From 24b9c948c77edd9ce45b9b98bc245f7395628d82 Mon Sep 17 00:00:00 2001
From: Francesco Mecca <me@francescomecca.eu>
Date: Mon, 6 Jul 2020 11:39:00 +0200
Subject: [PATCH] DANNATO GALLA CHE VUOLE VEDERE COSA HO SCRITTo

---
 ...0d170f8063d6728500a6795104201c4072f7d4.png | Bin 0 -> 764 bytes
 ...de31bd34b1ae579873d2150bf0083eeeb96097.png | Bin 0 -> 639 bytes
 .../apprendimento_automatico/preparazione.org |  53 ++++++++++++++++++
 todo.org                                      |   2 +
 4 files changed, 55 insertions(+)
 create mode 100644 anno3/apprendimento_automatico/ltximg/org-ltximg_3a0d170f8063d6728500a6795104201c4072f7d4.png
 create mode 100644 anno3/apprendimento_automatico/ltximg/org-ltximg_82de31bd34b1ae579873d2150bf0083eeeb96097.png

diff --git a/anno3/apprendimento_automatico/ltximg/org-ltximg_3a0d170f8063d6728500a6795104201c4072f7d4.png b/anno3/apprendimento_automatico/ltximg/org-ltximg_3a0d170f8063d6728500a6795104201c4072f7d4.png
new file mode 100644
index 0000000000000000000000000000000000000000..86b82cfa509926f02ab1ff58e20fccf939c82148
GIT binary patch
literal 764
zcmV<Y0t5YtP)<h;3K|Lk000e1NJLTq006WA000>T0{{R3YGD~M0000mP)t-s0002&
z@AO_@VNOp_KR-b(FED<8f^BbcA0Hsy-{hU2qm7S}%+J#f4-c%bvc12<8E?e600009
za7bBm000ie000ie0hKEb8vp<Ta!Eu%R7ef2R84CWQ4~GSOlD#}TKoq?VhIRBC`FMX
zJX(v2E&_H@Tu2biMvzC5QUoD{xCoM+-3UT<u7rRT+_-lm46S4#h~2po`UeEhd-G+I
znQ?5q<h^&_z4x8m+;9%Ch*_`j1BGq?@nsRH*|&v};o&HZTCLFg52vy30__NB9C?|J
z`E&)vhT~-xmG+1>#?_4$dh$6&nZ;4^#hvZt;?1S#p6FD%pMg<v`%s`SPxvLdZ0E2G
zeE6DO`yG3PF1*|U%EM9Ku2*YKp#Cruy86Vs*237V)$z-?;?6<Ww@|NP?N$<qc$XBN
ziS^ZeXq7xmOlNGjVK*z^#v8z-)9E~#%I-$RRpvUasbqLDJ$k~q2qTOH=KvU>GJGwf
z__+&n7UhtToU0B3xCDL%IC_)Rbqtx&bzC&#t;1T!`v>?K$D8~EVVeG;tM74|URtA5
zaoB53dsQ57iukRR^c}}vboD(>Gp?q4Ci^S2eI{7-NJ_Fi=vwi2uIqi=7E2N&inglI
zM;;lJk}N0mDVO5!9CRD^aT!%tBXZl)P97PQk}MCpR{WiXHo9o^fOsrr^l%S(WKc@7
zJb+gGorNv~Zy!@Npwv;xUI~R27rqQ?wM>;k4HZC>zthkYfOwxO9!lWcpk$BVMS27>
zsMIo523<8ogS6!$f1&SsoZRjTYG?J-X%kwhqmn(pYhMPnTK<C!hPXV<6SIZMPxF8S
z;oO#wDSIW(dNYtgrIv{@_y<Osd%&NsttfaD6?<;zyWaYsS|-V0T$1iRi-4}P$Wn!_
u+I%y;U6Ck*VL{e;ew3A6C})eD&wm5@Tbm>O;q;9F0000<MNUMnLSTY#J7E?8

