | Alan Jo | Alan Jo | Aug 29, 2023 |
> [Exponentiation](https://en.wikipedia.org/wiki/Exponentiation)
| 760c53a791ee4d6696e819b079afe066 |
|
Integer | Number Theory Notion | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 18, 2023 |
### Integers
|Title|
|:-:|
|[1](https://texonom.com/1-494cb164ce5048c99866448c8dc5f48f)|
|[2](https://texonom.com/2-f87b41419520484591161c45dbf0aaa7)|
|[3](https://texonom.com/3-d7deec1b0e0e406eaa594e29218c2d26)|
|[4](https://texonom.com/4-9f5b54f869184ad0be2cf11b0f4d7031)|
|[5](https://texonom.com/5-50102157c9554e94a2166d81a9bf79c9)|
### Integer usages
|Title|
|:-:|
|[relatively prime](https://texonom.com/relatively-prime-66d4089ceeb6443eabfac48dd9196b2c)|
| e87e20fb8fb94fe98202d49d95aefbdc |
|
relatively prime | Integer usages | Sep 17, 2023 | Alan Jo | Alan Jo | Sep 18, 2023 |
์๋ก์
### relatively prime
| 66d4089ceeb6443eabfac48dd9196b2c |
|
1 | Integers | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 | 494cb164ce5048c99866448c8dc5f48f |
||
2 | Integers | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 | f87b41419520484591161c45dbf0aaa7 |
||
3 | Integers | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 | d7deec1b0e0e406eaa594e29218c2d26 |
||
4 | Integers | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 | 9f5b54f869184ad0be2cf11b0f4d7031 |
||
5 | Integers | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 | [Golden Ratio](https://texonom.com/golden-ratio-863df65a00bd48eeab9a8866949d89da) | 50102157c9554e94a2166d81a9bf79c9 |
|
Irrational Number | Real Number Type | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 |
ํจํด์ ์ฃผ๊ธฐ์ ์ผ๋ก ํ์ผ๋งํ ์ ์๋ค๋ ์ฆ๊ฑฐ
### Irrational Numbers
|Title|
|:-:|
|[Golden Ratio](https://texonom.com/golden-ratio-863df65a00bd48eeab9a8866949d89da)|
> [Irrational number](https://en.wikipedia.org/wiki/Irrational_number)
| 1da708bf326a4e6cb8938e54179cb6bc |
|
Rational Number | Real Number Type | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 |
> [Rational number](https://en.wikipedia.org/wiki/Rational_number)
| 131e8af784874e9a9eb4cd4a39d517b6 |
|
Golden Ratio | Irrational Numbers | Sep 3, 2023 | Alan Jo | Alan Jo | Sep 3, 2023 | [5](https://texonom.com/5-50102157c9554e94a2166d81a9bf79c9) |
5๊ฐํ์ ๋๊ฐ์ ๊ณผ ๋ชจ์๋ฆฌ์ ๋น์จ
phi is symbol
> [The Infinite Pattern That Never Repeats](https://www.youtube.com/watch?v=48sCx-wBs34)
| 863df65a00bd48eeab9a8866949d89da |
**Antiderivative** | Derivation Notion | Sep 20, 2023 | Alan Jo | Alan Jo | Sep 20, 2023 |
> [Antiderivative](https://en.wikipedia.org/wiki/Antiderivative)
| 7e0e92c4cdcb4bc48c323100aa512c81 |
|
Logistic Map | Dynamical System Notion | Aug 28, 2023 | Alan Jo | Alan Jo | Aug 28, 2023 |
### Logistic Map Notion
|Title|
|:-:|
|[Feigenbaum constant](https://texonom.com/feigenbaum-constant-0935910d28f84e1aae1802e2076e40d6)|
| d968681610c749e9983e28f97ee5c50b |
|
Feigenbaum constant | Logistic Map Notion | Aug 28, 2023 | Alan Jo | Alan Jo | Aug 28, 2023 | [Fractal](https://texonom.com/fractal-c4ae0e4ab1cf4e8db2c9d4f3e7412114) | 0935910d28f84e1aae1802e2076e40d6 |
|
