numerical linear algebra - initial SVD tutorial

Author: daslu

projects/math/numerical-linalg/notebooks/movie/Video_003.mp4

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+;; # Background Removal with SVD
+
+;; [original Fast.ai notebook](https://nbviewer.org/github/fastai/numerical-linear-algebra-v2/blob/master/nbs/02-Background-Removal-with-SVD.ipynb)
+
+(ns svd
+  (:require [tablecloth.api :as tc]
+            [com.phronemophobic.clj-media :as clj-media]
+            [com.phronemophobic.clj-media.model :as clj-media.model]
+            [tech.v3.datatype :as dtype]
+            [tech.v3.tensor :as tensor]
+            [tech.v3.libs.buffered-image :as bufimg]
+            [scicloj.kindly.v4.kind :as kind]
+            [fastmath.matrix :as mat])
+  (:import (org.apache.commons.math3.linear
+            SingularValueDecomposition)))
+
+(def video-path
+  "notebooks/movie/Video_003.mp4")
+
+(kind/video
+ {:src video-path})
+
+(clj-media/probe video-path)
+
+
+(def first-image
+  (reduce (fn [_ frame] (clj-media.model/image
+                         frame))
+          nil
+          (clj-media/frames
+           (clj-media/file video-path)
+           :video
+           {:format (clj-media/video-format
+                     {:pixel-format
+                      :pixel-format/rgba})})))
+
+
+first-image
+
+(def first-tensor
+  (bufimg/as-ubyte-tensor
+   first-image))
+
+first-tensor
+
+
+
+(def images
+  (time
+   (into []
+         (map clj-media.model/image)
+         (clj-media/frames
+          (clj-media/file video-path)
+          :video
+          {:format (clj-media/video-format
+                    {:pixel-format
+                     :pixel-format/rgba})}))))
+
+(count images)
+
+
+(def tensors
+  (mapv bufimg/as-ubyte-tensor images))
+
+
+(count tensors)
+
+
+(def all-frames-as-one-rectangular-tensor
+  (let [row-size (->> tensors
+                      first
+                      dtype/shape
+                      (apply *))]
+    (tensor/compute-tensor [row-size
+                            (count tensors)]
+                           (fn [j i]
+                             (-> (tensors i)
+                                 (tensor/reshape [row-size])
+                                 (get j)))
+                           :uint8)))
+
+
+(def all-frames-as-one-image
+  (time
+   (bufimg/tensor->image
+    all-frames-as-one-rectangular-tensor)))
+
+
+all-frames-as-one-image
+
+
+(def all-frames-as-one-matrix
+  (->> all-frames-as-one-rectangular-tensor
+       (take 10000)
+       (map double-array)
+       (mat/rows->RealMatrix)))
+;; 10000x350
+
+
+(def svd
+  (SingularValueDecomposition.
+   all-frames-as-one-matrix))
+
+(.getSingularValues svd)