literal 0
HcmV?d00001

diff --git a/anno3/apprendimento_automatico/ltximg/org-ltximg_82de31bd34b1ae579873d2150bf0083eeeb96097.png b/anno3/apprendimento_automatico/ltximg/org-ltximg_82de31bd34b1ae579873d2150bf0083eeeb96097.png
new file mode 100644
index 0000000000000000000000000000000000000000..45ee882d045c8a72cd330dff4d13b24f1962ed4d
GIT binary patch
literal 639
zcmV-_0)YLAP)<h;3K|Lk000e1NJLTq005r=000^U0{{R3TS$|*0000mP)t-s0002&
z@AO_@VNOp_KR-b(FED<8f^BbcA0Hsy-{hU2qm7S}%+J#f4-c%bvc12<8E?e600009
za7bBm000ie000ie0hKEb8vp<S^+`lQR7ee_RLe@kKomWuF%z`)@du$*3W5+s+=wtJ
zV!=&87ve&TkM4v)1l<V5$D)h=fFOu_p&$h}{zIu^K@j^1#V_zS)5qjtlH$;5?>+a-
zncGRu0K<&L*(}T~s}Hj#lzY3mJ!x)CgmQ)|?$k=a%jZyQLdgqh8^|1la*$a^CXK~h
zI7_MWCnfQRhLtt!<X3eS_$U^O$9{$vIpto&m6w4sl9jswYh?N#V+wPiPZ^E-*d4n1
z@h8jBm+`!ZSAQu4dDKr}$$E;OlRAt=+gRXlYg`2*<5mt@kF?SY{`|E&dnOWcQt0Gv
z_Rj+hydQF0<#@wg3dn>YkTE$abaEGOv``~KREg586ER{$3yzC@(%CvL32hf~I;2aW
z+u@bCqz;?s=NH~CoHNXuO+=re5OfKUV4LQRX!ZVbthdv<t&<Bumq53}@yf#=9R@B9
z28EzYpev{?S-lQB<ftyE0u|MVqL0;8!9w7IDA2Nqq0yn!WHW%1JBtz}zeW5=l)h4D
za9iYNlzR|`94DMd-y&p_2J{RhLWYTF8g&<)LkuiJHeoQ2AQ3W5JkzLxW}DRq79pE7
zaINPhLWYTF8dVU7(qz&iROwqp0~scsX<UNe1(|j(qdbt}GNo^u3FMhjkbWsFU>&8X
Z@e4URe}Q%?3k3iG002ovPDHLkV1jE#5$6B^

literal 0
HcmV?d00001

diff --git a/anno3/apprendimento_automatico/preparazione.org b/anno3/apprendimento_automatico/preparazione.org
index 526a8eb..55eca08 100644
--- a/anno3/apprendimento_automatico/preparazione.org
+++ b/anno3/apprendimento_automatico/preparazione.org
@@ -555,3 +555,56 @@ do:
 until (no change in μ₁, ..., μₖ
 ritorna μ₁, ..., μₖ
 #+END_SRC
+*** K-Medoids clustering
+#+BEGIN_SRC
+Input: input data D⊆X; k \#clusters; Distance metric Dis: X×X→R
+Inizializza casualmente k punti μ₁, ..., μₖ ∈D
+repeat
+    assign each x∈D to argminⱼ Dis(x,μⱼ)
+    for j=1 to k do:
+        Dⱼ ← {x∈D| x assigned to cluster j}
+        μⱼ = argmin_{x∈Dⱼ} ∑_{x'∈Dⱼ} Dis(x,x')
+until no change in μ₁, ..., μₖ
+return μ₁, ..., μₖ
+#+END_SRC
+*** TODO Proximity graph for measuring clusters (Silhouettes)
+*** Hierarchical clustering
+Non richiede di fissare k.
+Il ~dendrogram~ e` un albero binario con gli elementi di D come
+foglie.
+- Linkage function: L: 2ˣ×2ˣ→R: calcola la distanza fra due subset
+  dell'instance space data una metrica per la distanza.
+  + Single linkage: smallest pairwise distance fra elementi
+  + Complete linkage: largest pointwise distance
+  + Average linkage: average pointwise distance
+  + Centroid linkage: distanza fra i centroidi
+- HAC(D, L)
+#+BEGIN_SRC
+Input: D⊆X; linkage function L
+Inizializza clusters di singleton
+creae una foglia a livello zero per ogni punto
+repeat:
+    trova la coppia <x,y> con il minore linkage e merge
+    genera parent di <x,y>
+until si ottiene un solo cluster
+return constructed dendrogram
+#+END_SRC
+** Kernels
+Disₖ(x,y) = sqrt K(x,x) + 2K(x,y) + K(y,y)
+| pseudo metric quando k e` un kernel semidefinito
+- Kernelized K-Means
+#+BEGIN_SRC
+inputs: D⊆X; k
+randomly initialize D₁, ..., Dₖ; (D₁ ∪ ... ∪ Dₖ = D)
+repeat
+    assign each x to argminⱼ 1/|Dⱼ| ∑_y Disₖ(x,y)
+    for j = 1 ... k:
+        Dⱼ ← {x∈D | x assigned to cluster j}
+until no change in D₁,...,Dₖ
+return D₁, ..., Dₖ
+#+END_SRC
+- Cosine similarity: $cos θ = \frac{x\cdot y}{\Vert{x}\Vert \cdot
+  \Vert{y} \Vert} = \frac{K(x,y)}{\sqrt{K(x,x)\times K(y,y)}}$
+** 5-cross validation
+dividi il dataset in 5 partizioni, 4 per il training set 1 per il test
+set e permuta.
diff --git a/todo.org b/todo.org
index f0258c7..4f7b265 100644
--- a/todo.org
+++ b/todo.org
@@ -26,11 +26,13 @@
   + [ ] (w_0,w_1) ortogonale all'iperpiano
   + [ ] dimostrazione dualita` grangiana
   + [ ] Mercer condition
+  + [ ] kernel semidefinito
 - [ ] Meo [0/3]
   + [ ] Vedi bene gini index
   + [ ] Ranking e regression trees
   + [ ] subgroup discovery and ongoing
   + [ ] Voronoi
+  + [ ] Proximity graph for measuring clusters
 - [X] Esercizi [3/3]
   - [X] es1: perche` min_impurity decrease
   - [X] chiedi a Galla`, Marco e Naz quali sono tutti gli es