Recursion-tree method | Recurrence relation Notion | Sep 7, 2023 | Alan Jo | Alan Jo | Sep 10, 2023 | [Recurrence relation](https://texonom.com/recurrence-relation-1c0b90005c30437fa61c5e049782e4be) |
- depth
- count
| e45153b2672b4ff2ba0abea475c3b898 |
Fibonacci sequence | Sequences | Sep 12, 2023 | Alan Jo | Alan Jo | Sep 12, 2023 | [Golden Ratio](https://texonom.com/golden-ratio-863df65a00bd48eeab9a8866949d89da) |
### rounded to the nearest integer with golden ratio ฯ
$$F_n = \phi^n/\sqrt{5}$$
> [Fibonacci sequence](https://en.wikipedia.org/wiki/Fibonacci_sequence)
| 830af82ec2bf49cc90da16fd1a201b14 |
Power Series | Famous Series | Aug 29, 2023 | Alan Jo | Alan Jo | Aug 29, 2023 |
### Power Series Notion
|Title|
|:-:|
|[Power Function](https://texonom.com/power-function-c15a66fd32864a3c803d9ba30779b55a)|
> [Exponentiation](https://en.wikipedia.org/wiki/Exponentiation#Power_functions)
| c191ba27a1de41d8b2ea7e33b56fe9f6 |
|
CTFS | Fourier Series Notion | Sep 13, 2023 | Alan Jo | Alan Jo | Sep 13, 2023 |
### CTFS Notion
|Title|
|:-:|
|[CTFS First difference](https://texonom.com/ctfs-first-difference-6c307c6c0fb1452a8442f7bc9229ca18)|
| bfcd6b43900e44d983ae5c6537338b8b |
|
DTFS | Fourier Series Notion | Sep 13, 2023 | Alan Jo | Alan Jo | Sep 20, 2023 | [Data Sampling](https://texonom.com/data-sampling-306f8190c55c47578e818b4b303bc8fd) [Dirac comb](https://texonom.com/dirac-comb-ebd54bc025f0461cb83b296b3b8ea112) [CTFS](https://texonom.com/ctfs-bfcd6b43900e44d983ae5c6537338b8b) |
### ****Discrete Time Fourier series****
### DTFS Notion
|Title|
|:-:|
|[DTFS Multiplication](https://texonom.com/dtfs-multiplication-e0e390cd5bc34dbbbb4ec3d8e690344d)|
|[DTFS Time shift](https://texonom.com/dtfs-time-shift-7b0fc22164b5479e9eb149d2fff0a1a8)|
|[DTFS First difference](https://texonom.com/dtfs-first-difference-e7d41ae304374b5a916646a25c3fe343)|
|[DTFS Frequency shift](https://texonom.com/dtfs-frequency-shift-8378a648341e4d07a72a1897b7df3c95)|
|[DTFS Even signal](https://texonom.com/dtfs-even-signal-e77f4d7f219c4bf4886dffe4893b60bd)|
|[DTFS odd signal](https://texonom.com/dtfs-odd-signal-d1c904d2345e469d87db80baec2d8a91)|
| 924b5dfa43dd46638de66cc15f61b538 |
Fourier Series Basis | Fourier Series Notion | Sep 13, 2023 | Alan Jo | Alan Jo | Sep 13, 2023 | [Periodic Function](https://texonom.com/periodic-function-3fa775a544934003bfbf39101551d1e1) |
### Basic building block is like this
[Amplitude](https://texonom.com/amplitude-abc47e7b6d1c417cabc5b8a17f1d04ed) $A$, [Frequency](https://texonom.com/frequency-8eb9bc9db08549c98a519d7938c8eb11) $\omega$, [Variable](https://texonom.com/variable-5461090e225a4cc587a754af46ba4f3e) $x$, [Phase](https://texonom.com/phase-a46bfc607627430bbeef12e593b51e75) $\phi$
Add enough of these to get any periodic signal you want even if non-periodic signal
$$Asin(\omega x + \phi)$$
| 64de5af81a8643c3a9f92f8e8e9bb2bb |
Fourier Series Tilda function | Fourier Series Notion | Sep 20, 2023 | Alan Jo | Alan Jo | Sep 20, 2023 |
tilda function is non-[Periodic Function](https://texonom.com/periodic-function-3fa775a544934003bfbf39101551d1e1)
when we sample, it become periodic
time ์ฃผ๊ธฐ ์ ํธ์์ samplingํ๋ฉด ๊ฐ๊ฐ ๊ณ์๊ฐ ๋์ด ๋ฐ๋ ๋๋ฉ์ธ์ด ์ฃผ๊ธฐ๊ฐ ๋๋ค!
> [What does tilde on top of functions mean in fourier series and fourier transforms?](https://math.stackexchange.com/questions/3286976/what-does-tilde-on-top-of-functions-mean-in-fourier-series-and-fourier-transform)
| b8495f56f23a4f58897df1dadacbce11 |
|
**Parseval's theorem** | Fourier Series Notion | Sep 13, 2023 | Alan Jo | Alan Jo | Sep 18, 2023 | [Conservation of Energy](https://texonom.com/conservation-of-energy-d38bcc0c84854c998af26eae9b775503) |
### The average power is the sum of average powers in all harmonics
So [Trivial](https://texonom.com/trivial-2d7ac81afb304cedac671daa7dcba202)
### [DTFS](https://texonom.com/dtfs-924b5dfa43dd46638de66cc15f61b538)
$$\frac{1}{N}\sum|x[n]|^2 = \sum|a_k|^2$$
> [Parseval's theorem](https://en.wikipedia.org/wiki/Parseval's_theorem)
| d132edfc5b734643934a11b42bcdc075 |
CTFS First difference | CTFS Notion | Sep 18, 2023 | Alan Jo | Alan Jo | Sep 18, 2023 | [DTFS First difference](https://texonom.com/dtfs-first-difference-e7d41ae304374b5a916646a25c3fe343) |
k์ $w_0$ ๋งํผ ์ฆํญ
| 6c307c6c0fb1452a8442f7bc9229ca18 |
DTFS Even signal | DTFS Notion | Sep 18, 2023 | Alan Jo | Alan Jo | Sep 18, 2023 | e77f4d7f219c4bf4886dffe4893b60bd |
||
DTFS First difference | DTFS Notion | Sep 18, 2023 | Alan Jo | Alan Jo | Sep 18, 2023 | [CTFS First difference](https://texonom.com/ctfs-first-difference-6c307c6c0fb1452a8442f7bc9229ca18) |
๋ฏธ๋ถ ๋นผ๋ ๊ฒ
๊ณ ์ฃผํ ์ฆํญ ๋๋ ์ด์ ๊ฐ ๋ญ์ง
$$b_k = (1 - d^{-j2\pi\frac{K}{N}})a_k \newline = (1 - cos2\pi\frac{k}{n} + jsin2\pi\frac{k}{N})a_k\newline = e^{-J\pi \frac{k}{N}} (e^{j\pi\frac{k}{N}} - e^{-j\pi\frac{k}{N}})$$
$$ = e^{-J\pi \frac{k}{N}} (2jsin\pi\frac{k}{N})$$
์ ๋๊ฐํ๋ฉด $(2sin\pi\frac{k}{N})$ ์ธ๋ฐ $\pi$ ์์ ๊ฐ์ฅ ๋์์ ๊ณ ์ฃผํ ์คํญ?
| e7d41ae304374b5a916646a25c3fe343 |
DTFS Frequency shift | DTFS Notion | Sep 18, 2023 | Alan Jo | Alan Jo | Sep 18, 2023 | 8378a648341e4d07a72a1897b7df3c95 |
||
DTFS Multiplication | DTFS Notion | Sep 18, 2023 | Alan Jo | Alan Jo | Sep 18, 2023 | e0e390cd5bc34dbbbb4ec3d8e690344d |
||
DTFS odd signal | DTFS Notion | Sep 18, 2023 | Alan Jo | Alan Jo | Sep 18, 2023 | d1c904d2345e469d87db80baec2d8a91 |
||
DTFS Time shift | DTFS Notion | Sep 18, 2023 | Alan Jo | Alan Jo | Sep 18, 2023 | 7b0fc22164b5479e9eb149d2fff0a1a8 |
||
Power Function | Power Series Notion | Aug 29, 2023 | Alan Jo | Alan Jo | Aug 29, 2023 | [Exponentiation](https://texonom.com/exponentiation-760c53a791ee4d6696e819b079afe066) |
> [Exponentiation](https://en.wikipedia.org/wiki/Exponentiation#Power_functions)
| c15a66fd32864a3c803d9ba30779b55a |
**โด** | Math Notations | Apr 18, 2023 | Alan Jo | Alan Jo | Apr 18, 2023 |
therefore
ฮป
| 55846ea0b211445eac195302ef05a253 |
|
i.e. | Math Notations | Apr 18, 2023 | Alan Jo | Alan Jo | Apr 18, 2023 |
id est
that is to say
๋ค์๋งํด
| e7a22100284644baba8d29b3efca627f |
|
s.t. | Math Notations | Apr 18, 2023 | Alan Jo | Alan Jo | Apr 18, 2023 |
subject to
| 8a2143a45d1c4d10a922758e3ed43c7e |
|
Coefficient | Math Terms | Sep 26, 2022 | Alan Jo | Alan Jo | Sep 26, 2022 | [Parameter](https://texonom.com/parameter-55a333ae102c4181b8055c37f2f6523e). |
## multiplicative factor
When coefficient themselves variable, they may be called parameter
- **constant coefficient**
- leading coefficient
> [Coefficient - Wikipedia](https://en.wikipedia.org/wiki/Coefficient)
| 029076fc7a2a44ffb758f47643b287f8 |
Constant | Math Terms | Jun 28, 2022 | Alan Jo | Alan Jo | Apr 25, 2023 |
### Named Constant can be
| 95f3cfb07e2b41e2abf9b372dc4580a0 |
|
Convexity | Math Terms | Apr 18, 2023 | Alan Jo | Alan Jo | Apr 18, 2023 |
1. ์์์ ๋ ์ ์ ์ ํํ์ ๋, ์ด ๋ ์ ์ ์๋ ์ ๋ถ ์์ ๋ชจ๋ ์ ๋ค๋ ๋ชจ๋ ํด๋น ํจ์๋ ์งํฉ์ ์ํฉ๋๋ค.
2. ์ด๋ค ๋ ์ ์ ์ ํํ์ ๋, ์ด ๋ ์ ์ฌ์ด์ ๋ชจ๋ ์ ๋ค์ด ํด๋น ํจ์๋ ์งํฉ์ ์ํ๋ ๊ฒฝ์ฐ, ์ด ํจ์๋ ์งํฉ์ strictly convexํ๋ค๊ณ ํฉ๋๋ค.
| f4f40f0e40664c40ad939e0588332c98 |
|
Function | Math Terms | Jan 16, 2022 | Alan Jo | Alan Jo | Jun 9, 2023 | [Procedure](https://texonom.com/procedure-ceeb514c1bc740b5a138e8627d676151) |
### Function Notion
|Title|
|:-:|
|[Parameter](https://texonom.com/parameter-55a333ae102c4181b8055c37f2f6523e)|
|[Argument](https://texonom.com/argument-47c946e3b55348ce8e8eb9b52d2ced2d)|
|[Symmetric Function](https://texonom.com/symmetric-function-0e6c5059331d4beca8e710b8412b7c67)|
### Function Usages
|Title|
|:-:|
|[Indicator function](https://texonom.com/indicator-function-5ea9115797524c1f87477c9520029756)|
|[Iverson bracket](https://texonom.com/iverson-bracket-e68288a0fbd44405aa65eb9f3a6ebf5d)|
|[Min Function](https://texonom.com/min-function-76f7ff5e65e542498595d99327da49f2)|
|[Max Function](https://texonom.com/max-function-4c82ae04a4cd4141b7d5b602accd538d)|
| 33bb8d51c8fb45eb8816aff02783312d |
Graph | Math Terms | Jun 28, 2022 | Alan Jo | Alan Jo | Jun 28, 2022 |
### Graph Notion
|Title|
|:-:|
|[Axis](https://texonom.com/axis-d944de07ba5245cb892ceb680ff47a46)|
| 9fa69b720b0945ca95838a4beb225dd9 |
|
Identity | Math Terms | May 2, 2023 | Alan Jo | Alan Jo | May 2, 2023 |
ํญ๋ฑ์
| 18eb1418af9e4857ac30cde9b0309783 |
|
Isomorphism | Math Terms | Apr 22, 2021 | Alan Jo | Alan Jo | Apr 3, 2022 |
ํน์ ์์ฑ๋ค์ ๋ํด์๋ง ๊ฐ์ ๊ทธ ์์ฑ๋ค๊ณผ ๊ด๋ จ๋ ์ง์ ๋ง์ ๊ณต์ ํ๋ ๊ฐ์
> [๋ค์๋ณด๋ ์ปค๋ง](https://overcurried.com/%EB%8B%A4%EC%8B%9C%EB%B3%B4%EB%8A%94%20%EC%BB%A4%EB%A7%81/)
| 13a057640cbe4c099b41951b6c12c265 |
|
Lemma | Math Terms | May 25, 2023 | Alan Jo | Alan Jo | May 25, 2023 |
๋ณด์กฐ์ ๋ฆฌ
| 066bbea0d32c423090bb4d90d4519e4b |
|
Math Equality | Math Terms | Apr 22, 2021 | Alan Jo | Alan Jo | Apr 3, 2022 |
๋ ์กด์ฌ๊ฐ ์์ ํ ๊ฐ์ ๋ ์ค ํ๋์ ๋ํ ๋ชจ๋ ์ง์ ์ด ๊ฐ์ ์์์ผ๋ก ๋ค๋ฅธ ํ๋์๊ฒ ์ ์ฉ
> [๋ค์๋ณด๋ ์ปค๋ง](https://overcurried.com/%EB%8B%A4%EC%8B%9C%EB%B3%B4%EB%8A%94%20%EC%BB%A4%EB%A7%81/)
| 4773a8618a7c429e8ef14f65c3dc5a1d |
|
Math Inequality | Math Terms | Sep 13, 2023 | Alan Jo | Alan Jo | Sep 13, 2023 | fa08a99a32bc4a2191aa7ce9ef9ccc4e |
||
Maximal | Math Terms | May 26, 2023 | Alan Jo | Alan Jo | May 26, 2023 |
๊ทน์
| b28b33bf3d2144d7924ae106d2392c7f |
|
Maximum | Math Terms | May 26, 2023 | Alan Jo | Alan Jo | May 26, 2023 |
์ต์
| 0aa3bbca7ed34bb8bce858da0b7872c8 |
|
Overflow | Math Terms | Feb 8, 2020 | Alan Jo | Alan Jo | Mar 22, 2023 |
## ์ ์ - ์๊ณ๋ฅผ ๋์ด ๊ฐ์ด ์ด์ํ ๊ฐ์ ๊ฐ์ง๋ ๊ฒ
- ์ต์์๊ณ๋ ์ต๋์๊ณ๋ ๊ฐ์ด overflow๋ผ๊ณ ํ๋ค
> [Security Check Required](https://www.facebook.com/160620167972435/posts/497039144330534/)
| ee37eee498e44823bc4a5f57a27f2254 |
|
Pointwise | Math Terms | May 25, 2023 | Alan Jo | Alan Jo | May 25, 2023 | [Operator](https://texonom.com/operator-db2bc37a04ce4c48ad0f456fb346acdc) |
pointwise ์ฐ์ฐ, ์ฆ ์ ์ ์์ญ์ ๊ฐ ์ ์ ๋ํด ๋ณ๋๋ก ํจ์ ๊ฐ์ ์ฐ์ฐ์ ์ ์ฉํ์ฌ ํจ์์ ์ ์๋ ์ฐ์ฐ
๊ฐ element์ point wise ์ฆ ๊ฐ์๋ ์์กด์ ์ผ๋ก๋ง ๋ผ๋ฆฌ๋ผ๋ฆฌ
| 1061f373526241a18ef3b748ecc346ca |
Polynomial | Math Terms | Sep 26, 2022 | Alan Jo | Alan Jo | Sep 26, 2022 |
Expression consisting of [Variable](https://texonom.com/variable-5461090e225a4cc587a754af46ba4f3e) and [Coefficient](https://texonom.com/coefficient-029076fc7a2a44ffb758f47643b287f8) that involves only the operations of **addition, subtraction, multiplication**
๋คํญ์
| 14ca2c5ac10b4e818e6fdb57b5d02ef2 |
|
Trivial | Math Terms | Jan 23, 2022 | Alan Jo | Alan Jo | Jan 23, 2022 |
๋น์ฐํ
์ค์ํ์ง ์์
์๋ช
ํ
| 2d7ac81afb304cedac671daa7dcba202 |
|
Underflow | Math Terms | Feb 8, 2020 | Alan Jo | Alan Jo | Aug 21, 2021 |
## ์ ์ - ํ๊ณ๋ฅผ ๋์ด ๊ฐ์ด ์ด์ํ ๊ฐ์ ๊ฐ์ง๋ ๊ฒ
### ๋ถ๋์์์ ์ด ์ ๋ฐ๋๋ฅผ ์๋ ๊ฒ | 3bff2ba71ec14a9da92122801e0839cc |
|
Variable | Math Terms | Sep 26, 2022 | Alan Jo | Alan Jo | Jun 25, 2023 |
### Variable Notion
|Title|
|:-:|
|[degree of freedom](https://texonom.com/degree-of-freedom-d848e57b9c524973b625d99f43f66bb8)|
### Variables
|Title|
|:-:|
|[Local variables](https://texonom.com/local-variables-c5048dceb2d54b41883e1935c5f5da56)|
|[Dynamic Variable](https://texonom.com/dynamic-variable-d8ace5e56bb748c797c91d7d23ab3051)|
|[Global Variable](https://texonom.com/global-variable-4f73f093a3074de0a5be1f202285f17a)|
|[Latent Variable](https://texonom.com/latent-variable-c2bb1127d53444018b2d0eaab231cc6c)|
|[Categorical variable](https://texonom.com/categorical-variable-cbeda9034bbb4de2b62d612641bc2d79)|
| 5461090e225a4cc587a754af46ba4f3e |
|
Argument | Function Notion | Mar 22, 2023 | Alan Jo | Alan Jo | Apr 25, 2023 | [Parameter](https://texonom.com/parameter-55a333ae102c4181b8055c37f2f6523e) |
### Usually refer actual value not variable
Default Arguments is default data and should be after other parameters
| 47c946e3b55348ce8e8eb9b52d2ced2d |
Function Property | Function Notion | Sep 13, 2023 | Alan Jo | Alan Jo | Sep 13, 2023 |
### Function Properties
|Title|
|:-:|
|[Linearity](https://texonom.com/linearity-53be0991221249d794ed8047fe36ecb5)|
|[Additivity](https://texonom.com/additivity-95271c035d7e4a38bc7ebeef3b67c3cf)|
|[Homogeneity](https://texonom.com/homogeneity-1bcee2b1f7a347d1b361a818ba704c97)|
|[Symmetric Function](https://texonom.com/symmetric-function-0e6c5059331d4beca8e710b8412b7c67)|
|[Periodic Function](https://texonom.com/periodic-function-3fa775a544934003bfbf39101551d1e1)|
|[Concave function](https://texonom.com/concave-function-f22d1ea5086b4af2bf40c220f9de71b9)|
| f8c41eb4d9804c6abe24f1ab378cb75c |
|
Parameter | Function Notion | Sep 26, 2022 | Alan Jo | Alan Jo | Apr 25, 2023 | [Coefficient](https://texonom.com/coefficient-029076fc7a2a44ffb758f47643b287f8) [Argument](https://texonom.com/argument-47c946e3b55348ce8e8eb9b52d2ced2d) |
## **variable in the declaration of the function**
usually not a actual value
### Actual Parameter
์ค์ ํจ์๊ฐ ๋์ํ๋๋ฐ ๋ณด๋ด์ง๋ Parameter
### Formal Parameter
ํจ์ ์์์ ์ฌ์ฉ๋๋ parameter
Formal parameter is placeholder
> [[ํ๋ก๊ทธ๋๋ฐ์ธ์ด] Formal parameter, Actual parameter, ๊ทธ๋ฆฌ๊ณ parameter passing](https://yunmap.tistory.com/entry/ํ๋ก๊ทธ๋๋ฐ์ธ์ด-Formal-parameter-Actual-parameter-๊ทธ๋ฆฌ๊ณ -parameter-passing)
| 55a333ae102c4181b8055c37f2f6523e |
S****ymmetric Function**** | Function Properties | May 13, 2023 | Alan Jo | Alan Jo | Sep 13, 2023 |
### S****ymmetric Function Notion****
|Title|
|:-:|
|[Asymmetric Function](https://texonom.com/asymmetric-function-983363cc0469430196e0ea10156f1627)|
### S****ymmetric Functions****
|Title|
|:-:|
|[Even Function](https://texonom.com/even-function-85aa19cb97ad4af49c9de05f1c601b46)|
|[Odd Function](https://texonom.com/odd-function-34ae3b77527b4618a3bc926c68df05ec)|
| 0e6c5059331d4beca8e710b8412b7c67 |
|
Additivity | Function Properties | Sep 13, 2023 | Alan Jo | Alan Jo | Sep 13, 2023 |
## Superposition principle
$$f(x_1 + x_2) = f(x_1) + f(x_2)$$
> [Superposition principle](https://en.wikipedia.org/wiki/Superposition_principle)
| 95271c035d7e4a38bc7ebeef3b67c3cf |
|
Concave function | Function Properties | Sep 20, 2023 | Alan Jo | Alan Jo | Sep 20, 2023 | [Convexity](https://texonom.com/convexity-f4f40f0e40664c40ad939e0588332c98) |
> [Concave function](https://en.wikipedia.org/wiki/Concave_function)
| f22d1ea5086b4af2bf40c220f9de71b9 |
Homogeneity | Function Properties | Sep 13, 2023 | Alan Jo | Alan Jo | Sep 13, 2023 | 1bcee2b1f7a347d1b361a818ba704c97 |
||
Linearity | Function Properties | Sep 13, 2023 | Alan Jo | Alan Jo | Sep 13, 2023 |
- [Homogeneity](https://texonom.com/homogeneity-1bcee2b1f7a347d1b361a818ba704c97)
- [Additivity](https://texonom.com/additivity-95271c035d7e4a38bc7ebeef3b67c3cf)
> [Linearity](https://en.wikipedia.org/wiki/Linearity)
| 53be0991221249d794ed8047fe36ecb5 |
|
**Periodic Function** | null | null | null | null | null | null |
### **Periodic Functions**
|Title|
|:-:|
|[Non-sinusoidal waveform](https://texonom.com/non-sinusoidal-waveform-51ff8ccafe744b21a36ef836e6739177)|
> [Periodic function](https://en.wikipedia.org/wiki/Periodic_function)
| 3fa775a544934003bfbf39101551d1e1 |
**Non-sinusoidal waveform** | Periodic Functions | Sep 13, 2023 | Alan Jo | Alan Jo | Sep 13, 2023 |
### **Non-sinusoidal waveforms**
|Title|
|:-:|
|[Square wave](https://texonom.com/square-wave-f730f0419f3843c389357eecc59f8d94)|
> [Non-sinusoidal waveform - Wikipedia](https://en.wikipedia.org/w/index.php?title=Non-sinusoidal_waveform&redirect=no)
| 51ff8ccafe744b21a36ef836e6739177 |
|
Boxcar function | Template Gallery | Mar 21, 2023 | Alan Jo | Alan Jo | Sep 20, 2023 | [Rectangular function](https://texonom.com/rectangular-function-4d71deb4ffec44379df7cb97eb078dc9) |
> [Boxcar function](https://en.wikipedia.org/wiki/Boxcar_function)
> [Boxcar averager](https://en.wikipedia.org/wiki/Boxcar_averager)
| fdf2d3b368f540bbbdaab928819f8da4 |
Subsets and Splits